Type:	Package
Title:	Single-Case Data Analyses for Single and Multiple Baseline Designs
Version:	0.68.0
Date:	2026-04-01
Depends:	R (≥ 4.1.0)
Imports:	stats, nlme, MCMCglmm, utils, methods, graphics, car, gt, knitr, kableExtra, readxl, magrittr, miniUI, rstudioapi
Suggests:	testthat (≥ 3.0.0), shiny, yaml, scplot
Description:	A collection of procedures for analysing, visualising, and managing single-case data. Multi-phase and multi-baseline designs are supported. Analysing methods include regression models (multilevel, multivariate, bayesian), between case standardised mean difference, overlap indices ('PND', 'PEM', 'PAND', 'NAP', 'PET', 'tau-u', 'IRD', 'baseline corrected tau', 'CDC'), and randomization tests. Data preparation functions support outlier detection, handling missing values, scaling, and custom transformations. An export function helps to generate html, word, and latex tables in a publication friendly style. A shiny app allows to use scan in a graphical user interface. More details can be found in the online book 'Analyzing single-case data with R and scan', Juergen Wilbert (2026) https://jazznbass.github.io/scan-Book/.
License:	GPL (≥ 3)
URL:	https://github.com/jazznbass/scan/, https://jazznbass.github.io/scan-Book/, https://jazznbass.github.io/scan/
BugReports:	https://github.com/jazznbass/scan/issues
LazyData:	true
Encoding:	UTF-8
RoxygenNote:	7.3.3
Config/testthat/edition:	3
NeedsCompilation:	no
Packaged:	2026-04-01 07:26:45 UTC; wilbert
Author:	Juergen Wilbert [cre, aut], Timo Lueke [aut]
Maintainer:	Juergen Wilbert <juergen.wilbert@uni-muenster.de>
Repository:	CRAN
Date/Publication:	2026-04-01 08:00:02 UTC

Single-Case Data Analyses

Description

A collection of procedures for analysing, visualising, and managing single-case data.

Author(s)

Juergen Wilbert [aut, cre]

See Also

Useful links:

• https://github.com/jazznbass/scan/

• https://jazznbass.github.io/scan-Book/

• https://jazznbass.github.io/scan/

• Report bugs at https://github.com/jazznbass/scan/issues

Select an scdf case by name

Description

Selects a single case from a scdf object by its name.

Usage

## S3 method for class 'scdf'
x$i

## S3 method for class 'scdf'
x[i]

Arguments

Value

A scdf object containing only the selected case.

Author(s)

Juergen Wilbert

Pipe

Description

Several functions in scan are designed to work with pipes ⁠\%>\%⁠. This pipe function is directly imported from magrittr.

Details

Since R 4.1 a pipe operator |> is included in base R. This pipe operator can be used along with scan perfectly fine.

Dummy function to inherit global descriptions of parameters

Description

This function is only used to inherit parameter descriptions in the documentation of other functions. It has no other purpose and is not meant to be called directly.

Usage

.inheritParams(
  data,
  scdf,
  dvar,
  mvar,
  pvar,
  decreasing,
  phases,
  model,
  contrast,
  contrast_level,
  contrast_slope,
  trend,
  level,
  slope,
  nice,
  ...
)

Arguments

Value

No return value.

Author(s)

Juergen Wilbert

Add Dummy Variables for Piecewise Linear Models

Description

Adds dummy variables to an scdf for calculating piecewise linear models.

Usage

add_dummy_variables(
  scdf,
  model = c("W", "H-M", "B&L-B"),
  contrast_level = c("first", "preceding"),
  contrast_slope = c("first", "preceding")
)

Arguments

Details

This function creates dummy variables for phase levels and phase slopes according to the specified piecewise regression model. It supports different contrast coding schemes for both level and slope contrasts.

Examples

add_dummy_variables(
 scdf = exampleABC, 
 model = "W", 
 contrast_level = "first", 
 contrast_slope = "first"
)

Add level-2 data to an scdf

Description

Merges variables with corresponding case names from a data.frame with an scdf.

Usage

add_l2(scdf, data_l2, cvar = "case")

Arguments

Details

This function is mostly used in combination with the hplm() function. It adds level-2 variables to each single-case data frame in an scdf based on matching case names.

Value

An scdf with added level-2 variables.

Author(s)

Juergen Wilbert

See Also

hplm()

Other data manipulation functions: as.data.frame.scdf(), as_scdf(), batch_apply(), fill_missing(), moving_median(), print.sc_outlier(), ranks(), rescale(), scdf(), select_cases(), set_vars(), shift(), smooth_cases(), standardize(), truncate_phase()

Examples

## Example with the default case variable name 'case'
Leidig2018 |> add_l2(Leidig2018_l2)
## Example with a different case variable name in the L2 data
Leidig2018_l2_renamed <- Leidig2018_l2
names(Leidig2018_l2_renamed)[2] <- "subject"
Leidig2018 |> add_l2(Leidig2018_l2_renamed, cvar = "subject")

ANOVA Table for Piecewise Linear Models

Description

Model comparison for piecewise regression models fitted with plm(), hplm(), or mplm() using likelihood ratio tests.

Usage

## S3 method for class 'sc_plm'
anova(object, ...)

## S3 method for class 'sc_hplm'
anova(object, ...)

## S3 method for class 'sc_mplm'
anova(object, ...)

Arguments

Details

The function performs likelihood ratio tests to compare nested piecewise regression models. It extracts the underlying model from the sc_plm, sc_hplm, or sc_mplm object and passes them to the generic anova() function for model comparison.

Value

An object of class anova containing the results of the model comparison.

Examples

## For glm models with family = "gaussian"
mod1 <- plm(exampleAB$Johanna, level = FALSE, slope = FALSE)
mod2 <- plm(exampleAB$Johanna)
anova(mod1, mod2)
## For glm models with family = "poisson"
mod0 <- plm(example_A24, formula = injuries ~ 1, family = "poisson")
mod1 <- plm(example_A24, trend = FALSE, family = "poisson")
anova(mod0, mod1, mod2)
## For glm with family = "binomial"
mod0 <- plm(
  exampleAB_score$Christiano, 
  formula = values ~ 1, 
  family = "binomial", 
  var_trials = "trials"
)
mod1 <- plm(
  exampleAB_score$Christiano, 
  trend = FALSE, 
  family = "binomial", 
  var_trials = "trials"
)
anova(mod0, mod1)
## For multilevel models:
mod0 <- hplm(Leidig2018, trend = FALSE, slope = FALSE, level = FALSE)
mod1 <- hplm(Leidig2018, trend = FALSE)
mod2 <- hplm(Leidig2018)
anova(mod0, mod1, mod2)
## For mplm
mod0 <- mplm(
  Leidig2018$`1a1`, 
  update = . ~  1, dvar = c("academic_engagement", "disruptive_behavior")
)
mod1 <- mplm(
  Leidig2018$`1a1`, 
  trend = FALSE, 
  dvar = c("academic_engagement", "disruptive_behavior")
)
mod2 <- mplm(
  Leidig2018$`1a1`, 
  dvar = c("academic_engagement", "disruptive_behavior")
)

anova(mod0, mod1, mod2)

Creating a long format data frame from several single-case data frames (scdf).

Description

The as.data.frame function transposes an scdf into one long data frame. Additionally, a data frame can be merged that includes level 2 data of the subjects. This might be helpful to prepare data to be used with other packages than scan.

Usage

## S3 method for class 'scdf'
as.data.frame(x, ..., l2 = NULL, id = "case")

Arguments

Value

Returns one data frame with data of all single-cases structured by the case variable.

Author(s)

Juergen Wilbert

See Also

Other data manipulation functions: add_l2(), as_scdf(), batch_apply(), fill_missing(), moving_median(), print.sc_outlier(), ranks(), rescale(), scdf(), select_cases(), set_vars(), shift(), smooth_cases(), standardize(), truncate_phase()

Examples

## Convert the list of three single-case data frames from Grosche (2011)
### into one long data frame
Grosche2011
Grosche2011_long <- as.data.frame(Grosche2011)
Grosche2011_long

## Combine an scdf with data for l2
Leidig2018_long <- as.data.frame(Leidig2018, l2 = Leidig2018_l2)
names(Leidig2018_long)
summary(Leidig2018_long)

as_scdf

Description

Converts a data frame to an scdf object.

Usage

as_scdf(
  object,
  cvar = "case",
  pvar = "phase",
  dvar = "values",
  mvar = "mt",
  phase_names = NULL,
  sort_cases = FALSE
)

Arguments

Value

An scdf.

See Also

Other data manipulation functions: add_l2(), as.data.frame.scdf(), batch_apply(), fill_missing(), moving_median(), print.sc_outlier(), ranks(), rescale(), scdf(), select_cases(), set_vars(), shift(), smooth_cases(), standardize(), truncate_phase()

Apply a function to each element in an scdf.

Description

This function applies a given function to each case of a multiple case scdf, returning a list of the output of each function call.

Usage

batch_apply(scdf, fn, simplify = FALSE)

Arguments

Details

If simplify is TRUE and the function returns a vector of values, the output is combined into a data frame with case names as additional columns.

This is particularly useful for applying statistical models or summary statistics to each case in an scdf.

Value

A list of the output of each function call.

Author(s)

Juergen Wilbert

See Also

Other data manipulation functions: add_l2(), as.data.frame.scdf(), as_scdf(), fill_missing(), moving_median(), print.sc_outlier(), ranks(), rescale(), scdf(), select_cases(), set_vars(), shift(), smooth_cases(), standardize(), truncate_phase()

Examples

batch_apply(exampleAB, coef(plm(.)))

Between-Case Standardized Mean Difference

Description

Calculates a standardized mean difference from a multilevel model as described in Pustejovsky et al. (2014)

Usage

between_smd(
  data,
  method = c("REML", "MCMCglmm"),
  ci = 0.95,
  include_residuals = TRUE,
  ...
)

## S3 method for class 'sc_bcsmd'
print(x, digits = 2, ...)

## S3 method for class 'sc_bcsmd'
export(
  object,
  caption = NA,
  footnote = NA,
  filename = NA,
  digits = 2,
  round = 2,
  ...
)

Arguments

Details

The BC-SMD is calculate as ⁠BC-SMD = Phase difference / sqrt(residual + random_intercept)⁠. This is most closely related to Cohen's d. If you want to have the most exact estimation based on the between case variance, you have to exclude the residual variance by setting the argument include_residuals = FALSE you get ⁠BC-SMD = Phase difference / sqrt(random_intercept)⁠. The 'base' model only includes the phase level as a predictor like originally proposed by Hedges et al. Whereas the 'Full plm' model includes the trend and the phase slope as additional predictors.

Value

An object of class sc_bcsmd. It is a list containing the following elements:

• models: A list of data frames containing the BC-SMD results for each model calculated.

• ci: The width of the confidence/credible interval.

• method: The method used for model estimation.

Functions

• print(sc_bcsmd): Print results

• export(sc_bcsmd): export results

Author(s)

Juergen Wilbert

References

Pustejovsky, J. E., Hedges, L. V., & Shadish, W. R. (2014). Design-Comparable Effect Sizes in Multiple Baseline Designs: A General Modeling Framework. Journal of Educational and Behavioral Statistics, 39(5), 368–393. https://doi.org/10.3102/1076998614547577

Examples

## Create a example scdf:
des <- design(
  n = 150,
  phase_design = list(A1 = 10, B1 = 10, A2 = 10, B2 = 10, C = 10),
  level = list(B1 = 1, A2 = 0, B2 = 1, C = 1),
  rtt = 0.7,
  random_start_value = TRUE
)
study <- random_scdf(des)

## Standard BC-SMD return:
between_smd(study)

## Specify the model and provide an hplm object:
model <- hplm(study, contrast_level = "preceding", slope = FALSE,  trend = FALSE)
between_smd(model)

## excluding the residuals gives a more accurate estimation:
between_smd(model, include_residuals = FALSE)

Bayesian Piecewise Linear Model (bplm)

Description

Computes a bayesian (hierarchical) piecewise linear model based on a Markov chain Monte Carlo sampler. The function automatically creates the fixed and random part of the regression model.

Usage

bplm(
  data,
  dvar,
  pvar,
  mvar,
  model = c("W", "H-M", "B&L-B"),
  contrast_level = c("first", "preceding"),
  contrast_slope = c("first", "preceding"),
  trend = TRUE,
  level = TRUE,
  slope = TRUE,
  random_trend = FALSE,
  random_level = FALSE,
  random_slope = FALSE,
  fixed = NULL,
  random = NULL,
  update_fixed = NULL,
  ...
)

## S3 method for class 'sc_bplm'
print(x, digits = 3, ...)

## S3 method for class 'sc_bplm'
export(
  object,
  caption = NA,
  footnote = NA,
  filename = NA,
  round = 2,
  nice = TRUE,
  ...
)

Arguments

Details

The function uses the MCMCglmm::MCMCglmm() function to fit the model. The default model includes fixed trend, level, and slope effects as well as a random intercept for each single-case. The fixed part of the model can be changed by providing a custom formula to the fixed argument or by using the update_fixed argument. The random part of the model can be changed by providing a custom formula to the random argument or by setting the random_trend, random_level, or random_slope arguments to TRUE.

