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Log-likelihood of the two-level VAR(1) at given parameters (MAR)

Source: R/fit_fiml.R
loglik_fiml.Rd

Evaluates, without fitting, the likelihood that fit_fiml maximizes: the Gaussian likelihood of the answered states under the two-level VAR(1) with random person means, skipped prompts integrated out as missing at random. Useful for comparing fits, for profile likelihoods, and for checking a fit against the trace of the EM iterations.

Usage

loglik_fiml(
  data,
  vars,
  Phi,
  Psi,
  mu,
  Sigma_mu,
  Sigma0 = stationary_cov(Phi, Psi),
  id = "id",
  time = "time",
  R = "R"
)

Arguments

data

Long data frame with one row per scheduled prompt.

vars

Names of the state columns.

Phi, Psi, mu, Sigma_mu, Sigma0

Parameter values: the \(p \times p\) lagged-coefficient matrix, the \(p \times p\) innovation covariance, the length-\(p\) population mean, the \(p \times p\) between-person covariance of the person means, and the \(p \times p\) covariance of the within-person deviation at the first prompt (by default the stationary covariance implied by Phi and Psi).

id, time

Names of the person and prompt-index columns.

R

Name of the response-indicator column (0/1, no NA). If the default name is not among the columns of data, a prompt counts as answered when all vars are non-missing; any other name must exist.

Value

A single number, the log-likelihood of the observed states under the two-level VAR(1) with the given parameters, skipped prompts treated as missing at random.

Examples

sim <- simulate_ema(N = 20, n_prompts = 15, seed = 1)
f <- fit_fiml(sim$data, sim$vars)
loglik_fiml(sim$data, sim$vars, f$Phi, f$Psi, f$mu, f$Sigma_mu)
#> [1] -1168.637
# the likelihood at the population parameters is lower than at the ML estimates
p <- default_params()
loglik_fiml(sim$data, sim$vars, p$Phi, p$Psi, p$mu, p$Sigma_mu)
#> [1] -1191.993