Simulate several models for the same simulated people

Draws the subject values of every component, and any covariates, from one multivariate normal distribution, then simulates each component's data with its own model and generator. Parameters of different models can therefore be correlated across subjects, which is what a study of individual differences across tasks or models needs.

Usage

simulate_components(
  components,
  n_subjects,
  cors = NULL,
  covariates = NULL,
  seed = NULL
)

Arguments

components

A list of recovery_component()s. If the list has names, they must be the component names.

n_subjects

The number of subjects, shared by every component.

cors

A correlation matrix over prefixed terms (<name>_<term>, such as m3_c_task1) and covariates; terms it does not name are uncorrelated. NULL means none are correlated. May be a function with no arguments, as in simulate_recovery().

covariates

Observed, error-free person variables drawn with the parameters, as in simulate_recovery(). A covariate name must differ from every component name and from every model's parameters and columns.

seed

A seed applied with withr::with_seed() around everything that is drawn; NULL leaves the random number generator alone.

Value

A list of class bmmtools_simulation_set with

• components: a named list of bmmtools_simulations, one per component, with its own unprefixed terms, no covariates and seed NA;

• truth: the tables of simulate_recovery() (population, subjects, sd, cor, covariates) over every component, with prefixed terms; cor holds every pair of varying terms and covariates;

• pars, sds: the realised values, prefixed and expanded over tasks;

• cors: the realised correlation matrix over the varying terms, then the covariates (NULL with fewer than two);

• covariates and covariate_data, a tibble with id and one column per covariate;

• links: every model's link table under prefixed names;

• specs: the components as given;

• n_subjects and seed (NA when none).

Details

Order of the draws. Inside the seed, each component's pars and then sds are evaluated, in component order, then cors. The subject values of all components are one draw, Z %*% chol(cors), over the varying terms, component by component. The generators then run in component order, and the covariates are drawn last, so adding a covariate never changes the responses. A set with one component and no covariates gives exactly the simulation simulate_recovery() gives with the same arguments and seed. Adding a component after another leaves the first one's subject values unchanged, but not its responses, because the draw for the added terms comes before the generators.

Covariates are not added to the components' data; they are in covariate_data and in truth$covariates.

What separate fits can recover. Each component is fitted on its own by fit_components(), so no fit knows about the correlation between its parameters and another model's. Correlating the estimates across fits attenuates the correlation by the reliabilities rel_a and rel_b of the two subject estimates: the point estimator of extract_correlations() is roughly rho * sqrt(rel_a * rel_b), and the draws estimator roughly rho * rel_a * rel_b, so neither recovers rho. A structural equation model of true against estimated values, from subject_table(), does; so would a joint multivariate fit of all components, which bmmtools does not support yet.

Examples

if (FALSE) { # \dontrun{
components <- list(
  recovery_component(
    bmm::mixture2p(resp_error = "y"),
    pars = c(kappa = log(8), thetat = qlogis(0.75)),
    n_trials = 60, sds = c(kappa = 0.3, thetat = 0.5), name = "m2p"
  ),
  recovery_component(
    bmm::sdm(resp_error = "y"),
    pars = c(c = log(3), kappa = log(5)),
    n_trials = 60, sds = c(c = 0.4), name = "sdm"
  )
)
cors <- diag(2)
dimnames(cors) <- rep(list(c("m2p_thetat", "sdm_c")), 2)
cors[1, 2] <- cors[2, 1] <- 0.6
set <- simulate_components(components,
  n_subjects = 100, cors = cors,
  seed = 1
)
fits <- fit_components(set, dir = "fits")
recover_correlations(fits, set, estimator = c("draws", "point"))
} # }