## ----echo = FALSE-------------------------------------------------------------

tab_legend <- "Math Formula corresponds to the mathematical notation for the model. R Formula corresponds to how one could write the model using R's model formula syntax (think `lm`, `glm`, `lmer`). ipmr shows an equivalent way to write this model in kernel formula or vital rate expression. Model Number indicates which rows are grouped together, as some models have too many terms to cleanly fit on a line, or have multiple equivalent representations."

styles <- c("style='width:150%;'")

knitr::kable(
  data.frame(

    Math    = c("$\\mu_G^{yr} = \\alpha_G + \\alpha_G^{yr} * \\beta_G * z$",
                         "$G(z',z) = f_G(z', \\mu_g^{yr}, \\sigma_G)$",
                "$Logit(\\mu_{s}^{plot,yr}) = \\alpha_s + \\alpha_{s}^{plot,yr} + \\beta * z$",
                "",
                "",
                "$log(\\mu_{r}^{yr}) = \\alpha_{r} + \\alpha_r^{yr} + (\\beta_r + \\beta_r^{yr}) * z$"),
    
    
    R = c("`size_2 ~ size_1 + (1 | year), family = gaussian()`",
          "",
          "`surv ~ size_1 + (1 | year) + (1 | plot), family = binomial()`",
          "`surv ~ size_1 + (1 | year) + (1 | plot), family = binomial()`",
          "",
          "`fec ~ size_1 + (size_1 | year), family = poisson()`"),
    
    
    ipmr = c("mu_g_**yr** = g_int + g_int_**yr** + g_slope * z",
             "g = dnorm(z_2, mu_g_**yr**, sd_g)",
             "s_**pl**_**yr** = s_int + s_int_**pl**_**yr** + s_slope * z",
             "s_**pl**_**yr** = s_int + s_int_**pl** + s_int_**yr** + s_slope * z",
             "s = inv_logit(s_**pl**_**yr**)",
             "r = exp(r_int + r_int_**yr** + (r_slope + r_slope_**yr**) * z)"),
    Model = c(1, 1, 2, 2, 2, 3)
  ),
  format    = "html",
  escape    = FALSE,
  col.names = c("Math Formula", "R Formula", "ipmr", "Model Number"),
  caption   = tab_legend,
  table.attr = styles
)



## ----eval = FALSE-------------------------------------------------------------
#  
#  library(lme4)
#  library(ipmr)
#  
#  grow_mod <- lmer(size_2 ~ size_1 + (1 | year), data = grow_data)
#  
#  surv_mod <- glmer(surv ~ size_1 + (1 | year), data = surv_data, family = binomial)
#  
#  repr_mod <- glm(repr ~ size_1, data = repr_data, family = binomial)
#  
#  recr_mod <- glm(recr ~ size_1, data = recr_data, family = poisson)
#  
#  rcsz_mu  <- mean(rcsz_data$size_2)
#  rcsz_sd  <- sd(rcsz_data$size_2)
#  

## ----eval = FALSE-------------------------------------------------------------
#  
#  beta_gs     <- fixef(grow_mod)
#  
#  alpha_g_yrs <- ranef(grow_mod)
#  
#  beta_ss     <- fixef(surv_mod)
#  
#  alpha_s_yrs <- ranef(surv_mod)
#  
#  

## ----eval = FALSE-------------------------------------------------------------
#  
#  repr_coef   <- coef(repr_mod)
#  
#  recr_coef   <- coef(recr_mod)
#  

## ----eval = FALSE-------------------------------------------------------------
#  
#  g_list <- as.list(beta_gs)
#  names(g_list) <- c("alpha_g", "beta_g")
#  
#  s_list <- as.list(beta_ss)
#  names(s_list) <- c("alpha_s", "beta_s")
#  
#  r_p_list <- as.list(recr_coef)
#  names(f_p_list ) <- c("alpha_r_p", "beta_r_p")
#  
#  r_r_list <- as.list(repr_coef)
#  names(r_r_list) <- c("alpha_r_r", "beta_r_r")
#  
#  r_d_list <- list(mu_r_d = rcsz_mu, sigma_r_d = rcsz_sd)
#  
#  all_fixed_params <- c(g_list, s_list, r_p_list, r_r_list, r_d_list)
#  