Value

An object of class sc_bplm with element:

• model - List containing information about the applied model.

• N - Number of single-cases.

• formula - A list containing the fixed and the random formulas of the hplm model.

• mcmglmm - Object of class MCMglmm.

• contrast - List with contrast definitions.

Functions

• print(sc_bplm): Print results

• export(sc_bplm): Export results as html table (see export())

Author(s)

Juergen Wilbert

See Also

Other regression functions: fetch(), hplm(), mplm(), plm(), print.sc_ac(), print.sc_bctau(), trend()

Examples

# plm regression
bplm(example_A24)

# Multilevel plm regression with random intercept
bplm(exampleAB_50, nitt = 5000)

# Adding a random slope
bplm(exampleAB_50, random_level = TRUE, nitt = 5000)

# Custom fixed formula
bplm(exampleAB_50, update_fixed = values ~ -1 + mt + phaseB +
  interB, nitt = 5000)

Check function arguments

Description

This function checks function arguments based on a set of predefined tests. It is intended for internal use within other functions to validate their arguments. #' @param ... A set of expressions defining the tests to be performed on the function arguments. Each expression should use one of the predefined test functions available within the scope of check_args().

Usage

check_args(...)

Value

This function does not return a value. If any of the tests fail, it raises an error with a descriptive message.

Extract coefficients from plm/hplm objects

Description

Extract coefficients from plm/hplm objects

Usage

## S3 method for class 'sc_plm'
coef(object, ...)

Arguments

Value

data frame with coefficient table

Examples

coefficients(plm(exampleAB$Johanna))

Combine single-case data frames into one scdf

Description

Combines several single-case data frames (scdf) into one scdf object.

Usage

combine(..., dvar = NULL, pvar = NULL, mvar = NULL, info = NULL, author = NULL)

## S3 method for class 'scdf'
c(...)

Arguments

Value

A scdf. If not set differently, the attributes of this scdf are copied from the first scdf provided (i.e the first argument of the function).

Author(s)

Juergen Wilbert

Convert scdf to R code

Description

Converts an scdf object into R code that can be used to recreate the object.

Usage

convert(
  scdf,
  file = "",
  study_name = "study",
  case_name = "case",
  inline = FALSE,
  indent = 2,
  silent = FALSE
)

Arguments

Details

This function is useful for exporting scdf objects for sharing or documentation purposes. The generated R code can be sourced to recreate the original scdf object.

Value

Returns a string (invisible).

Author(s)

Juergen Wilbert

See Also

Other io-functions: read_scdf(), write_scdf()

Examples

filename <- tempfile()
convert(exampleABC, file = filename)
source(filename)
all.equal(study, exampleABC)
unlink(filename)

List of old deprecated function names

Description

This is a list with functions names that have been replaced by new names which are in line with R syntax guidelines. The old function names still work. They are wrappers that call the new function.

Usage

tauUSC(...)

power_testSC(...)

fillmissingSC(...)

overlapSC(...)

randSC(...)

rand.test(...)

rciSC(...)

rSC(...)

readSC.excel(...)

readSC(...)

writeSC(...)

Arguments

Descriptive statistics for single-case data

Description

The describe() function provides common descriptive statistics for single-case data.

Usage

describe(data, dvar, pvar, mvar)

Arguments

Details

It computes the number of measurements, number of missing values, mean, median, standard deviation, median average deviation, minimum, maximum, and trend (slope of dependent variable regressed on measurement-time) for each phase of each single-case included in an scdf.

n = number of measurements; mis = number of missing vaues; m = mean; md = median; sd = standard deviation; mad = median average deviation; min = minimum; max = maximum; trend = weight of depended variable regressed on time (values ~ mt).

Value

A list containing a data frame of descriptive statistics (descriptives); the cse design (design); the number of cases (N).

Author(s)

Juergen Wilbert

See Also

overlap(), plot.scdf()

Examples

## Descriptive statistics for a study of three single-cases
describe(Grosche2011)

## Descriptives of a three phase design
describe(exampleABC)

## Write descriptive statistics to .csv-file
study <- describe(Waddell2011)
write.csv(study$descriptives, file = tempfile())

Generate a single-case design matrix for multiple random single-cases

Description

Generates a parameter list used for generating multiple random single-cases. This is used within the random_scdf function and the power_test function and for other Monte-Carlo tasks.

Usage

design(
  n = 1,
  phase_design = list(A = 5, B = 15),
  trend = 0,
  level = list(0),
  slope = list(0),
  start_value = 50,
  s = 10,
  rtt = 0.8,
  extreme_prop = list(0),
  extreme_range = c(-4, -3),
  missing_prop = 0,
  distribution = c("normal", "gaussian", "poisson", "binomial"),
  random_start_value = FALSE,
  n_trials = NULL,
  mt = NULL,
  B_start = NULL,
  m,
  phase.design,
  MT,
  B.start,
  extreme.p,
  extreme.d,
  missing.p
)

Arguments

Value

An object of class sc_design.

Author(s)

Juergen Wibert

Examples

 ## Create random single-case data and inspect it
 design <- design(
   n = 3, rtt = 0.75, slope = 0.1, extreme_prop = 0.1,
   missing_prop = 0.1
 )
 dat <- random_scdf(design, round = 1, random.names = TRUE, seed = 123)
 describe(dat)

 ## And now have a look at poisson-distributed data
 design <- design(
   n = 3, B_start = c(6, 10, 14), mt = c(12, 20, 22), start_value = 10,
   distribution = "poisson", level = -5, missing_prop = 0.1
 )
 dat <- random_scdf(design, seed = 1234)
 pand(dat, decreasing = TRUE)

Estimate single-case design

Description

This functions takes an scdf and extracts design parameters. The resulting object can be used to randomly create new scdf files with the same underlying parameters. This is useful for Monte-Carlo studies and bootstrapping procedures.

Usage

estimate_design(
  data,
  dvar,
  pvar,
  mvar,
  s = NULL,
  rtt = NULL,
  overall_effects = FALSE,
  overall_rtt = TRUE,
  model = "JW",
  ...
)

Arguments

Details

The function uses the plm function to estimate parameters for each single-case. If more than two single-cases are included in the scdf, the between case variance depicting the overall performance (s) is estimated unless s is provided. The reliability of the measurements (rtt) is estimated for each case unless rtt is provided. If overall_rtt is set to TRUE, rtt estimations will be based on all cases and identical for each case. If overall_effects is set to TRUE, trend, level, and slope effect estimations will be identical for each case.

The resulting design object can be used as input for the random_scdf function to create new random scdf files based on the estimated parameters. This allows to create bootstrap samples or Monte-Carlo datasets based on the characteristics of an existing dataset.

Value

A list of parameters for each single-case. Parameters include name, length, and starting measurement time of each phase, trend, level, and slope effects for each phase, start value, standard deviation, and reliability for each case. This list can be used as input for the random_scdf function to create new random scdf files based on the estimated parameters.

Author(s)

Juergen Wilbert

Examples

# create a random scdf with predefined parameters
set.seed(1234)
design <- design(
  n = 10, trend = -0.02,
  level = list(0, 1), rtt = 0.8,
  s = 1
)
scdf<- random_scdf(design)

# Estimate the parameters based on the scdf and create a new random scdf
# based on these estimations
design_est <- estimate_design(scdf, rtt = 0.8)
scdf_est <- random_scdf(design_est)

# Analyze both datasets with an hplm model. See how similar the estimations
# are:
hplm(scdf, slope = FALSE)
hplm(scdf_est, slope = FALSE)

# Also similar results for pand and randomization tests:
pand(scdf)
pand(scdf_est)
rand_test(scdf)
rand_test(scdf_est)

Single-case example data sets

Description

The scan package comes with a set of fictitious and authentic single-case study data. These data sets can be used to practice single-case data analysis and to reproduce results from the respective publications.

• Beretvas2008 — Fictitious single-case intervention study from Beretvas & Chung, 2008.

• Borckardt2014 — Fictitious daily pain ratings evaluating a psychological treatment from Borckardt & Nash, 2014.

• byHeart2011 — Multiple-baseline (11 cases) flash card vocabulary learning (Wilbert, unpublished).

• example_A24 — Number of injuries on a German autobahn before and after implementation of a speedlimit (130km/h) (Ministerium fuer Infrastruktur und Landesplanung. Land Brandenburg).

• exampleA1B1A2B2 — Fictitious A1-B1-A2-B2 example dataset.

• exampleA1B1A2B2_zvt — Non-fictitious A1-B1-A2-B2 example with ZVT (intelligence measure) and D2 (concentration measure) scores.

• exampleAB — Fictitious AB example dataset with three cases.

• exampleAB_50 — Fictitious AB example dataset (50 cases)s.

• exampleAB_50.l2 — Level-2 data for exampleAB_50.

• exampleAB_add — Fictitious AB example with added covariates.

• exampleAB_decreasing — Fictitious AB example with an expected decreasing effect in the intervention phase.

• exampleAB_mpd — Fictitious example with different phase structures for each case.

• exampleAB_score — Fictitious AB example with binomial distributed score outcome.

• exampleAB_simple — Simple fictitious AB example with three cases.

• exampleABAB — Fictitious ABAB reversal design example.

• exampleABC — Fictitious ABC example dataset.

• exampleABC_150 — Fictitious ABC example (150 cases).

• exampleABC_50 — Fictitious ABC example (50 cases).

• exampleABC_outlier — Fictitious ABC example with outlier.

• example_atd — Fictitious AB alternating treatment design.

• example_stranger - Example for screen time of Stranger Things characters.

• Grosche2011 — Multiple-baseline (three cases) from a direct-instructive reading intervention (Grosche, 2011).

• Grosche2014 — Multiple-baseline (3×3 materials) reading intervention (Grosche, Lueke, & Wilbert, unpublished).

• GruenkeWilbert2014 — Multiple-baseline (six cases) from a story mapping reading intervention (Gruenke, Wilbert, & Stegemann-Calder, 2013).

• Huber2014 — Multiple-baseline (four cases) with DBR ratings from a behavioral compliance intervention (Huber, unpublished).

• Huitema2000 — Fictitious single-case intervention study (Huitema & McKean, 2000).

• Lenz2013 — Fictitious example (Lenz, 2013).

• Leidig2018 — Multiple-baseline good behavior game intervention (Leidig et al., 2022).

• Leidig2018_l2 — Level-2 data for Leidig2018 (Leidig et al., 2022).

• Parker2007 — Example dataset after Parker et al. (2007).

• Parker2009 — Example dataset after Parker et al. (2009).

• Parker2009b — Example dataset after Parker & Vannest (2009).

• Parker2011 — Example dataset after Parker et al. (2011).

• Parker2011b — Example from Parker, Vannest, & Davis (2011).

• SSDforR2017 — Example from the R package SSDforR.

• Tarlow2017 — Fictitious single-case intervention study (Tarlow, 2017).

• Waddell2011 — Fictitious single-case intervention study (Waddell, Nassar, & Gustafson, 2011).

Usage

data(exampleAB, package = "scan")

Author(s)

Juergen Wilbert

References

Beretvas, S., & Chung, H. (2008). An evaluation of modified R2-change effect size indices for single-subject experimental designs. Evidence-Based Communication Assessment and Intervention, 2, 120–128.

Borckardt, J. J., & Nash, M. R. (2014). Simulation modelling analysis for small sets of single-subject data collected over time. Neuropsychological Rehabilitation, 24, 492–506.

Gruenke, M., Wilbert, J., & Stegemann-Calder, K. (2013). Analyzing the effects of story mapping on the reading comprehension of children with low intellectual abilities. Learning Disabilities: A Contemporary Journal, 11, 51–64.

Grosche, M. (2011). Effekte einer direkt-instruktiven Foerderung der Lesegenauigkeit. Empirische Sonderpaedagogik, 3, 147–161.

Huitema, B. E., & McKean, J. W. (2000). Design specification issues in time-series intervention models. Educational and Psychological Measurement, 60, 38–58.

Lenz, A. S. (2013). Calculating Effect Size in Single-Case Research: A Comparison of Nonoverlap Methods. Measurement and Evaluation in Counseling and Development, 46(1), 64–73.

Leidig, T., Casale, G., Wilbert, J., Hennemann, T., Volpe, R. J., Briesch, A., & Grosche, M. (2022). Individual, generalized, and moderated effects of the good behavior game on at-risk primary school students: A multilevel multiple baseline study using behavioral progress monitoring. Frontiers in Education, 7. https://www.frontiersin.org/articles/10.3389/feduc.2022.917138

Parker, R. I., Hagan-Burke, S., & Vannest, K. (2007). Percentage of All Non-Overlapping Data (PAND) An Alternative to PND. The Journal of Special Education, 40(4), 194-204.

