Likelihood-ratio comparison of nested gllvmTMB fits

Sequential nested likelihood-ratio comparison of two or more ordinary (ML, unpenalised, non-MSPL) gllvmTMB fits, sorted by increasing free parameter count. Each adjacent pair is classified as either an interior fixed-effect step (plain Wilks chi-square applies) or a rank (boundary) step of exactly one new latent dimension (the Self-Liang chi-bar-square mixture is used, as an explicitly documented approximation – see Details). Anything else – more than one new latent dimension in a step, a change to covstruct routes/family, or a fixed-effect change combined with a rank change in the same step – is refused with a named reason rather than guessed at.

Usage

# S3 method for class 'gllvmTMB_multi'
anova(object, ..., test = c("chibar", "chisq", "none"))

# S3 method for class 'anova.gllvmTMB_multi'
print(x, digits = 4, ...)

Arguments

object, ...

Two or more fits from gllvmTMB().

test

One of "chibar" (default: chi-bar-square for rank steps, plain chi-square for interior fixed-effect steps), "chisq" (plain chi-square everywhere – conservative (its p-value is too large, understating the evidence) at a rank/boundary step, and flagged as such in the returned table's notes), or "none" (report the table with no p-values).

x

An "anova.gllvmTMB_multi" object.

digits

Number of significant digits printed in the comparison table.

Value

A data.frame of class c("anova.gllvmTMB_multi", "data.frame") with columns model, formula, d (latent rank, NA if not applicable), npar, logLik, deviance, df (parameter-count change from the previous row), LRT, test (method actually used, or "refused"), and p.value. An attribute "note" carries a per-row explanation (recommended alternative when refused; the approximation caveat for chi-bar rows).

Comparability (refused outright)

anova() aborts, naming the reason, if the fits: are not all gllvmTMB_multi objects; include an LA-MSPL fit; include a REML = TRUE fit; use different integration engines (Laplace vs AGHQ) or a loading ridge; were fit to different data (row count, or the response itself), or different families/links; or are not fixed-effect-nested when ordered by parameter count. It also refuses (per-step, in the returned table's test/note columns rather than aborting the whole call) any adjacent pair that changes more than the latent rank d by more than one dimension, or that changes both the fixed effects and the rank in the same step – compare those in separate steps instead.

The rank-step chi-bar-square is an approximation

The Self & Liang (1987) chi-bar-square mixture (chibar2_pvalue()) is derived for q INDEPENDENT scalar boundary variance components with regular Fisher information elsewhere. A newly added latent-loading column is p - d free parameters (this package's rr() lower-triangular identifiability convention), but they are not literally independent scalar variances: at the null (the new column exactly 0) the associated latent score itself becomes unidentified, which is closer to the "testing the number of factors" / reduced-rank-testing literature (known to have non-standard LRT asymptotics in general) than to Self & Liang's setting. anova() uses the chi-bar-square mixture as an approximation and labels every rank-step p-value with this caveat in the table's notes rather than presenting it as an exact result. Treat this result as a model-selection aid, not as a generally calibrated hypothesis test.

See also

chibar2_pvalue(), select_lv()