## ----eval = FALSE-------------------------------------------------------------
#  
#  g_alpha_list <- as.list(unlist(alpha_g_yrs))
#  names(g_alpha_list) <- paste("alpha_g_", 2001:2006, sep = "")
#  
#  s_alpha_list <- as.list(unlist(alpha_s_yrs))
#  names(s_alpha_list) <- paste("alpha_s_", 2001:2006, sep = "")
#  

## ----eval = FALSE-------------------------------------------------------------
#  
#  all_params <- c(all_fixed_params, g_alpha_list, s_alpha_list)
#  

## ----made up parameters for testing chunk below, echo = FALSE, message = FALSE, warning = FALSE----

library(ipmr)

all_fixed_params <- list(
  alpha_g   = 0.2,
  beta_g    = 1.01,
  sigma_g   = 0.2,
  alpha_s   = -0.1,
  beta_s    = 0.3,
  alpha_r_p = -1,
  beta_r_p  = 0.7,
  alpha_r_r = 0.2,
  beta_r_r  = 0.2,
  mu_r_d    = 0.4,
  sigma_r_d = 0.1
)

g_alpha_list <- as.list(rnorm(6)) %>%
  setNames(
    paste('alpha_g_', 2001:2006, sep = "")
  )
s_alpha_list <- as.list(rnorm(6)) %>%
  setNames(
    paste('alpha_s_', 2001:2006, sep = "")
  )

all_params <- c(all_fixed_params, g_alpha_list, s_alpha_list)


## ----eval = FALSE-------------------------------------------------------------
#  
#  ex_ipm <-init_ipm(sim_gen    = "simple",
#                    di_dd      = "di",
#                    det_stoch  = "stoch",
#                    kern_param = "kern") %>%
#    define_kernel(
#  
#      # The _yr index is appended as a suffix with an underscore. Notice how the formula
#      # from Eq 2 is translated into the formula argument and the kernel name
#  
#      name             = "P_yr",
#      family           = "CC",
#      formula          = s_yr * g_yr,
#  
#      # We also modify each parameter name is indexed as well.
#      # Here, I've split out the linear predictor and the inverse logit
#      # transformation into separate steps to avoid over cluttering
#  
#      s_lin_p          = alpha_s + alpha_s_yr + beta_s * z_1,
#      s_yr             = 1 / (1 + exp(- s_lin_p)),
#  
#      # We do the same with growth as we did with survival and the P_yr formula
#  
#      g_yr             = dnorm(z_2, mu_g_yr, sigma_g),
#      mu_g_yr          = alpha_g + alpha_g_yr + beta_g * z_1,
#  
#      data_list        = all_params,
#      states           = list(c("z")),
#  
#      # We signal that the kernel has parameter sets
#  
#      uses_par_sets    = TRUE,
#  
#      # And provide the values that each index can take as a named list.
#      # The name(s) in this list MUST match the index used in the expressions.
#  
#      par_set_indices = list(yr = 2001:2006),
#      evict_cor        = TRUE,
#      evict_fun        = truncated_distributions("norm", "g_yr")
#    ) %>%
#  
#    # This kernel doesn't get anything special because there are no
#    # time-varying parameter values.
#  
#    define_kernel(
#      name          = "F",
#      family        = "CC",
#      formula       = r_p * r_r * r_d,
#      r_p_lin_p     = alpha_r_p + beta_r_p * z_1,
#      r_p           = 1 / (1 + exp( -r_p_lin_p)),
#      r_r           = exp(alpha_r_r + beta_r_r * z_1),
#      r_d           = dnorm(z_2, mu_r_d, sigma_r_d),
#      data_list     = all_params,
#      states        = list(c("z")),
#      uses_par_sets = FALSE,
#      evict_cor     = TRUE,
#      evict_fun     = truncated_distributions("norm", "r_d")
#    ) %>%
#    define_impl(
#      make_impl_args_list(
#        kernel_names = c("P_yr", "F"),
#        int_rule     = rep("midpoint", 2),
#        state_start    = rep("z", 2),
#        state_end      = rep("z", 2)
#      )
#    ) %>%
#    define_domains(
#      z = c(0.1, 10, 50)
#    ) %>%
#    define_pop_state(
#      n_z = runif(50)
#    ) %>%
#    make_ipm(
#      iterate    = TRUE,
#      iterations = 100,
#      kernel_seq = sample(2001:2006, size = 100, replace = TRUE),
#      normalize_pop_size = TRUE
#    )
#  