Parker, R. I., Vannest, K. J., & Brown, L. (2009). The improvement rate difference for single-case research. Exceptional Children, 75(2), 135-150.

Parker, R. I., & Vannest, K. (2009). An improved effect size for single-case research: Nonoverlap of all pairs. Behavior Therapy, 40(4), 357-367.

Parker, R. I., Vannest, K. J., Davis, J. L., & Sauber, S. B. (2011). Combining Nonoverlap and Trend for Single-Case Research: Tau-U. Behavior Therapy, 42(2), 284–299. https://doi.org/10.1016/j.beth.2010.08.006

Parker, R. I., Vannest, K. J., & Davis, J. L. (2011). Effect Size in Single-Case Research: A Review of Nine Nonoverlap Techniques. Behavior Modification, 35(4), 303-322. https://doi.org/10.1177/0145445511399147

Tarlow, K. R. (2017). An Improved Rank Correlation Effect Size Statistic for Single-Case Designs: Baseline Corrected Tau. Behavior Modification, 41(4), 427–467. https://doi.org/10.1177/0145445516676750

Waddell, D. E., Nassar, S. L., & Gustafson, S. A. (2011). Single-Case Design in Psychophysiological Research: Part II: Statistical Analytic Approaches. Journal of Neurotherapy, 15, 160–169.

Export scan objects to html or latex

Description

Export creates html files of tables or displays them directly in the viewer pane of rstudio. When applied in rmarkdown/quarto, tables can also be created for pdf/latex output.

Usage

export(object, ...)

## S3 method for class 'sc_desc'
export(
  object,
  caption = NA,
  footnote = NA,
  filename = NA,
  flip = FALSE,
  round = 2,
  ...
)

## S3 method for class 'sc_nap'
export(
  object,
  caption = NA,
  footnote = NA,
  filename = NA,
  select = c("Case", "NAP", "NAP Rescaled", "w", "p", "d", "R²"),
  round = 2,
  ...
)

## S3 method for class 'sc_overlap'
export(
  object,
  caption = NA,
  footnote = NULL,
  filename = NA,
  round = 2,
  decimals = 2,
  flip = FALSE,
  ...
)

## S3 method for class 'sc_pem'
export(object, caption = NA, footnote = NA, filename = NA, round = 2, ...)

## S3 method for class 'sc_pet'
export(object, caption = NA, footnote = NA, filename = NA, round = 1, ...)

## S3 method for class 'sc_pnd'
export(
  object,
  caption = NA,
  footnote = NA,
  filename = NA,
  select = c("Case", "PND", "Total", "Exceeds"),
  round = 2,
  ...
)

## S3 method for class 'sc_power'
export(object, caption = NA, footnote = NA, filename = NA, round = 3, ...)

## S3 method for class 'sc_smd'
export(
  object,
  caption = NA,
  footnote = NA,
  filename = NA,
  select = c("Case", `Mean A` = "mA", `Mean B` = "mB", `SD A` = "sdA", `SD B` = "sdB",
    `SD Cohen` = "sd cohen", `SD Hedges` = "sd hedges", "Glass' delta", "Hedges' g",
    "Hedges' g correction", "Hedges' g durlak correction", "Cohen's d"),
  round = 2,
  decimals = 2,
  flip = FALSE,
  ...
)

## S3 method for class 'sc_trend'
export(
  object,
  caption = NA,
  footnote = NA,
  filename = NA,
  round = 3,
  decimals = NULL,
  ...
)

## S3 method for class 'scdf'
export(
  object,
  summary = FALSE,
  caption = NA,
  footnote = NA,
  filename = NA,
  cols,
  round = 2,
  ...
)

## S3 method for class 'scdf_summary'
export(object, caption = NA, footnote = NA, filename = NA, round = 2, ...)

Arguments

Details

The function uses either the kableExtra or the gt package to create the tables. The default engine can be set via the option scan.export.engine. Additional options for kable and kable_styling can be set via the options scan.export.kable and scan.export.kable_styling. The default options can be viewed and modified via options("scan.export.kable") and options("scan.export.kable_styling").

Value

Returns or displays a specially formatted html (or latex) file.

Fetches elements from scan objects

Description

The fetch function is a getter function for scan objects returned from regression functions such as plm(), hplm(), bplm(), and mplm(). It allows users to extract specific elements from these objects, such as the fitted model.

Usage

fetch(object, what, ...)

Arguments

Value

An object of the respective regression model class.

Author(s)

Juergen Wilbert

See Also

Other regression functions: bplm(), hplm(), mplm(), plm(), print.sc_ac(), print.sc_bctau(), trend()

Examples

# plm regression
model1 <- plm(example_A24)
fetch(model1, what = "model") |> summary()
# Multilevel plm regression
model2 <- hplm(exampleAB_50)
fetch(model2, what = "model") |> summary()
# Bayesian plm regression
model3 <- bplm(exampleAB_50, nitt = 5000)
fetch(model3, what = "model") |> summary()

Replacing missing measurement points in single-case data

Description

The fillmissing() function replaces missing measurements in single-case data. It linearly interpolates missing data points between two existing measurements for all variables except the measurement time and phase. The measurement time variable is filled with the missing time points. The phase variable is copied from the previous measurement time point. If mt values are missing (NA), they are also interpolated if interpolate_na = TRUE.

Usage

fill_missing(data, dvar, mvar, pvar, interpolate_na = TRUE)

Arguments

Details

The fill_missing() function is designed to handle single-case data with missing measurement points. It performs linear interpolation to estimate the missing values based on the existing data points. The function iterates through each single-case in the provided single-case data frame (scdf) and identifies gaps in the measurement time variable. For each gap, it calculates the step size for linear interpolation and fills in the missing values for all target variables (i.e., all variables except the measurement time and phase). The interpolated data points are then added to the single-case data frame, and the final result is sorted by measurement time. This function is particularly useful for preparing single-case data for further analysis, such as calculating overlap indices or conducting randomization tests, where continuous measurement times are required. It ensures that the data is complete by filling in the missing measurement points in a systematic manner.

Value

A single-case data frame with interpolated missing data points.

Author(s)

Juergen Wilbert

See Also

Other data manipulation functions: add_l2(), as.data.frame.scdf(), as_scdf(), batch_apply(), moving_median(), print.sc_outlier(), ranks(), rescale(), scdf(), select_cases(), set_vars(), shift(), smooth_cases(), standardize(), truncate_phase()

Examples

## In his study, Grosche (2011) could not realize measurements each
## single week for all participants. During the course of 100 weeks,
## about 20 measurements per person at different times were administered.

## Fill missing values in a single-case dataset with discontinuous
## measurement times
Grosche2011filled <- fill_missing(Grosche2011)
study <- c(Grosche2011[2], Grosche2011filled[2])
names(study) <- c("Original", "Filled")
study

## An example with multiple interpolated variables

rolf_n <- exampleAB_add
rolf_n[[1]] <- rolf_n[[1]][-c(3,7,8),]
rolf_f <- fill_missing(rolf_n)
study1 <- c("original" = exampleAB_add, "interpolated" = rolf_f)
study1

## Example with missing NAs in measurement time
Maggie2 <- random_scdf(design(level = list(0,1)), seed = 123)
Maggie2_n <- Maggie2
Maggie2_n[[1]][c(5,12:14,20), "mt"] <- NA
Maggie2_f <- fill_missing(Maggie2_n)
study2 <- c("original" = Maggie2, "interpolated" = Maggie2_f)
study2

Hierarchical piecewise linear model / piecewise regression for multiple cases

Description

The hplm() function computes a hierarchical piecewise regression model. It extends the standard piecewise regression model to multiple cases by estimating fixed and random effects. The function uses the lme function of the nlme package to fit linear mixed-effects models. The model can include random intercepts and random slopes for level, trend, and treatment effects. Additionally, it allows for the inclusion of autoregressive structures and unequal variances across phases. The function also provides options for likelihood ratio tests to compare models with and without random slope effects, as well as the calculation of intraclass correlations (ICC) to assess the proportion of variance attributable to between-case differences. This function is particularly useful for analyzing data from multiple single-case experimental designs (SCEDs) where observations are nested within cases.

Usage

hplm(
  data,
  dvar,
  pvar,
  mvar,
  model = c("W", "H-M", "B&L-B", "JW"),
  contrast = c("first", "preceding"),
  contrast_level = NA,
  contrast_slope = NA,
  method = c("ML", "REML"),
  control = list(opt = "optim"),
  random.slopes = FALSE,
  lr.test = FALSE,
  ICC = TRUE,
  trend = TRUE,
  level = TRUE,
  slope = TRUE,
  random_trend = FALSE,
  random_level = FALSE,
  random_slope = FALSE,
  fixed = NULL,
  random = NULL,
  ar = 0,
  unequal_variances = FALSE,
  update.fixed = NULL,
  data.l2 = NULL,
  ...
)

## S3 method for class 'sc_hplm'
print(x, digits = 3, bcsmd = FALSE, casewise = FALSE, ...)

## S3 method for class 'sc_hplm'
export(
  object,
  caption = NA,
  footnote = NA,
  filename = NA,
  round = 2,
  nice = TRUE,
  casewise = FALSE,
  ...
)

## S3 method for class 'sc_hplm'
coef(object, casewise = FALSE, ...)

Arguments

Value

An object of class sc_hplm.

• model | List containing infromation about

• N | Number of single-cases.

• formula | A list containing the fixed and the random formulas of the hplm model.

• hplm | Object of class lme contaning the multilevel model.

• model.0 | Object of class lme containing the zero model.

• ICC | List containing intraclass correlation and test parameters.

• model.without | Object of class gls containing the fixed effect model.

• contrast | List with contrast definitions.

Functions

• print(sc_hplm): Print results

• export(sc_hplm): Export results as html table (see export())

• coef(sc_hplm): Extract model coefficients

Model specification

The fixed effects part of the model can be specified using the fixed argument, while the random effects part can be specified using the random argument. If not provided, default formulas based on the specified model type (e.g., "B&L-B") are created. The function also allows for the inclusion of autoregressive structures through the ar argument and unequal variances across phases through the unequal_variances argument.

Random slopes

By setting the random.slopes argument to TRUE, the model will include random slope effects for level, trend, and treatment effects. This allows for individual differences in how cases respond to these effects.

Likelihood ratio tests

If the lr.test argument is set to TRUE, the function will perform likelihood ratio tests to compare models with and without random slope effects. This helps to determine whether including random slopes significantly improves model fit.

Intraclass correlation

If the ICC argument is set to TRUE, the function will calculate the intraclass correlation coefficient (ICC) to assess the proportion of variance attributable to between-case differences. This provides insight into the degree of similarity among observations within the same case.

Author(s)

Juergen Wilbert

See Also

Other regression functions: bplm(), fetch(), mplm(), plm(), print.sc_ac(), print.sc_bctau(), trend()

Examples

## Compute hplm model on a MBD over fifty cases (restricted log-likelihood)
hplm(exampleAB_50, method = "REML", random.slopes = FALSE)

## Analyzing with additional L2 variables
Leidig2018 |>
  add_l2(Leidig2018_l2) |>
  hplm(update.fixed = .~. + gender + migration + ITRF_TOTAL*phaseB,
       slope = FALSE, random.slopes = FALSE, lr.test = FALSE
  )

Import scdf – RStudio Addin

Description

Import scdf – RStudio Addin

Usage

import_scdf()

IRD - Improvement rate difference

Description

ird() calculates the robust improvement rate difference as proposed by Parker and colleagues (2011).

Usage

ird(data, dvar, pvar, decreasing = FALSE, phases = c(1, 2))

## S3 method for class 'sc_ird'
print(x, digits = 3, ...)

## S3 method for class 'sc_ird'
export(object, caption = NA, footnote = NA, filename = NA, round = 3, ...)

Arguments

Details

The adaptation of the improvement rate difference for single-case phase comparisons was developed by Parker and colleagues (2009). A variation called robust improvement rate difference was proposed by Parker and colleagues in 2011. This function calculates the robust improvement rate difference. It follows the formula suggested by Pustejovsky (2019). For a multiple case design, ird is based on the overall improvement rate of all cases which is the average of the irds for each case.

Functions

• print(sc_ird): Print results

• export(sc_ird): Export results to html

References

Parker, R. I., Vannest, K. J., & Brown, L. (2009). The improvement rate difference for single-case research. Exceptional Children, 75(2), 135-150.

Parker, R. I., Vannest, K. J., & Davis, J. L. (2011). Effect Size in Single-Case Research: A Review of Nine Nonoverlap Techniques. Behavior Modification, 35(4), 303-322. https://doi.org/10.1177/0145445511399147

Pustejovsky, J. E. (2019). Procedural sensitivities of effect sizes for single-case designs with directly observed behavioral outcome measures. Psychological Methods, 24(2), 217-235. https://doi.org/10.1037/met0000179

See Also

Other overlap functions: nap(), overlap(), pand(), pem(), pet(), pnd(), print.sc_cdc(), select_phases(), tau_u()

Test for scdf objects

Description

Tests for objects of type "scdf".

