rtmpt (version 2.0-3)

sim_ertmpt_data_SBC: Simulate data from an RT-MPT model

Description

Simulate data from RT-MPT models using ertmpt_model objects. The difference to sim_ertmpt_data is that here only scalars are allowed. This makes it usable for simulation-based calibration (SBC; Talts et al., 2018). You can specify the random seed, number of subjects, number of trials, and some parameters (same as prior_params from fit_ertmpt).

Usage

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

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.,

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 and has the same defaults. 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_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.

• 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. The default is set to 100.

• 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.

• var_of_mu_gamma: The group-specific variance of the mean parameter. Its default is 10.

• 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)). The default is 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_SIGMA*I). 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_GAMMA*I). Its default is 1.

• prec_epsilon: This is epsilon in the paper. It is the precision of mu_alpha and all 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].

Author

Raphael Hartmann

References

Talts, S., Betancourt, M., Simpson, D., Vehtari, A., & Gelman, A. (2018). Validating Bayesian inference algorithms with simulation-based calibration. arXiv preprint arXiv:1804.06788.

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)

params <- list(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 <- rtmpt:::sim_ertmpt_data_SBC(model, seed = 123, n.subj = 40, 
                                      n.trials = 30, params = params)