## ----eval = FALSE-------------------------------------------------------------
#  
#  library(ipmr)
#  
#  set.seed(51)
#  
#  # Set up the sites, and the parameters
#  
#  sites <- LETTERS[1:6]
#  
#  all_pars <- list(
#    r_i       = 0.6,
#    r_sb1     = 0.2,
#    r_sb2     = 0.3,
#    s_sb1     = 0.4,
#    s_sb2     = 0.1,
#    mu_c_d    = 4,
#    sigma_c_d = 0.9,
#    sigma_g   = 3,
#    beta_s_z    = 2.5,
#    beta_s_prec = 0.3,
#    beta_s_temp = -0.5,
#    beta_g_z    = 0.99,
#    beta_g_prec = 0.01,
#    beta_g_temp = 0.1,
#    beta_c_p_z    = 0.4,
#    beta_c_p_prec = 0.6,
#    beta_c_p_temp = -0.3,
#    beta_c_r_z    = 0.005,
#    beta_c_r_prec = -0.3,
#    beta_c_r_temp = 0.9
#  )
#  
#  g_alphs <- rnorm(6, mean = 4.5, sd = 1) %>%
#    as.list() %>%
#    setNames(
#      paste('alpha_g_', sites, sep = "")
#    )
#  
#  s_alphs <- rnorm(6, mean = -7, sd = 1.5) %>%
#    as.list() %>%
#    setNames(
#      paste('alpha_s_', sites, sep = "")
#    )
#  
#  c_p_alphs <- rnorm(6, mean = -10, sd = 2)  %>%
#    as.list() %>%
#    setNames(
#      paste('alpha_c_p_', sites, sep = "")
#    )
#  
#  c_r_alphs <- runif(6, 0.01, 0.1) %>%
#    as.list() %>%
#    setNames(
#      paste('alpha_c_r_', sites, sep = "")
#    )
#  
#  
#  all_pars <- c(all_pars,
#                g_alphs,
#                s_alphs,
#                c_p_alphs,
#                c_r_alphs)
#  
#  # This list contains parameters that define the distributions for environmental
#  # covariates
#  
#  env_params <- list(
#    temp_mu = 12,
#    temp_sd = 2,
#    prec_shape = 1000,
#    prec_rate  = 2
#  )
#  
#  # This function samples the environmental covariate distributions and returns
#  # the values in a named list. We can reference the names in the list in our
#  # vital rate expressions.
#  
#  sample_fun <- function(env_params) {
#  
#    temp <- rnorm(1, env_params$temp_mu, env_params$temp_sd)
#  
#    prec <- rgamma(1, env_params$prec_shape, env_params$prec_rate)
#  
#    out  <- list(temp = temp,
#                 prec = prec)
#  
#    return(out)
#  
#  }
#  