Usage

is.scdf(x)

Arguments

Value

Returns TRUE or FALSE depending on whether its argument is of scdf type or not.

Author(s)

Juergen Wilbert

Transform every single case of a single case data frame

Description

Takes an scdf and applies transformations to each individual case. This is useful to calculate or modify new variables.

Usage

moving_median(x, lag = 1)

moving_mean(x, lag = 1)

local_regression(x, mt = 1:length(x), f = 0.2)

set_na_at(x, first_of, positions = 0)

center_at(x, at = TRUE, shift = 0, part = 0)

first_of(x, positions = 0)

across_cases(...)

all_cases(...)

rowwise(...)

## S3 method for class 'scdf'
transform(`_data`, ...)

Arguments

Details

This function is a method of the generic transform() function. Unlike the generic version, expressions are evaluated serially: the result of one expression is used as the basis for subsequent computations.

Several helper functions can be used inside expressions:

• n(): returns the number of measurements in a case.

• all_cases(): extracts the values of a variable across all cases. Takes an expression as argument. For example:

  • mean(all_cases(values)) calculates the mean of values across all cases.

  • mean(all_cases(values[phase == "A"])) calculates the mean of all values where phase == "A".

• rowwise(): applies a calculation separately to each row. Example: rowwise(sum(values, mt, na.rm = TRUE)).

• across_cases(): creates new variables or replaces existing ones across all cases. Example: across_cases(values_ranked = rank(values, na.last = "keep")) ranks the values variable across all cases and creates a new variable values_ranked.

Value

An scdf.

Author(s)

Juergen Wilbert

See Also

Other data manipulation functions: add_l2(), as.data.frame.scdf(), as_scdf(), batch_apply(), fill_missing(), print.sc_outlier(), ranks(), rescale(), scdf(), select_cases(), set_vars(), shift(), smooth_cases(), standardize(), truncate_phase()

Examples

## Creates a single-case with frequency distributions. The proportion and
## percentage of the frequencies are calculated with transform:
design <- design(
 n = 3,
 level = 5,
 distribution = "binomial",
 n_trials = 20,
 start_value = 0.5
)
study <- random_scdf(design)
transform(study, proportion = values/trials, percentage = proportion * 100)

## Z standardize the dependent variable and add two new variables:
exampleAB |>
  transform(
    values = scale(values),
    mean_values = mean(values),
    sd_values = sd(values)
  )

## Use `all` to calculate global variables.
exampleAB |>
  transform(
    values_center_case = values - mean(values[phase == "A"]),
    values_center_global = values - mean(all(values[phase == "A"])),
    value_dif = values_center_case - values_center_global
  )

## Use `across_cases` to calculate or replace a variable with values from
## all cases. E.g., standardize the dependent variable:
exampleABC |>
  transform(
    across_cases(values = scale(values))
  )

## Rank transform the values based on all cases vs. within each case:
exampleABC |>
  transform(
    across_cases(values_across = rank(values, na.last="keep")),
    value_within = rank(values, na.last="keep")
  )

## Three helper functions to smooth the data
Huber2014$Berta |>
transform(
  "compliance (moving median)" = moving_median(compliance),
  "compliance (moving mean)" = moving_mean(compliance),
  "compliance (local regression)" = local_regression(compliance, mt)
)

## Function first_of() helps to set NAs for specific phases.
## E.g., you want to replace the first two values of phase A and the first
## value of phase B and its preceding value.

byHeart2011 |>
  transform(
    values = set_na_at(values, phase == "A", 0:1),
    values = set_na_at(values, phase == "B", -1:0)
  )

Multivariate Piecewise linear model / piecewise regression

Description

The mplm() function computes a multivariate piecewise regression model. The function automatically creates the regression formula based on the provided data and the selected options. The default model includes trend, level, and slope effects for each dependent variable. The regression formula can be changed by providing a custom formula to the update argument.

Usage

mplm(
  data,
  dvar,
  mvar,
  pvar,
  model = c("W", "H-M", "B&L-B", "JW"),
  contrast = c("first", "preceding"),
  contrast_level = c(NA, "first", "preceding"),
  contrast_slope = c(NA, "first", "preceding"),
  trend = TRUE,
  level = TRUE,
  slope = TRUE,
  formula = NULL,
  update = NULL,
  na.action = na.omit,
  ...
)

## S3 method for class 'sc_mplm'
print(x, digits = "auto", std = FALSE, ...)

## S3 method for class 'sc_mplm'
export(
  object,
  caption = NA,
  footnote = NA,
  filename = NA,
  nice = TRUE,
  std = FALSE,
  decimals = 2,
  ...
)

Arguments

Details

The function currently only supports single-case data (i.e., one case per dataset). For multilevel piecewise regression models, please use the hplm function.

Value

Functions

• print(sc_mplm): Print results

• export(sc_mplm): Export results as html

Author(s)

Juergen Wilbert

See Also

Other regression functions: bplm(), fetch(), hplm(), plm(), print.sc_ac(), print.sc_bctau(), trend()

Examples

res <- mplm(Leidig2018$`1a1`,
  dvar = c("academic_engagement", "disruptive_behavior")
)
print(res)
## also report standardized coefficients:
print(res, std = TRUE)

Remove missing values from scdf

Description

Removes any row with a missing value from each single-case data frame in an scdf.

Usage

## S3 method for class 'scdf'
na.omit(object, ...)

Arguments

Value

A scdf object.

Author(s)

Juergen Wilbert

Nonoverlap of all Pairs (NAP)

Description

The nap() function calculates the nonoverlap of all pairs (NAP; Parker & Vannest, 2009). NAP summarizes the overlap between all pairs of phase A and phase B data points. If an increase of phase B scores is expected, a non-overlapping pair has a higher phase B data point. The NAP equals number of pairs showing no overlap / number of pairs where ties are counted as half non-overlaps. Because NAP can take values between 0 and 100 percent where values below 50 percent indicate an inverse effect, an nap rescaled from -100 to 100 percent where negative values indicate an inverse effect is also displayed (nap_{rescaled} = 2 * nap - 100).

Usage

nap(data, dvar, pvar, decreasing = FALSE, phases = c(1, 2))

Arguments

Details

If a decrease of phase B scores is expected, set the argument decreasing = TRUE.

Value

Author(s)

Juergen Wilbert

References

Parker, R. I., & Vannest, K. (2009). An improved effect size for single-case research: Nonoverlap of all pairs. Behavior Therapy, 40, 357-367.

See Also

Other overlap functions: ird(), overlap(), pand(), pem(), pet(), pnd(), print.sc_cdc(), select_phases(), tau_u()

Examples

## Calculate NAP for a study with  lower expected phase B scores
## (e.g. aggressive behavior)
gretchen <- scdf(c(A = 12, 14, 9, 10, B = 10, 6, 4, 5, 3, 4))
nap(gretchen, decreasing = TRUE)

## Request NAP for all cases from the Grosche2011 scdf
nap(Grosche2011)

## Calculate NAP for phase 1 and phase 3 of an ABAB design
nap(exampleABAB, phases = c(1, 3))

Overlap indices for single-case data

Description

The overlap function provides the most common overlap indices for single-case data and some additional statistics.

Usage

overlap(data, dvar, pvar, mvar, decreasing = FALSE, phases = c(1, 2))

Arguments

Details

It computes PND, PEM, PET, NAP, PAND, IRD, Tau-U, mean difference, difference in trend, SMD, and Hedges-g for each single-case included in an scdf.

See corresponding functions of PND, PEM, PET, NAP, PAND for calculation. Tau_U(A) reports "A vs. B - Trend A" whereas Tau_U(BA) reports "A vs. B + Trend B - Trend A". Base_Tau is baseline corrected tau (correction applied when autocorrelation in phase A is significant). Diff_mean is the mean difference. Diff_trend is the difference in the regression estimation of the dependent variable on measurement-time (x ~ mt) for each phase. SMD is the mean difference divided by the standard deviation of phase A. Hedges_g is the mean difference divided by the pooled standard deviation: \sqrt{ (n_A - 1)sd_A^2 + (n_B - 1)sd_B^2 \over n_A + n_B - 2 } with a hedges correction applied: Hedges_g * (1 - \frac{3}{4n - 9} ) ).

Value

Author(s)

Juergen Wilbert

See Also

pnd(), pem(), pet(), nap(), pand(), ird(), tau_u(), corrected_tau()

Other overlap functions: ird(), nap(), pand(), pem(), pet(), pnd(), print.sc_cdc(), select_phases(), tau_u()

Examples

## Display overlap indices for one single-case
overlap(Huitema2000, decreasing = TRUE)

## Display overlap indices for six single-cases
overlap(GruenkeWilbert2014)

## Combining phases for analyszing designs with more than two phases
overlap(exampleA1B1A2B2, phases = list(c("A1","A2"), c("B1","B2")))

Percentage of all non-overlapping data

Description

The pand() function calculates the percentage of all non-overlapping data (PAND; Parker, Hagan-Burke, & Vannest, 2007), an index to quantify a level increase (or decrease) in performance after the onset of an intervention.

Usage

pand(
  data,
  dvar,
  pvar,
  decreasing = FALSE,
  phases = c(1, 2),
  method = c("sort", "minimum")
)

## S3 method for class 'sc_pand'
print(x, ...)

## S3 method for class 'sc_pand'
export(object, caption = NA, footnote = NA, filename = NA, round = 1, ...)

Arguments

Details

PAND was proposed by Parker, Hagan-Burke, and Vannest in 2007. The authors emphasize that PAND is designed for application in a multiple case design with a substantial number of measurements, technically at least 20 to 25, but preferably 60 or more. PAND is defined as 100% minus the percentage of data points that need to be removed from either phase in order to ensure nonoverlap between the phases. Several approaches have been suggested to calculate PAND, leading to potentially different outcomes. In their 2007 paper, Parker and colleagues present an algorithm for computing PAND. The algorithm involves sorting the scores of a time series, including the associated phases, and comparing the resulting phase order with the original phase order using a contingency table. To account for ties, the algorithm includes a randomization process where ties are randomly assigned to one of the two phases. Consequently, executing the algorithm multiple times could yield different results. It is important to note that this algorithm does not produce the same results as the PAND definition provided earlier in the same paper. However, it offers the advantage of allowing the calculation of an effect size measure phi, and the application of statistical tests for frequency distributions. Pustejovsky (2019) presented a mathematical formulation of Parker's original definition for comparing two phases of a single case:

PAND = \frac{1}{m+n}max\{(i+j)I(y^A_{i}<y^B_{n+1-j}\}

This formulation provides accurate results for PAND, but the original definition has the drawback of an unknown distribution under the null hypothesis, making a statistical test difficult. The pand() function enables the calculation of PAND using both methods. The first approach (method = "sort") follows the algorithm described above, with the exclusion of randomization before sorting to avoid ambiguity. It calculates a phi measure and provides the results of a chi-squared test and a Fisher exact test. The second approach (method = "minimum") applies the aforementioned formula. The code of this function is based on the code of the SingleCaseES package (function calc_PAND). For a multiple case design, overlaps are calculated for each case, summed, and then divided by the total number of measurements. No statistical test is conducted for this method.

Value

Functions

• print(sc_pand): Print results

• export(sc_pand): Export results as html table (see export())

Author(s)

Juergen Wilbert

References

Parker, R. I., Hagan-Burke, S., & Vannest, K. (2007). Percentage of All Non-Overlapping Data (PAND): An Alternative to PND. The Journal of Special Education, 40, 194-204.

Parker, R. I., & Vannest, K. (2009). An Improved Effect Size for Single-Case Research: Nonoverlap of All Pairs. Behavior Therapy, 40, 357-367.

Pustejovsky, J. E. (2019). Procedural sensitivities of effect sizes for single-case designs with directly observed behavioral outcome measures. Psychological Methods, 24(2), 217-235. https://doi.org/10.1037/met0000179

Pustejovsky JE, Chen M, Swan DM (2023). SingleCaseES: A Calculator for Single-Case Effect Sizes. R package version 0.7.1.9999, https://jepusto.github.io/SingleCaseES/.

See Also

Other overlap functions: ird(), nap(), overlap(), pem(), pet(), pnd(), print.sc_cdc(), select_phases(), tau_u()

Examples

## REplication of the Parker et al. 2007 example
pand(Parker2007)

## Calculate the PAND with an expected decrease of phase B scores
cubs <- scdf(c(20,22,24,17,21,13,10,9,20,9,18), B_start = 5)
pand(cubs, decreasing = TRUE)

Percent exceeding the median (PEM)

Description

The pem function returns the percentage of phase B data exceeding the phase A median. Additionally, a chi square test against a 50/50 distribution is computed. Different measures of central tendency can be addressed for alternative analyses.

Usage

pem(
  data,
  dvar,
  pvar,
  decreasing = FALSE,
  binom.test = TRUE,
  chi.test = FALSE,
  FUN = median,
  phases = c(1, 2),
  ...
)

Arguments

Details

The Percent Exceeding the Median is calculated as the percentage of data points in phase B that exceed the median of phase A. If the decreasing argument is set to TRUE, the percentage of data points in phase B that are below the median of phase A is calculated. The PEM is expressed as a percentage ranging from 0 to 100. Higher values indicate a greater degree of improvement from phase A to phase B.

