Marginal-MML sandwich covariance for a mixed-subjects fit

Computes the full sandwich covariance for the scalar marginal-MML PPI++ estimator from fit_mixed_subjects_mml(). The bread uses Louis's (1982) observed marginal-information formula

Usage

vcov_mixed_subjects_mml(object, ridge = 1e-08, ...)

Arguments

object

A scalar-lambda fit_mixed_subjects_mml() fit.

ridge

Ridge regularization for bread inversion.

...

Unused.

Value

A \(2J \times 2J\) covariance matrix with attributes bread and meat.

Details

$$A_\lambda^\mathrm{marg} = H_\lambda^\mathrm{comp} - I_\lambda^\mathrm{miss}$$

rather than the EM/complete-data Hessian used by vcov_mixed_subjects(). Using the complete-data Hessian as the bread for a marginal-MML estimator would over-state efficiency by ignoring the missing-information correction.

The meat uses the standard marginal per-person score vectors (posteriors at the converged parameters), which is identical to vcov_mixed_subjects().

When is this function called automatically? The vcov() method for "mixedsubjects_fit" objects (see stats::vcov()) dispatches here whenever isTRUE(object$mml) && length(object$lambda) == 1. For vector-lambda fits, or for frozen expected-count fits, the existing vcov_mixed_subjects() is used.

See also

vcov_mixed_subjects() for the frozen expected-count version. The internal louis_missing_info() helper computes the missing-information correction.