## ----eval = FALSE-------------------------------------------------------------
#  
#  ex_ipm <- init_ipm(sim_gen    = "general",
#                     di_dd      = "di",
#                     det_stoch  = "stoch",
#                     kern_param = "param") %>%
#    define_kernel(
#  
#      name = "P_site",
#      family = "CC",
#  
#      # site is appended so that we don't have to write out s_A, s_B, etc.
#  
#      formula          = s_site * g_site * d_z,
#  
#      s_site_lin       = alpha_s_site +
#                         beta_s_z * z_1 +
#                         beta_s_prec * prec +
#                         beta_s_temp * temp,
#      s_site           = 1 / (1 + exp(-s_site_lin)),
#      mu_g_site        = alpha_g_site +
#                         beta_g_z * z_1 +
#                         beta_g_prec * prec +
#                         beta_g_temp * temp,
#      g_site           = dnorm(z_2, mu_g_site, sigma_g),
#      data_list        = all_pars,
#      states           = list(c("z")),
#      uses_par_sets    = TRUE,
#      par_set_indices = list(site = LETTERS[1:6]),
#      evict_cor        = TRUE,
#      evict_fun        = truncated_distributions("norm", "g_site")
#    ) %>%
#    define_kernel(
#      name             = "F_site",
#      family           = "CC",
#      formula          = c_p_site * c_r_site * c_d * d_z,
#      c_p_site_lin     = alpha_c_p_site +
#                         beta_c_p_z * z_1 +
#                         beta_c_p_prec * prec +
#                         beta_c_p_temp * temp,
#      c_p_site         = 1 / (1 + exp(-c_p_site_lin)),
#      c_r_site         = exp(alpha_c_r_site +
#                             beta_c_r_z * z_1 +
#                             beta_c_r_prec * prec +
#                             beta_c_r_temp * temp),
#      c_d              = dnorm(z_2, mu_c_d, sigma_c_d),
#      data_list        = all_pars,
#      states           = list(c("z", "sb1", "sb2")),
#      uses_par_sets    = TRUE,
#      par_set_indices = list(site = LETTERS[1:6]),
#      evict_cor        = TRUE,
#      evict_fun        = truncated_distributions("norm", "c_d")
#      ) %>%
#    define_kernel(
#      name             = "go_sb_1_site",
#      family           = "CD",
#      formula          = (1 - r_i) * c_p_site * c_r_site * d_z,
#      c_p_site_lin     = alpha_c_p_site +
#                         beta_c_p_z * z_1 +
#                         beta_c_p_prec * prec +
#                         beta_c_p_temp * temp,
#      c_p_site         = 1 / (1 + exp(-c_p_site_lin)),
#      c_r_site         = exp(alpha_c_r_site +
#                             beta_c_r_z * z_1 +
#                             beta_c_r_prec * prec +
#                             beta_c_r_temp * temp),
#      data_list        = all_pars,
#      states           = list(c("z", "sb1")),
#      uses_par_sets    = TRUE,
#      par_set_indices = list(site = LETTERS[1:6]),
#      evict_cor        = FALSE
#    ) %>%
#    define_kernel(
#      name          = "go_sb_2",
#      family        = "DD",
#      formula       = s_sb1 * (1 - r_sb1),
#      data_list     = all_pars,
#      states        = list(c("sb1", "sb2")),
#      uses_par_sets = FALSE,
#      evict_cor     = FALSE
#    ) %>%
#    define_kernel(
#      name          = "leave_sb_1",
#      family        = "DC",
#      formula       = s_sb1 * r_sb1 * c_d,
#      c_d           = dnorm(z_2, mu_c_d, sigma_c_d),
#      data_list     = all_pars,
#      states        = list(c("z", "sb1")),
#      uses_par_sets = FALSE,
#      evict_cor     = TRUE,
#      evict_fun     = truncated_distributions("norm", "c_d")
#    ) %>%
#    define_kernel(
#      name          = "leave_sb_2",
#      family        = "DC",
#      formula       = s_sb2 * r_sb2 * c_d,
#      c_d           = dnorm(z_2, mu_c_d, sigma_c_d),
#      data_list     = all_pars,
#      states        = list(c("z", "sb2")),
#      uses_par_sets = FALSE,
#      evict_cor     = TRUE,
#      evict_fun     = truncated_distributions("norm", "c_d")
#    ) %>%
#    define_impl(
#      make_impl_args_list(
#        kernel_names = c("P_site",
#                         "F_site",
#                         "go_sb_1_site",
#                         "go_sb_2",
#                         "leave_sb_1",
#                         "leave_sb_2"),
#        int_rule     = rep("midpoint", 6),
#        state_start    = c("z", "z", "z", "sb1", "sb1", "sb2"),
#        state_end      = c("z", "z", "sb1", "sb2", "z", "z")
#      )
#    ) %>%
#    define_domains(
#      z = c(0.1, 100, 200)
#    ) %>%
#    define_pop_state(
#      n_z   = runif(200),
#      n_sb1 = 20,
#      n_sb2 = 20
#    ) %>%
#    define_env_state(
#      env_state = sample_fun(env_params),
#      data_list = list(env_params = env_params,
#                       sample_fun = sample_fun)
#    ) %>%
#    make_ipm(
#      iterations         = 20,
#      kernel_seq         = sample(LETTERS[1:6], 20, replace = TRUE),
#      normalize_pop_size = TRUE
#    )
#  
#  lambda(ex_ipm)