Author(s)

Juergen Wilbert

See Also

Other overlap functions: ird(), nap(), overlap(), pand(), pet(), pnd(), print.sc_cdc(), select_phases(), tau_u()

Examples

## Calculate the PEM including the Binomial and Chi-square tests for a single-case
dat <- random_scdf(5, level = 0.5)
pem(dat, chi.test = TRUE)

Percent exceeding the trend (PET)

Description

The pet function returns the percentage of Phase B data points that exceed the prediction based on the Phase A trend. A binomial test against a 50/50 distribution is calculated. It also calculates the percentage of Phase B data points that exceed the upper (or lower) 95 percent confidence interval of the predicted progression.

Usage

pet(data, dvar, pvar, mvar, ci = 0.95, decreasing = FALSE, phases = c(1, 2))

Arguments

Details

The PET is calculated by first fitting a linear model to the Phase A data to estimate the trend. Then, for each data point in Phase B, it is determined whether it exceeds the predicted value from the Phase A trend. The PET is the percentage of Phase B data points that exceed this predicted value. Additionally, a binomial test is performed to assess whether the observed PET is significantly greater than what would be expected by chance (i.e., 50%).

Value

Author(s)

Juergen Wilbert

See Also

Other overlap functions: ird(), nap(), overlap(), pand(), pem(), pnd(), print.sc_cdc(), select_phases(), tau_u()

Examples

## Calculate the PET and use a 99%-CI for the additional calculation
# create random example data
design <- design(n = 5, slope = 0.2)
dat <- random_scdf(design, seed = 23)
pet(dat, ci = .99)

Piecewise linear model / piecewise regression

Description

The plm function computes a piecewise regression model (see Huitema & McKean, 2000) for one case. The function automatically creates the default model which includes trend, level, and slope effects. The model can be changed with trend, level, and slope arguments or by providing a custom formula.

Usage

plm(
  data,
  dvar,
  pvar,
  mvar,
  AR = 0,
  model = c("W", "H-M", "B&L-B", "JW"),
  family = "gaussian",
  trend = TRUE,
  level = TRUE,
  slope = TRUE,
  contrast = c("first", "preceding"),
  contrast_level = c(NA, "first", "preceding"),
  contrast_slope = c(NA, "first", "preceding"),
  formula = NULL,
  update = NULL,
  na.action = na.omit,
  r_squared = TRUE,
  var_trials = NULL,
  dvar_percentage = FALSE,
  ...
)

## S3 method for class 'sc_plm'
print(
  x,
  lag_max = 3,
  ci = 0.95,
  q = FALSE,
  r_squared = getOption("scan.rsquared"),
  ...
)

## S3 method for class 'sc_plm'
export(
  object,
  caption = NA,
  footnote = NA,
  filename = NA,
  nice = TRUE,
  ci = 0.95,
  q = FALSE,
  round = 2,
  r_squared = getOption("scan.rsquared"),
  ...
)

Arguments

Details

The function uses the glm function of the stats package or the gls function of the nlme package (for auto-regression models).

Value

An object of class sc_plm.

Functions

• print(sc_plm): Print

• export(sc_plm): Export results as html table (see export())

Author(s)

Juergen Wilbert

References

Beretvas, S., & Chung, H. (2008). An evaluation of modified R2-change effect size indices for single-subject experimental designs. Evidence-Based Communication Assessment and Intervention, 2, 120-128.

Huitema, B. E., & McKean, J. W. (2000). Design specification issues in time-series intervention models. Educational and Psychological Measurement, 60, 38-58.

See Also

Other regression functions: bplm(), fetch(), hplm(), mplm(), print.sc_ac(), print.sc_bctau(), trend()

Examples

## Compute a piecewise regression model for a random single-case
set.seed(123)
AB <- design(
  phase_design = list(A = 10, B = 20),
  level = list(A = 0, B = 1), slope = list(A = 0, B = 0.05),
  trend = 0.05
)
dat <- random_scdf(design = AB)
plm(dat, AR = 3)

## Another example with a more complex design
A1B1A2B2 <- design(
  phase_design = list(A1 = 15, B1 = 20, A2 = 15, B2 = 20),
  level = list(A1 = 0, B1 = 1, A2 = -1, B2 = 1),
  slope = list(A1 = 0, B1 = 0.0, A2 = 0, B2 = 0.0),
  trend = 0.0)
dat <- random_scdf(design = A1B1A2B2, seed = 123)
plm(dat, contrast = "preceding")

## no slope effects were found. Therefore, you might want to the drop slope
## estimation:
plm(dat, slope = FALSE, contrast = "preceding")

## and now drop the trend estimation as well
plm(dat, slope = FALSE, trend = FALSE, contrast = "preceding")

## A poisson regression
example_A24 |>
  plm(family = "poisson")

## A binomial regression (frequencies as dependent variable)
plm(exampleAB_score$Christiano, family = "binomial", var_trials = "trials")

## A binomial regression (percentage as dependent variable)
exampleAB_score$Christiano |>
  transform(percentage = values/trials) |>
  set_dvar("percentage") |>
  plm(family = "binomial", var_trials = "trials", dvar_percentage = TRUE)
## Print
plm(exampleAB$Johanna) |> 
  print(ci = 0.9, r_squared = c("delta", "partial"))
## Export
plm(exampleAB$Johanna) |> export()

(Deprecated) Plot single-case data

Description

This function provides a plot of a single-case or multiple single-cases.

Usage

## S3 method for class 'scdf'
plot(...)

plotSC(
  data,
  dvar,
  pvar,
  mvar,
  ylim = NULL,
  xlim = NULL,
  xinc = 1,
  lines = NULL,
  marks = NULL,
  phase.names = NULL,
  xlab = NULL,
  ylab = NULL,
  main = "",
  case.names = NULL,
  style = getOption("scan.plot.style"),
  ...
)

Arguments

Value

Returns a plot of one or multiple single-cases.

Author(s)

Juergen Wilbert

Examples

## Request the default plot of the data from Borckhardt (2014)
plot(Borckardt2014)

## Plot the three cases from Grosche (2011) and visualize the phase A trend
plot(Grosche2011, style = "grid", lines = "trendA")

## Request the local regression line for Georg from that data set and customize the plot
plot(Grosche2011$Georg, style = "sienna", ylim = c(0,NA),
       xlab = "Training session", ylab = "Words per minute",
       phase.names = c("Baseline", "Intervention"), xinc = 5,
       lines = list(type = "loreg", f = 0.2, lty = "solid", col = "black", lwd = 3))

## Plot a random MBD over three cases and mark interesting MTs
dat <- random_scdf(design = design(3))
plot(dat, marks = list(positions = list(c(2,4,5),c(1,2,3),c(7,8,9)), col = "blue",
       cex = 1.4), style = c("grid", "annotate", "tiny"))

Plot random distribution

Description

This function takes the return of the rand_test function and creates a histogram with the distribution of the rand sample statistics.

Usage

plot_rand(
  object,
  type = "hist",
  xlab = NULL,
  ylab = NULL,
  title = NULL,
  text_observed = "observed",
  color = "lightgrey",
  ...
)

Arguments

Percentage of non-overlapping data (PND)

Description

This function returns the percentage of non-overlapping data. Due to its error-proneness the PND should not be used, but nap or pand instead (see Parker & Vannest, 2009).

Usage

pnd(data, dvar, pvar, decreasing = FALSE, phases = c(1, 2))

Arguments

Details

PND is calculated by determining the number of data points in phase B that exceed the highest data point in phase A (or are lower than the lowest data point in phase A for decreasing data) divided by the total number of data points in phase B. This value is then multiplied by 100 to get a percentage value.

Value

Author(s)

Juergen Wilbert

See Also

Other overlap functions: ird(), nap(), overlap(), pand(), pem(), pet(), print.sc_cdc(), select_phases(), tau_u()

Examples

## Calculate the PND for multiple single-case data
pnd(GruenkeWilbert2014)

Empirical power analysis for single-case data

Description

Conducts a Monte-Carlo study on the test-power and alpha-error probability of a statistical function.

Usage

power_test(
  design,
  method = c("plm_level", "rand", "tauU"),
  effect = "level",
  n_sim = 100,
  design_is_one_study = TRUE,
  alpha_test = TRUE,
  power_test = TRUE,
  binom_test = FALSE,
  binom_test_alpha = FALSE,
  binom_test_power = FALSE,
  binom_test_correct = FALSE,
  ci = FALSE,
  alpha_level = 0.05
)

Arguments

Details

Based on a design() object, a large number of single-cases are generated and re-analysed with a provided statistical function. The proportion of significant analyses is the test power. In a second step, a specified effect of the design object is set to 0 and again single-cases are generated and re-analysed. The proportion of significant analyses is the alpha error probability.

Value

A data frame with the power, alpha error, and correct proportions for each provided method. If binomial tests are requested, p values for these tests are also provided. If confidence intervals are requested, these are also provided.

Author(s)

Juergen Wilbert

See Also

random_scdf(), design()

Examples

## Assume you want to conduct a single-case study with 15 measurements
## (phases: A = 6 and B = 9) using a highly reliable test and
## an expected level effect of d = 1.4.
## A (strong) trend effect is trend = 0.05. What is the power?
## (Note: n_sims is set to 10. Set n_sims to 1000 for a serious calculation.)
design <- design(
  n = 1, phase_design = list(A = 6, B = 9),
  rtt = 0.8, level = 1.4, trend = 0.05
)
power_test(design, n_sim = 10)

## Would you achieve higher power by setting up a MBD with three cases?
design <- design(
  n = 3, phase_design = list(A = 6, B = 9),
  rtt = 0.8, level = 1.4, trend = 0.05
)
power_test(design, n_sim=10, method=list("hplm_level", "rand", "tauU_meta"))

Print methods for scan objects

Description

Print methods for scan objects

Usage

## S3 method for class 'sc_desc'
print(x, digits = "auto", ...)

## S3 method for class 'sc_design'
print(x, ...)

## S3 method for class 'sc_nap'
print(x, digits = "auto", nice = TRUE, complete = FALSE, ...)

## S3 method for class 'sc_overlap'
print(x, digits = "auto", ...)

## S3 method for class 'sc_pem'
print(x, ...)

## S3 method for class 'sc_pet'
print(x, digits = 3, ...)

## S3 method for class 'sc_pnd'
print(x, ...)

## S3 method for class 'sc_power'
print(x, duration = FALSE, digits = 1, ...)

## S3 method for class 'sc_rci'
print(x, digits = 3, ...)

## S3 method for class 'sc_smd'
print(x, digits = "auto", ...)

## S3 method for class 'sc_trend'
print(x, digits = 3, ...)

Arguments

Autocorrelation within and across phases

Description

The autocorr function calculates autocorrelations within each phase and across all phases.

Usage

## S3 method for class 'sc_ac'
print(x, digits = "auto", ...)

## S3 method for class 'sc_ac'
export(object, caption = NA, footnote = NA, filename = NA, round = 3, ...)

autocorr(data, dvar, pvar, mvar, lag_max = 3, lag.max, ...)

Arguments

Details

Autocorrelations are computed using the acf() function from the stats package. For each single-case in the scdf object, a data frame is returned containing the autocorrelations for each phase and for all phases up to the specified lag.

Value

A data frame containing separate autocorrelations for each phase and for all phases (for each single-case). If lag_max exceeds the length of a phase minus one, NA is returned for this cell.

Functions

• print(sc_ac): Print method

• export(sc_ac): Export results to html

Author(s)

Juergen Wilbert

See Also

acf()

Other regression functions: bplm(), fetch(), hplm(), mplm(), plm(), print.sc_bctau(), trend()

Examples

## Compute autocorrelations for a list of four single-cases up to lag 2.
autocorr(Huber2014, lag_max = 2)

Baseline corrected tau

Description

Kendall's tau correlation for the dependent variable and the phase variable is calculated after correcting for a baseline trend.

Usage

## S3 method for class 'sc_bctau'
print(x, nice = TRUE, digits = "auto", ...)

## S3 method for class 'sc_bctau'
export(
  object,
  caption = NA,
  footnote = NA,
  filename = NA,
  nice = TRUE,
  round = 2,
  ...
)

corrected_tau(
  data,
  dvar,
  pvar,
  mvar,
  phases = c(1, 2),
  alpha = 0.05,
  continuity = FALSE,
  tau_method = c("b", "a")
)

Arguments

Details

This method has been proposed by Tarlow (2016). The baseline data are checked for a significant autocorrelation (based on Kendall's Tau). If so, a non-parametric Theil-Sen regression is applied for the baseline data where the dependent values are regressed on the measurement time. The resulting slope information is then used to predict data of the B-phase. The dependent variable is now corrected for this baseline trend and the residuals of the Theil-Sen regression are taken for further calculations. Finally, Kendall's tau is calculated for the dependent variable and the dichotomous phase variable. The function here provides two extensions to this procedure: The more accurate continuity correction is applied when continuity = TRUE.

