R: Simulate data from RT-MPT models

sim_ertmpt_data {rtmpt}

R Documentation

Simulate data from RT-MPT models

Description

Simulate data from RT-MPT models using ertmpt_model objects. You can specify the random seed, number of subjects, number of trials per tree, and some parameters (mainly the same as prior_params from fit_ertmpt).

Usage

sim_ertmpt_data(model, seed, n.subj, n.trials, params = NULL)

Arguments

`model`	A list of the class `ertmpt_model`.
`seed`	Random seed number.
`n.subj`	Number of subjects.
`n.trials`	Number of trials per tree.
`params`	Named list of parameters from which the data will be generated. This must be the same named list as `prior_params` from `fit_ertmpt`, except for "mean_of_mu_alpha" and "var_of_mu_alpha", and has the same defaults. The difference to `prior_params` is, that vectors are allowed, but must match the length of the parameters in the `model`. It is not recommended to use the defaults since they lead to many probabilities close or equal to `0` and/or `1` and to RTs close or equal to `0`. Allowed parameters are: `mean_of_mu_alpha`: Probit transformed mean probability. If you want to have a group-level mean probability of `0.6`, use `mean_of_mu_alpha = qnorm(0.6)` in the `params` list. Default is `0` or `qnorm(.5)`. `var_of_mu_alpha`: Variance of the probit transformed group-level mean probability. If specified, mu_alpha will be sampled from N(`mean_of_mu_alpha, var_of_mu_alpha`). If not, mu_alpha `= mean_of_mu_alpha`. `mean_of_exp_mu_beta`: This is the expected exponential rate (`E(exp(beta)) = E(lambda)`) and `1/mean_of_exp_mu_beta` is the expected process time (`1/E(exp(beta)) = E(tau)`). The default mean is set to `10`, such that the expected process time is `0.1` seconds. For a mean process time of `200` ms, wirte `mean_of_exp_mu_beta = 1000/200`. `var_of_exp_mu_beta`: The group-specific variance of the exponential rates. Since `exp(mu_beta)` is Gamma distributed, the rate of the distribution is just mean divided by variance and the shape is the mean times the rate. If specified, exp(mu_beta) is sampled from Gamma`shape = mean_of_exp_mu_beta^2/var_of_exp_mu_beta, rate = mean_of_exp_mu_beta/var_of_exp_mu_beta`). If not, mu_alpha `= mean_of_exp_mu_beta`. `mean_of_mu_gamma`: This is the expected mean parameter of the encoding and response execution times, which follow a normal distribution truncated from below at zero, so `E(mu_gamma) < E(gamma)`. The default is `0`. For a mean motor time of `550` ms write `mean_of_mu_gamma = 550/1000`. `var_of_mu_gamma`: The group-specific variance of the mean parameter. If specified, mu_gamma is sampled from N(`mean_of_mu_gamma, var_of_mu_gamma`). If not, mu_gamma `= mean_of_mu_gamma`. `mean_of_omega_sqr`: This is the expected residual variance (`E(omega^2)`). The default is `0.005`. `var_of_omega_sqr`: The variance of the residual variance (`Var(omega^2)`). If specified, omega_sqr is sampled from GAMMA(`shape = mean_of_omega_sqr^2/var_of_omega_sqr, rate = mean_of_omega_sqr/var_of_omega_sqr`). If not, omega_sqr `= mean_of_omega_sqr`. `0.01`. The default of the mean and variance is equivalent to a shape and rate of `0.0025` and `0.5`, respectivly. `df_of_sigma_sqr`: Degrees of freedom for the individual variance of the response executions. The individual variance follows a scaled inverse chi-squared distribution with `df_of_sigma_sqr` degrees of freedom and `omega^2` as scale. `2` is the default and it should be an integer. `sf_of_scale_matrix_SIGMA`: The original scaling matrix (S) of the (scaled) inverse Wishart distribution for the process related parameters is an identity matrix `S=I`. `sf_of_scale_matrix_SIGMA` is a scaling factor, that scales this matrix (`S=sf_of_scale_matrix_SIGMAI`). Its default is `1`. `sf_of_scale_matrix_GAMMA`: The original scaling matrix (S) of the (scaled) inverse Wishart distribution for the encoding and motor execution parameters is an identity matrix `S=I`. `sf_of_scale_matrix_GAMMA` is a scaling factor that scales this matrix (`S=sf_of_scale_matrix_GAMMAI`). Its default is `1`. `prec_epsilon`: This is epsilon in the paper. It is the precision of xi (scaling parameter in the scaled inverse Wishart distribution). Its default is also `1`. `add_df_to_invWish`: If `P` is the number of parameters or rather the size of the scale matrix used in the (scaled) inverse Wishart distribution then `add_df_to_invWish` is the number of degrees of freedom that can be added to it. So `DF = P + add_df_to_invWish`. The default for `add_df_to_invWish` is `1`, such that the correlations are uniformly distributed within `[-1, 1]`. `SIGMA`: Variance-covariance matrix of the process-related parameters. It must match the number of process-related parameters to be estimated. If scalars or vectors are given, they will be transformed into diagonal matrices using `diag(SIGMA)`. If not specified it will be randomly generated using `diag(xi)%%rinvwishart(nu, S)%%diag(xi)`, where nu is the number of process-related group-level parameters to be estimated plus `add_df_to_invWish`, S is the identity matrix multiplied by `sf_of_scale_matrix_SIGMA`, and xi (randomly generated from N(`1, 1/prec_epsilon`)) are the scaling factors for the scaled inverse wishart distribution. If `SIGMA` is used, `sf_of_scale_matrix_SIGMA` and `add_df_to_invWish` will be ignored for the process-related parameters. `GAMMA`: Variance-covariance matrix of the motor time parameters. It must match the number of motor time parameters to be estimated. If scalars or vectors are given, they will be transformed into diagonal matrices using `diag(SIGMA)`. If not specified it will be randomly generated using `diag(xi)%%rinvwishart(nu, S)%%diag(xi)`, where nu is the number of motor time group-level parameters to be estimated plus `add_df_to_invWish`, S is the identity matrix multiplied by `sf_of_scale_matrix_GAMMA`, and xi (randomly generated from N(`1, 1/prec_epsilon`)) are the scaling factors for the scaled inverse wishart distribution. If `GAMMA` is used, `sf_of_scale_matrix_GAMMA` and `add_df_to_invWish` will be ignored for the motor time parameters.

