Can the aggregate data identify the comparator coefficients?

In the relaxed model the comparator coefficients beta_comparator are informed only by the aggregate rows. With K covariates there are K + 1 comparator parameters, so at least K + 1 distinct aggregate rows are needed, and under an identity link the rows must also differ in every covariate direction.

Usage

check_identification(x, verbose = TRUE, link = NULL)

Arguments

x: An mlumr_data object or a fitted relaxed mlumr_fit.
verbose: Print a readable report (default TRUE).
link: Planned link for an unfitted data object. Defaults to the family default. A fitted object always uses its stored link.

Value

Invisibly, a list with n_rows, n_distinct (rows that do not repeat another's integration grid), n_cov, n_rows_needed (K + 1), cond_inv, eff_dim, spread, singular_values, means (the scaled, centered subgroup mean matrix), diagnostic_scope ("identity" or "descriptive") and flagged.

Details

The subgroup mean profiles are centered, divided by the IPD covariate SDs and decomposed. cond_inv is the ratio of the smallest to the largest singular value and goes to 0 as the rows collapse onto a lower-dimensional set. eff_dim is the participation ratio of the squared singular values, the number of directions the rows effectively spread along, from 1 to K; it is 0 when the rows do not vary or cannot be decomposed. spread is the RMS distance of the rows from their center along the dominant direction, in IPD SDs; it supplies the absolute scale cond_inv lacks. For a normal identity-link model the subgroup means are the aggregate design and the screen flags cond_inv < 0.2 or spread < 0.05, which are package heuristics. For other links the integrated response also depends on each row's covariate distribution, so the geometry is descriptive only and flagged is NA unless there are too few rows. Reconstructed survival curves are refused, since a curve is not one scalar summary per row. Neither measure sees subgroup sizes or outcome precision, so confirm any verdict with the coefficient posterior and prior_sensitivity(). The subgroup-identification vignette works through the cases.

Examples

if (FALSE) { # \dontrun{
dat <- add_integration(combine_data(ipd, agd), n_int = 64, ...)
check_identification(dat)
} # }