Functions

• print(sc_bctau): Print results

• export(sc_bctau): Export results as html

References

Tarlow, K. R. (2016). An Improved Rank Correlation Effect Size Statistic for Single-Case Designs: Baseline Corrected Tau. Behavior Modification, 41(4), 427–467. https://doi.org/10.1177/0145445516676750

See Also

Other regression functions: bplm(), fetch(), hplm(), mplm(), plm(), print.sc_ac(), trend()

Examples

dat <- scdf(c(A = 33,25,17,25,14,13,15, B = 15,16,16,5,7,9,6,5,3,3,8,11,7))
corrected_tau(dat)

Conservative Dual-Criterion Method

Description

The cdc() function applies the Conservative Dual-Criterion Method (Fisher, Kelley, & Lomas, 2003) to scdf objects. It compares phase B data points to both phase A mean and trend (OLS, bi-split, tri-split) with an additional increase/decrease of .25 SD. A binomial test against a 50/50 distribution is computed and p-values below .05 are labelled "systematic change".

Usage

## S3 method for class 'sc_cdc'
print(x, nice = TRUE, ...)

## S3 method for class 'sc_cdc'
export(object, caption = NA, footnote = NA, filename = NA, nice = TRUE, ...)

cdc(
  data,
  dvar,
  pvar,
  mvar,
  decreasing = FALSE,
  trend_method = c("OLS", "bisplit", "trisplit"),
  conservative = 0.25,
  phases = c(1, 2)
)

Arguments

Value

Functions

• print(sc_cdc): Print results

• export(sc_cdc): Export html results

Author(s)

Timo Lueke

References

Fisher, W. W., Kelley, M. E., & Lomas, J. E. (2003). Visual Aids and Structured Criteria for Improving Visual Inspection and Interpretation of Single-Case Designs. Journal of Applied Behavior Analysis, 36, 387-406. https://doi.org/10.1901/jaba.2003.36-387

See Also

Other overlap functions: ird(), nap(), overlap(), pand(), pem(), pet(), pnd(), select_phases(), tau_u()

Examples

## Apply the CDC method (standard OLS line)
design <- design(n = 1, slope = 0.2)
dat <- random_scdf(design, seed = 42)
cdc(dat)

## Apply the CDC with Koenig's bi-split and an expected decrease in phase B.
cdc(exampleAB_decreasing, decreasing = TRUE, trend_method = "bisplit")

## Apply the CDC with Tukey's tri-split, comparing the first and fourth phase
cdc(exampleABAB, trend_method = "trisplit", phases = c(1,4))

## Apply the Dual-Criterion (DC) method (i.e., mean and trend without
##shifting).
cdc(
 exampleAB_decreasing,
 decreasing = TRUE,
 trend_method = "bisplit",
 conservative = 0
)

Handling outliers in single-case data

Description

Identifies and drops outliers within a single-case data frame (scdf). Outliers can be identified based on mean average deviation (MAD), standard deviation (SD), confidence intervals (CI), or Cook's Distance from a Piecewise Linear Regression Model.

Usage

## S3 method for class 'sc_outlier'
print(x, digits = "auto", ...)

## S3 method for class 'sc_outlier'
export(object, caption = NA, footnote = NA, filename = NA, ...)

outlier(
  data,
  dvar,
  pvar,
  mvar,
  method = c("MAD", "Cook", "SD", "CI"),
  criteria = 3.5
)

Arguments

Details

For method = "SD", criteria = 2 would refer t0 two standard deviations. For method = "MAD", criteria = 3.5 would refer to 3.5 times the mean average deviation. For method = "CI", criteria = 0.99 would refer to a 99 percent confidence interval. For method = "cook", criteria = "4/n" would refer to a Cook's Distance greater than 4/n.

Value

Functions

• print(sc_outlier): Print results

• export(sc_outlier): Export html results

Author(s)

Juergen Wilbert

See Also

Other data manipulation functions: add_l2(), as.data.frame.scdf(), as_scdf(), batch_apply(), fill_missing(), moving_median(), ranks(), rescale(), scdf(), select_cases(), set_vars(), shift(), smooth_cases(), standardize(), truncate_phase()

Examples

## Identify outliers using 1.5 standard deviations as criterion
susanne <- random_scdf(level = 1.0)
res_outlier <- outlier(susanne, method = "SD", criteria = 1.5)
res_outlier

## Identify outliers in the original data from Grosche (2011)
## using Cook's Distance greater than 4/n as criterion
res_outlier <- outlier(Grosche2011, method = "Cook", criteria = "4/n")
res_outlier

Randomization Tests for single-case data

Description

The rand_test function computes a randomization test for single or multiple baseline single-case data. The function is based on an algorithm from the SCRT package (Bulte & Onghena, 2009, 2012), but rewritten and extended for the use in AB designs.

Usage

## S3 method for class 'sc_rand'
print(x, ...)

## S3 method for class 'sc_rand'
export(object, caption = NA, footnote = NA, filename = NA, ...)

rand_test(
  data,
  dvar,
  pvar,
  statistic = c("Mean B-A", "Mean A-B", "Median B-A", "Median A-B", "Mean |A-B|",
    "Median |A-B|", "SMD hedges", "SMD glass", "W-test", "T-test", "NAP",
    "NAP decreasing", "Slope B-A", "Slope A-B"),
  statistic_function = NULL,
  number = 500,
  complete = FALSE,
  limit = 5,
  startpoints = NA,
  exclude.equal = FALSE,
  phases = c(1, 2),
  graph = FALSE,
  output = NULL,
  seed = NULL
)

Arguments

Value

An object of class sc_rand. It is a list containing the following elements:

Functions

• print(sc_rand): Print results

• export(sc_rand): Export html results

Details

Predefinded statisic

Use the statistic argument to choose a predefnied statistic. The following comparisons are possible:

• ⁠Mean A-B⁠: Uses the difference between the mean of phase A and the mean of phase B. This is appropriate if a decrease of scores was expected for phase B.

• ⁠Mean B-A⁠: Uses the difference between the mean of phase B and the mean of phase A. This is appropriate if an increase of scores was expected for phase B.

• ⁠Mean |A-B|⁠: Uses the absolute value of the difference between the means of phases A and B.

• ⁠Median A-B⁠: The same as ⁠Mean A-B⁠, but based on the median.

• ⁠Median B-A⁠: The same as ⁠Mean B-A⁠, but based on the median.

• ⁠SMD hedges / SMD glass⁠: Standardizes mean difference of B-A as Hedges's g or Glass' delta.

• NAP: Non-overlap of all pairs.

• W-test: Wilcoxon-test statistic W.

• T-test: T-test statistic t.

Create own statistic function

Use the statistic_function argument to proved your own function in a list. This list must have an element named statistic with a function that takes two arguments a and b and returns a single numeric value. E.g. ⁠list(statistic = function(a, b) mean(a) - mean(b)⁠. A second element of the list is named aggregate which takes a function with one numeric argument that returns a numeric argument. This function is used to aggregate the values of a multiple case design. If you do not provide this element, it uses the default function(x) sum(x)/length(x). The third optional argument is name which provides a name for your user function.

Author(s)

Juergen Wilbert

References

Bulte, I., & Onghena, P. (2009). Randomization tests for multiple-baseline designs: An extension of the SCRT-R package. Behavior Research Methods, 41, 477-485.

Bulte, I., & Onghena, P. (2012). SCRT: Single-Case Randomization Tests. Available from: https://CRAN.R-project.org/package=SCRT

Examples

## Compute a randomization test on the first case of the byHeart2011 data and include a graph
rand_test(byHeart2011[1], statistic = "Median B-A", graph = TRUE, seed = 123)

## Compute a randomization test on the Grosche2011 data using complete permutation
rand_test(Grosche2011, statistic = "Median B-A", complete = TRUE, limit = 4, seed = 123)

Print an scdf

Description

Print an scdf

Usage

## S3 method for class 'scdf'
print(
  x,
  cases = getOption("scan.print.cases"),
  rows = getOption("scan.print.rows"),
  cols = getOption("scan.print.cols"),
  long = getOption("scan.print.long"),
  digits = getOption("scan.print.digits"),
  ...
)

Arguments

Details

Print options for scdf objects could be set globally: option(scan.print.cases = "all"), option(scan.print.rows = 10), option(scan.print.cols = "main"), option(scan.print.long = TRUE), option(scan.print.digits = 0), option(scan.print.scdf.name = FALSE)

Single-case data generator

Description

The random_scdf function generates random single-case data frames for monte-carlo studies and demonstration purposes. design is used to set up a design matrix with all parameters needed for the random_scdf function.

Usage

random_scdf(design = NULL, round = NA, random_names = FALSE, seed = NULL, ...)

Arguments

Details

The generated data can be normally distributed, Poisson-distributed, or binomially distributed. The default is normally distributed data.

Value

A single-case data frame. See scdf to learn about this format.

Author(s)

Juergen Wibert

Examples

## Create random single-case data and inspect it
design <- design(
  n = 3, rtt = 0.75, slope = 0.1, extreme_prop = 0.1,
  missing_prop = 0.1
)
dat <- random_scdf(design, round = 1, random_names = TRUE, seed = 123)
describe(dat)

## And now have a look at poisson-distributed data
design <- design(
  n = 3, B_start = c(6, 10, 14), mt = c(12, 20, 22), start_value = 10,
  distribution = "poisson", level = -5, missing_prop = 0.1
)
dat <- random_scdf(design, seed = 1234)
pand(dat, decreasing = TRUE)

(Deprecated) Rank-transformation of single-case data files

Description

This function is superseded by the more versatile transform.scdf function.

Usage

ranks(data, var, grand = TRUE, ...)

Arguments

Value

An scdf object where the values of the variable(s) are replaced with ranks.

Author(s)

Juergen Wilbert

See Also

Other data manipulation functions: add_l2(), as.data.frame.scdf(), as_scdf(), batch_apply(), fill_missing(), moving_median(), print.sc_outlier(), rescale(), scdf(), select_cases(), set_vars(), shift(), smooth_cases(), standardize(), truncate_phase()

Examples

# The ranks function is deprecated. Please use transform:
res1 <- ranks(Huber2014, var = "compliance")
res2 <- transform(Huber2014, across_cases(compliance = rank(compliance, na.last="keep")))
identical(res1, res2)

res1 <- ranks(Huber2014, var = "compliance", grand = FALSE)
res2 <- transform(Huber2014, compliance = rank(compliance, na.last="keep"))
identical(res1, res2)

Reliable change index

Description

The rci() function computes indices of reliable change (Wise, 2004) and corresponding descriptive statistics.

Usage

rci(data, dvar, pvar, rel, ci = 0.95, graph = FALSE, phases = c(1, 2))

Arguments

Details

The reliable change index (RCI) indicates whether the change in scores from phase A to phase B is statistically reliable, that is, whether the change is larger than would be expected due to measurement error alone. The RCI can be calculated using different methods (Jacobsen & Truax, 1991; Christensen & Mendoza, 1986). The most common method is that of Jacobsen and Truax (1991) which uses the standard error of measurement in phase A to calculate the RCI. Christensen and Mendoza (1986) proposed an alteration of the RCI which uses the standard error of the difference between phase A and phase B means. Both methods are implemented in the rci() function.

Author(s)

Juergen Wilbert

References

Christensen, L., & Mendoza, J. L. (1986). A method of assessing change in a single subject: An alteration of the RC index. Behavior Therapy, 17, 305-308.

Jacobson, N. S., & Truax, P. (1991). Clinical Significance: A statistical approach to defining meaningful change in psychotherapy research. Journal of Consulting and Clinical Psychology, 59, 12-19.

Wise, E. A. (2004). Methods for analyzing psychotherapy outcomes: A review of clinical significance, reliable change, and recommendations for future directions. Journal of Personality Assessment, 82, 50 - 59.

Examples

## Report the RCIs of the first case from the byHeart data and include a graph
rci(byHeart2011[1], graph = TRUE, rel = 0.8)

Load single-case data from files

Description

Use the read_scdf function to load single-case data csv, excel, or yaml files.

Usage

read_scdf(
  file,
  cvar = "case",
  pvar = "phase",
  dvar = "values",
  mvar = "mt",
  sort_cases = FALSE,
  phase_names = NULL,
  type = NA,
  na = c("", "NA"),
  sort.labels = NULL,
  phase.names = NULL,
  ...
)

Arguments

Details

The data file must be in a "long" format with one column for case identifiers, one column for phase identifiers, one column for measurement time, and one column for the dependent variable values. Each row represents a single measurement.

Value

Returns a single-case data frame. See scdf to learn about the format of these data frames.