Value

A list of the class ertmpt_sim containing

data: the data.frame with the simulated data,
gen_list: a list containing lists of the group-level and subject-specific parameters for the process-related parameters and the motor-related parameters, and the trial-specific probabilities, process-times, and motor-times,
specs: some specifications like the model, seed number, etc.,

Author(s)

Raphael Hartmann

Examples

########################################################################################
# Detect-Guess variant of the Two-High Threshold model.
# The encoding and motor execution times are assumed to be different for each response.
########################################################################################

mdl_2HTM <- "
# targets
do+(1-do)*g     ; 0
(1-do)*(1-g)    ; 1

# lures
(1-dn)*g        ; 0
dn+(1-dn)*(1-g) ; 1

# do: detect old; dn: detect new; g: guess
"

model <- to_ertmpt_model(mdl_file = mdl_2HTM)

# random group-level parameters
params <- list(mean_of_mu_alpha = 0, 
               #var_of_mu_alpha = 1
               mean_of_exp_mu_beta = 10, 
               var_of_exp_mu_beta = 10, 
               mean_of_mu_gamma = 0.5, 
               var_of_mu_gamma = 0.0025, 
               mean_of_omega_sqr = 0.005, 
               var_of_omega_sqr = 0.000025,
               df_of_sigma_sqr = 10, 
               sf_of_scale_matrix_SIGMA = 0.1, 
               sf_of_scale_matrix_GAMMA = 0.01, 
               prec_epsilon = 10,
               add_df_to_invWish = 5)

sim_dat <- sim_ertmpt_data(model, seed = 123, n.subj = 40, n.trials = 30, params = params)

# fixed group-level parameters
params <- list(mean_of_mu_alpha = 0, 
               mean_of_exp_mu_beta = 10, 
               mean_of_mu_gamma = 0.5, 
               mean_of_omega_sqr = 0.005, 
               df_of_sigma_sqr = 10, 
               sf_of_scale_matrix_SIGMA = 0.1, 
               sf_of_scale_matrix_GAMMA = 0.01, 
               prec_epsilon = 10,
               add_df_to_invWish = 5,
               SIGMA = diag(9),   # independent process-related params
               GAMMA = diag(2))   # independent motor time params

sim_dat <- sim_ertmpt_data(model, seed = 123, n.subj = 40, n.trials = 30, params = params)

[Package rtmpt version 2.0-1 Index]