Author(s)

Juergen Wilbert

See Also

read.table(), readRDS()

Other io-functions: convert(), write_scdf()

Examples

## Read SC-data from a file named "study1.csv" in your working directory
# study1 <- read_scdf("study1.csv")

## Read SC-data from a .csv-file with semicolon as field and comma as decimal separator
# study2 <- read_scdf("study2.csv", sep = ";", dec = ",")

## write_scdf and read_scdf
filename <- file.path(tempdir(), "test.csv")
write_scdf(exampleA1B1A2B2_zvt, filename)
dat <- read_scdf(filename, cvar = "case", pvar = "part", dvar = "zvt", mvar = "day")
res1 <- describe(exampleA1B1A2B2_zvt)$descriptives
res2 <- describe(dat)$descriptives
all.equal(res1,res2)

Rescales values of an scdf

Description

This function scales the measured values of an scdf file. It allows for mean centering and standardization across all cases included in an scdf.

Usage

rescale(data, ..., m = 0, sd = 1)

Arguments

Value

An scdf with the scaled values.

Author(s)

Juergen Wilbert

See Also

Other data manipulation functions: add_l2(), as.data.frame.scdf(), as_scdf(), batch_apply(), fill_missing(), moving_median(), print.sc_outlier(), ranks(), scdf(), select_cases(), set_vars(), shift(), smooth_cases(), standardize(), truncate_phase()

Examples

## Standardize a multiple case scdf and compute an hplm
exampleAB_50 |>
  rescale(values, mt) |>
  hplm()

Samples random names

Description

Generates random names for cases. Names are sampled from a predefined list of neutral, male, female, or mixed names.

Usage

sample_names(n = 1, type = "neutral", seed = NULL)

Arguments

Details

This function is useful for anonymizing case names in datasets or for generating random identifiers.

Value

A character vector with random names.

Examples

sample_names(3)

Single case data frame constructor

Description

scdf() is the constructor for objects of class scdf. It stores data from single-case studies in a structured format suitable for analysis with the scan package.

Usage

scdf(
  ...,
  B_start = NULL,
  phase_starts = NULL,
  phase_design = NULL,
  name = NULL,
  dvar = "values",
  pvar = "phase",
  mvar = "mt"
)

Arguments

Details

If no variable matching the name of the dependent variable is provided (the default name is values, which can be changed via the dvar argument), and the first provided variable is unnamed, that variable will be interpreted as the dependent variable.

If no measurement-time variable is provided (default name mt, configurable via the mvar argument), measurement times are automatically defined as a sequence ⁠(1, 2, 3, ..., n)⁠.

If the dependent variable is a named vector, the names will be used to define a phase design. For example, values = c(A = 2, 3, 5, 4, 3, B = 6, 5, 4, 3) will be interpreted as an AB phase design with five measurements in phase A and four in phase B.

If a vector matching the name of the phase variable is provided, it will be used to define the phase design directly. Otherwise, the phase design can be defined in three alternative ways: via the B_start argument, via the phase_starts argument, or via the phase_design argument.

If B_start is provided, a simple AB phase design is assumed, with phase A starting at measurement time 1 and phase B starting at the measurement time indicated by B_start. If phase_starts is provided, the phase design is constructed based on the measurement times indicated in the vector. If phase_design is provided, it is used directly to define the phase design. If multiple of these options are provided, the priority order is: phase_design, phase_starts, B_start, phase variable in data frame, names of dependent variable.

If none of these options are provided, an error is raised.

The function can be used to create single-case data frames for multiple cases separately, which can then be combined into a list for multiple-case analyses.

See also the convenience function transform.scdf to add new variables to an existing scdf object.

See the package vignettes for further examples on how to create and work with scdf objects.

See the section on Data structure in the documentation of the scan package for further details on the scdf data structure.

Value

Returns a single-case data frame scdf suitable for all functions in the scan package.

Author(s)

Juergen Wilbert

See Also

Other data manipulation functions: add_l2(), as.data.frame.scdf(), as_scdf(), batch_apply(), fill_missing(), moving_median(), print.sc_outlier(), ranks(), rescale(), select_cases(), set_vars(), shift(), smooth_cases(), standardize(), truncate_phase()

Examples

## Scores on a letter naming task were collected on eleven days in a row.
## The intervention started after the fifth measurement,
## so the first B phase measurement was 6 (B_start = 6).
klaas <- scdf(
  c(5, 7, 8, 5, 7, 12, 16, 18, 15, 14, 19),
  B_start = 6, name = "Klaas"
)
describe(klaas)

# Alternative: using named vector
klaas <- scdf(
  c(A = 5, 7, 8, 5, 7, B = 12, 16, 18, 15, 14, 19),
  name = "Klaas"
)

# Alternative: using phase_design
klaas <- scdf(
  c(5, 7, 8, 5, 7, 12, 16, 18, 15, 14, 19),
  phase_design = c(A = 5, B = 6), name = "Klaas"
)

# Alternative: using phase_starts
klaas <- scdf(
  c(5, 7, 8, 5, 7, 12, 16, 18, 15, 14, 19),
  phase_starts = c(A = 1, B = 7), name = "Klaas"
)

## Unfortunately in a similar study there were no data collected on
## days 3 and 9. Use NA to pass them to the function:
emmi <- scdf(c(5, 7, NA, 5, 7, 12, 16, 18, NA, 14, 19),
  phase_design = c(A = 5, B = 6), name = "Emmi"
)
describe(emmi)

## In a MBD over three cases, data were collected eleven days in a row.
## Intervention starting points differ between subjects as they were
## randomly assigned. The three SCDFs are then combined in a list for
## further conjoined analyses.
charlotte <- scdf(c(A = 5, 7, 10, 5, 12, B = 7, 10, 18, 15, 14, 19))
theresa <- scdf(c(A = 3, 4, 3, 5, B = 7, 4, 7, 9, 8, 10, 12))
tonia <- scdf(c(A = 9, 8, 8, 7, 5, 7, B = 6, 14, 15, 12, 16))
mbd <- c(charlotte, theresa, tonia)
names(mbd) <- c("Charlotte", "Theresa", "Tonia")
overlap(mbd)

## In a classroom-based intervention it was not possible to measure outcomes
## every day, but only on schooldays. The sequence of measurements is passed
## to the package by using a vector of measurement times.
frida <- scdf(
  c(A = 3, 2, 4, 2, 2, 3, 5, 6, B = 8, 10, 8, 12, 14, 13, 12),
  mt = c(1, 2, 3, 4, 5, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18)
)
summary(frida)
describe(frida)

## example with two independent variables and four phases
jim <- scdf(
  zvt = c(47, 58, 76, 63, 71, 59, 64, 69, 72, 77, 76, 73),
  d2 = c(131, 134, 141, 141, 140, 140, 138, 140, 141, 140, 138, 140),
  phase_design = c(A1 = 3, B1 = 3, A2 = 3, B2 = 3), dvar = "zvt"
)
overlap(jim, phases = list(c("A1", "A2"), c("B1", "B2")))

Set and get scdf attributes

Description

Set and get scdf attributes

Usage

scdf_attr(x, var = NULL)

scdf_attr(x, var) <- value

dv(scdf)

mt(scdf)

phase(scdf)

Arguments

Value

Attribute value

Select a subset of cases from an scdf

Description

This function allows to select a subset of cases from an scdf by specifying either the case names or their numeric indices. Negative selection is also supported.

Usage

select_cases(scdf, ...)

Arguments

Value

An scdf with a subset of cases.

Author(s)

Juergen Wilbert

See Also

Other data manipulation functions: add_l2(), as.data.frame.scdf(), as_scdf(), batch_apply(), fill_missing(), moving_median(), print.sc_outlier(), ranks(), rescale(), scdf(), set_vars(), shift(), smooth_cases(), standardize(), truncate_phase()

Examples

select_cases(exampleAB, Johanna, Karolina)
select_cases(exampleAB, c(Johanna, Karolina))
select_cases(exampleAB, 1,2)
select_cases(exampleAB, 1:2)
select_cases(exampleAB, -Johanna)
select_cases(exampleAB, -c(Johanna, Karolina))
v <- c("Moritz", "Jannis")
select_cases(exampleA1B1A2B2, v)

Select and combine phases for overlap analyses

Description

Useful when working with pipe operators. This function allows to select and combine specific phases from an scdf for overlap analyses. For example, in an ABAB design one might want to combine both A phases and both B phases (e.g., A = c(1, 3), B = c(2, 4)). The resulting scdf can then be used in overlap functions such as overlap().

Usage

select_phases(data, A, B, phase_names = "auto")

Arguments

Details

This function selects and combines the specified phases from the input scdf and returns the resulting scdf with the selected phases only. This is particularly useful when working with pipe operators, allowing to select and combine phases before applying overlap functions. The resulting scdf contains only the selected and combined phases, with phase labels "A" and "B". If phase_names = "auto", phase names are generated from the combination of the names of the recombined phases. For example, combining phases 1 and 3 will result in the phase name "1_3". This function simplifies the process of preparing data for overlap analyses by allowing users to easily select and combine phases in a single step.

Value

An scdf with selected phases

Author(s)

Juergen Wilbert

See Also

Other overlap functions: ird(), nap(), overlap(), pand(), pem(), pet(), pnd(), print.sc_cdc(), tau_u()

Examples

exampleA1B1A2B2_zvt |>
  select_phases(A = c(1, 3), B = c(2, 4)) |>
  overlap()

Set analysis variables in an scdf object

Description

This function allows to set or change the dependent variable, measurement-time variable, and phase variable in an scdf object.

Usage

set_vars(data, dvar, mvar, pvar)

set_dvar(data, dvar)

set_mvar(data, mvar)

set_pvar(data, pvar)

Arguments

Value

An scdf object with updated variable settings.

Author(s)

Juergen Wilbert

See Also

Other data manipulation functions: add_l2(), as.data.frame.scdf(), as_scdf(), batch_apply(), fill_missing(), moving_median(), print.sc_outlier(), ranks(), rescale(), scdf(), select_cases(), shift(), smooth_cases(), standardize(), truncate_phase()

Examples

exampleAB_add |>
  set_dvar("depression") |>
  describe()

Shift values in a single-case data file

Description

This function has been superseded by the much more versatile transform.scdf function. Shifting the values might be helpful in cases where the measurement time is given as a time variable (see example below).

Usage

shift(data, value, var)

Arguments

Value

A scdf with shifted data

See Also

Other data manipulation functions: add_l2(), as.data.frame.scdf(), as_scdf(), batch_apply(), fill_missing(), moving_median(), print.sc_outlier(), ranks(), rescale(), scdf(), select_cases(), set_vars(), smooth_cases(), standardize(), truncate_phase()

Examples

### Shift the measurement time for a better estimation of the intercept
ex <- shift(example_A24, value = -1996)
plm(ex)

# Please use transform instead:
example_A24 |>
  transform(year = year - 1996) |>
  plm()

A Shiny app for scan

Description

Run a Shiny app with most of the scan functions.

Usage

shinyscan(
  scdf = NULL,
  quiet = TRUE,
  browser = c("external", "viewer"),
  theme = "cerulean",
  ...
)

Arguments

Details

This function launches a shiny application. You need to have scplot and shiny installed. These packages are suggested but not necessarily installed along with scan. shinyscan() will ask to install missing packages.

Value

This function launches a Shiny application.

Author(s)

Juergen Wilbert

Standardized mean differences for single-case data

Description

The smd() function provides various standardized mean effect sizes for single-case data.

Usage

smd(data, dvar, pvar, mvar, phases = c(1, 2))

Arguments

Details

It computes 'Cohen's d', 'Hedges' g', 'Hedges' g correction', 'Hedges' g durlak correction', and 'Glass' delta' for each single-case included in an scdf.

'sd cohen' is the (unweigted) average of the variance of phase A and B. 'sd Hedges' is the weighted average of the variance of phase A and B (with a degrees of freedom correction). 'Hedges' g' is the mean difference divided by 'sd Hedges'. 'Hedges' g correction' and 'Hedges' g durlak correction' are two approaches of correcting Hedges' g for small sample sizes. 'Glass' delta' is the mean difference divided by the standard deviation of the A-phase. 'Cohens d' is the mean difference divided by 'sd cohen'.

Author(s)

Juergen Wilbert

See Also

overlap(), describe()

Examples

smd(exampleAB)

Smoothing single-case data

Description

This function is superseded by the more versatile transform.scdf function. The smooth_cases function provides procedures to smooth single-case data (i.e., to eliminate noise). A moving average function (mean- or median-based) replaces each data point by the average of the surrounding data points step-by-step. With a local regression function, each data point is regressed by its surrounding data points.

Usage

smooth_cases(data, dvar, mvar, method = "mean", intensity = NULL, FUN = NULL)

Arguments

Details

moving_median, moving_mean, and local_regression are helper function for transform.scdf returning the smoothed values of a numeric vector.

Value

Returns a data frame (for each single-case) with smoothed data points. See scdf to learn about the format of these data frames.

Author(s)

Juergen Wilbert

See Also

Other data manipulation functions: add_l2(), as.data.frame.scdf(), as_scdf(), batch_apply(), fill_missing(), moving_median(), print.sc_outlier(), ranks(), rescale(), scdf(), select_cases(), set_vars(), shift(), standardize(), truncate_phase()

Examples

## Use the three different smoothing functions and compare the results
study <- c(
  "Original" = Huber2014$Berta,
  "Moving median" = smooth_cases(Huber2014$Berta, method = "median"),
  "Moving mean" = smooth_cases(Huber2014$Berta, method = "mean"),
  "Local regression" = smooth_cases(Huber2014$Berta, method = "regression")
)
plot(study)

Huber2014$Berta |>
transform(
  "compliance (moving median)" = moving_median(compliance),
  "compliance (moving mean)" = moving_mean(compliance),
  "compliance (local regression)" = local_regression(compliance, mt)
)

Standardize values of an scdf file

Description

This function is superseded by the much more versatile transform.scdf function (see example below). This function scales the measured values of an scdf file. It allows for mean centering and standardization based on each single-case data set or a scaling across all cases included in an scdf.

Usage

standardize(
  data,
  var,
  center = TRUE,
  scale = FALSE,
  m = 0,
  sd = 1,
  grand = TRUE
)

Arguments

Value

An scdf with the scaled values.

Author(s)

Juergen Wilbert

See Also

Other data manipulation functions: add_l2(), as.data.frame.scdf(), as_scdf(), batch_apply(), fill_missing(), moving_median(), print.sc_outlier(), ranks(), rescale(), scdf(), select_cases(), set_vars(), shift(), smooth_cases(), truncate_phase()

Examples

## Standardize a multiple case scdf and compute an hplm
exampleAB_50 |>
  standardize("values", center = TRUE, scale = TRUE) |>
  hplm()

## The more versatile transform function supersedes standardize:
exampleAB_50 |>
  transform(values = (values - mean(all(values))) / sd(all(values))) |>
  hplm()

(Deprecated) Create styles for single-case data plots

Description

The style_plot function is used to create graphical styles for a single-case plot

Usage

style_plot(style = "default", ...)

Arguments

Details

style_plot("") will return a list of predefined styles. Predefined styles can be combined style_plot(style = c("grid2", "tiny")) where settings of a latter style overwrite settings of the former. Additional style paramters are set following the style argument and can be combined with those: style_plot(style = "grid2", fill = "grey50", pch = 18).

Value

Returns a list to be provided for the style argument of the plot.scdf() function.

• fill If set, the area under the line is filled with the given color (e.g., fill = "tomato"). Use the standard R command colors() to get a list of all possible colours. fill is empty by default.

• annotations A list of parameters defining annotations to each data point. This adds the score of each MT to your plot.

  • "pos" Position of the annotations: 1 = below, 2 = left, 3 = above, 4 = right.

  • "col" Color of the annotations.

  • "cex" Size of the annotations.

  • "round" Rounds the values to the specified decimal.

• annotations = list(pos = 3, col = "brown", round = 1) adds scores rounded to one decimal above the data point in brown color to the plot.

• "names" A list of parameters defining the depiction of phase names (e.g. names = list(cex = 0.8, col = "red", side = 1): cex for size, col for color, and side for position). See mtext for more details.

• "lwd" Width of the plot line. Default is lwd = 2.

• "pch" Point type. Default is pch = 17 (triangles). Other options are for example: 16 (filled circles) or "A" (uses the letter A).

• "main" Main title of the plot.

• "mai" Sets the margins of the plot.

• "bty" Shape of the frame surrounding the inner plot

• "fill.bg" Background color of the plot. If a vector is provided, these colors will be assigned to phases (each phase name becomes a color).

• "grid" Color of a grid.

• "text.ABlag" Text displayed between phases.

• "cex.axis" Size of the axis annotations

• "las" Orientation of the axis annotations

• "col.lines" Color of the lines

• "col.dots" Color of the dots

• "col.seperator" Color of the phase seperating lines

• "col.bg" Color of the outer plot

• "col" General color setting for the plot

• "col.text" Color of all labels of the plot.

Author(s)

Juergen Wilbert

See Also

plot.scdf()

Examples

newstyle <- style_plot(style = "default")
newstyle$text.ABlag <- c("START", "END")
newstyle$col.dots <- ""
newstyle$annotations <- list(cex = 0.6, col = "grey10", offset = 0.4)
newstyle$names <- list(cex = 0.8, col = "blue", side = 1, adj = 1, line = -1, at = 31)
newstyle$fill.bg <- c("grey99", "grey95", "grey90")
plot(exampleABC, style = newstyle, main = "Example Plot")

Subset cases, rows, and variables of an scdf

Description

This function is mainly used to filter rows by a logical expression. It has also arguments to filter variables and cases.

Usage

## S3 method for class 'scdf'
subset(x, subset, select, cases, ...)

Arguments

Details

For subsetting rows, a logical expression can be provided in the subset argument. Missing values are treated as FALSE. The expression is evaluated within each single-case data frame of the scdf.

Value

An scdf.

Examples

exampleAB |>
  subset((values < 60 & phase == "A") | (values >= 60 & phase == "B"))
subset(exampleAB_add, select = c(-cigarrets, -depression))
subset(exampleAB, cases = c(Karolina, Johanna))
subset(exampleA1B1A2B2, phase %in% c("A1", "B2"), cases = Pawel:Moritz)

Summary function for an scdf object

Description

Provides a summary of an scdf object, including the number of cases, measurements per case, and design information.

Usage

## S3 method for class 'scdf'
summary(object, all_cases = FALSE, ...)

Arguments

Details

The summary includes:

• Total number of cases in the scdf.

• A table listing each case with the number of measurements and design.

• Variable names with annotations for phase, measurement-time, and dependent variable.

• Additional information and author details if available.

Author(s)

Juergen Wilbert

Tau-U for single-case data

Description

This function calculates indices of the Tau-U family as proposed by Parker et al. (2011a). It allows to calculate Tau-U values for single cases as well as overall Tau-U values across several single cases by applying a meta analysis.

Usage

tau_u(
  data,
  dvar,
  pvar,
  method = c("complete", "parker", "tarlow"),
  phases = c(1, 2),
  meta_analyses = TRUE,
  ci = 0.95,
  ci_method = c("z", "tau", "s"),
  meta_weight_method = c("z", "tau"),
  tau_method = c("b", "a"),
  continuity_correction = FALSE
)

## S3 method for class 'sc_tauu'
print(
  x,
  complete = FALSE,
  digits = "auto",
  select = c("Tau", "CI lower", "CI upper", "SD_S", "Z", "p"),
  nice_p = TRUE,
  ...
)

## S3 method for class 'sc_tauu'
export(
  object,
  caption = NA,
  footnote = NA,
  filename = NA,
  select = "auto",
  meta = FALSE,
  round = 3,
  decimals = 3,
  ...
)

Arguments

Details

Tau-U is an inconsistently operationalized construct. Parker et al. (2011b) describe a method which may result in Tau-U outside the [-1;1] interval. A different implementation of the method (provided at http://www.singlecaseresearch.org/calculators/tau-u) uses tau-b (instead of tau-a as in the original formulation by Parker). Bossart et. al (2018) describe inconsistencies in the results from this implementation as well. Another problems lies in the calculation in overall Tau-U values from several single cases. The function presented here applies a meta-analysis to gain the overall values. Each tau value is weighted by the inverse of the variance (ie. the tau standard error). The confidence intervals for single cases are calculated by Fisher-Z transforming tau, calculating the confidence intervals, and inverse transform them back to tau (see Long & Cliff, 1997).

Value

Functions

• print(sc_tauu): Print results

• export(sc_tauu): Export results as html table

Author(s)

Juergen Wilbert

References

Brossart, D. F., Laird, V. C., & Armstrong, T. W. (2018). Interpreting Kendall’s Tau and Tau-U for single-case experimental designs. Cogent Psychology, 5(1), 1–26. https://doi.org/10.1080/23311908.2018.1518687.

Long, J. D., & Cliff, N. (1997). Confidence intervals for Kendall’s tau. British Journal of Mathematical and Statistical Psychology, 50(1), 31–41. https://doi.org/10.1111/j.2044-8317.1997.tb01100.x

Parker, R. I., Vannest, K. J., & Davis, J. L. (2011a). Effect Size in Single-Case Research: A Review of Nine Nonoverlap Techniques. Behavior Modification, 35(4), 303–322. https://doi.org/10/dsdfs4

Parker, R. I., Vannest, K. J., Davis, J. L., & Sauber, S. B. (2011b). Combining Nonoverlap and Trend for Single-Case Research: Tau-U. Behavior Therapy, 42(2), 284–299. https://doi.org/10.1016/j.beth.2010.08.006

Tarlow, K. R. (2017, March). Tau-U for single-case research (R code). Retrieved from http://ktarlow.com/stats/

See Also

Other overlap functions: ird(), nap(), overlap(), pand(), pem(), pet(), pnd(), print.sc_cdc(), select_phases()

Examples

tau_u(Grosche2011$Eva)

## Replicate  tau-U calculation from Parker et al. (2011)
bob <- scdf(c(A = 2, 3, 5, 3, B = 4, 5, 5, 7, 6), name = "Bob")
res <- tau_u(bob, method = "parker")
print(res, complete = TRUE)

## Request tau-U for all single-cases from the Grosche2011 data set
tau_u(Grosche2011)

Trend analysis for single-cases data

Description

The trend() function provides an overview of linear trends in single case data. By default, it provides the intercept and slope of a linear and quadratic regression of measurement time on scores. Models are calculated separately for each phase and across all phases. For more advanced use, you can add regression models using the R-specific formula class.

Usage

trend(
  data,
  dvar,
  pvar,
  mvar,
  offset = "deprecated",
  first_mt = 0,
  model = NULL
)

Arguments

Details

The function computes separate regression models for each phase and for the whole data. By default two models are computed: a linear model and a quadratic model. Additionally, custom models can be specified using the model argument. The measurement time variable is adjusted such that the first measurement time point of each phase is set to the value specified in the first_mt argument (default = 0). This means that if first_mt = 0, the first measurement time point of each phase is set to 0, if first_mt = 1, the first measurement time point of each phase is set to 1, and so on. This adjustment allows for a more intuitive interpretation of the regression coefficients, especially the intercept, which then represents the estimated value at the beginning of each phase.

Value

A list of class sc_trend containing:

Author(s)

Juergen Wilbert

See Also

describe()

Other regression functions: bplm(), fetch(), hplm(), mplm(), plm(), print.sc_ac(), print.sc_bctau()

Examples

## Compute the linear and squared regression for a random single-case
design <- design(slope = 0.5)
matthea <- random_scdf(design)
trend(matthea)

## Besides the linear and squared regression models compute two custom models:
## a) a cubic model, and
## b) the values predicted by the natural logarithm of the
## measurement time.
design <- design(slope = 0.3)
ben <- random_scdf(design)
trend(
  ben,
  model = list("Cubic" = values ~ mt^3, "Log Time" = values ~ log(mt)),
  first_mt = 1 # must be set to 1 because log(0) would be -Inf
)

Truncate single-case data

Description

#' This function is superseded by the more versatile transform.scdf function. This function truncates data points at the beginning and / or end of each phase in each case.

Usage

truncate_phase(
  data,
  dvar,
  pvar,
  truncate = list(A = c(0, 0), B = c(0, 0)),
  na = TRUE
)

Arguments

Value

A truncated data frame (for each single-case).

Author(s)

Juergen Wilbert

See Also

Other data manipulation functions: add_l2(), as.data.frame.scdf(), as_scdf(), batch_apply(), fill_missing(), moving_median(), print.sc_outlier(), ranks(), rescale(), scdf(), select_cases(), set_vars(), shift(), smooth_cases(), standardize()

Examples

## Truncate the first two data points of both phases and compare the two 
## data sets
study <- c(
  "Original" = byHeart2011[1],
  "Selected" = truncate_phase(
    byHeart2011[1], truncate = list(A = c(2, 0), B = c(2, 0))
  )
)
plot(study)

Data output: Write single-case data to a .csv-file

Description

This function restructures and writes single-case data into a .csv-file.

Usage

write_scdf(data, filename = NULL, sep = ",", dec = ".", ...)

Arguments

Details

This is a wrapper for the write.table function with predefined parameters. It converts the single-case data file into a data frame and writes it to a .csv-file. Each single-case data set is stacked below each other and an additional column "case" is added to identify the different single-cases.

Value

Invisibly returns NULL.

Author(s)

Juergen Wilbert

See Also

write.table(), saveRDS()

Other io-functions: convert(), read_scdf()

Examples

## write single-case data to a .csv-file
filename <- tempfile(fileext = ".csv")
write_scdf(exampleAB, filename)

## write multiple cases to a .csv-file with semicolon as field and comma as
## decimal separator
write_scdf(Grosche2011, filename, sep = ";", dec = ",")

## read_scdf and write_scdf
write_scdf(exampleA1B1A2B2_zvt, filename)
dat <- read_scdf(filename, cvar = "case", pvar = "part",
                 dvar = "zvt", mvar = "day")
res1 <- describe(exampleA1B1A2B2_zvt)$descriptives
res2 <- describe(dat)$descriptives
all.equal(res1,res2)