Simulates indicators under the null model while preserving observed group sizes, refits both models, and compares their likelihood differences. Models must differ by exactly one individual profile or one group class, with the other count, covariance structure and centering mode fixed. Grand-mean centering is repeated in every simulated refit. Person-centred fits are refused because this model does not specify a generative distribution for the group baselines removed by that transformation. This is a native parametric bootstrap, not an implementation of Mplus TECH14. It does not use a chi-square reference distribution. Any failed/nonconverged or reversed replicate makes the p-value NA, avoiding silent deletion of difficult fits.
Usage
bootstrap_lrt(
null_model,
alternative_model,
data = NULL,
iter = 199L,
n_starts = 10L,
max_iter = 1000L,
tol = 1e-08,
seed = NULL
)Arguments
- null_model
Smaller, converged
multilpa()model, with or without membership covariates.- alternative_model
Larger model fitted to exactly the same data.
- data
Optional. The data both models were fitted to, used to verify both fitted likelihoods; when omitted it is rebuilt from what the null model stores.
- iter
Number of simulated datasets (at least two; use many for inference).
- n_starts
Number of starts for each simulated fit.
- max_iter
Maximum EM iterations for each simulated fit.
- tol
Relative likelihood convergence tolerance.
- seed
Optional seed: any whole number
set.seed()accepts. The caller's random-number state is restored on exit.
Value
An object of class multilpa_bootstrap_lrt, carrying the observed
statistic, the finite-simulation corrected p-value, its Monte Carlo
standard error, the measurement blocks held fixed in every fit, and one
record per replicate. Read it with the verbs that describe it:
as.data.frame() gives the single-row test result,
get_results(what = "replicates") one row per simulated replicate,
summary() the
test beside the replicate diagnostics, and plot() the simulated null
distribution with the observed statistic marked. Inspect failed starts,
boundary flags and likelihood replication before interpreting results.
Details
Fits made with missing = "fiml" are supported when both models were: every
replicate is given the observed data's missing cells before it is refitted,
preserving the pattern of available measurements. Calibration requires
missingness independent of the indicators and latent classes, conditional
on any fixed covariates. Carrying a fixed mask does not reproduce a general
MAR mechanism that depends on observed indicators, or an MNAR mechanism.
FIML estimation under MAR does not by itself validate this bootstrap under
MAR; the retained size study covers MCAR only.
Membership-covariate fits (multilpa(profile_covariates = , group_covariates = )) are supported: the covariates are held at their
observed values, group classes are drawn from the fitted group logits and
profiles from each row's profile logits, as the model conditions on the
covariates. Both models must use the same profile covariates, group
covariates and slope specification, except that a one-group-class null,
which cannot carry group covariates or slopes by group class, may be
compared with an alternative that adds them. When data is omitted it is
rebuilt from the alternative, whose columns include the null's. A
covariate replicate counts as valid when its likelihood has converged even
if a membership logit is still drifting, as it does for an empty or
separated class in an over-fitted alternative: the statistic reads only the
maximized likelihood, which such a fit has reached. The replicate table's
logits_settled column records whether both refits' logits had also
converged. The original models must be fully converged.
Models fitted with fixed, including those from fit_staged(), are
supported: every replicate is refitted with the same blocks held at the same
values, so the simulated statistics compare the same two constrained models
as the observed statistic does. The p-value is then conditional on that
measurement solution, which is treated as known and whose own uncertainty is
not propagated. A constrained pair whose nesting cannot be established is
refused rather than given a p-value.
Conditions
latents_bad_nesting when only one of the two models holds measurement
blocks fixed, when they hold different blocks, when they hold the same
blocks at different values, when they hold a measurement fixed while
differing in the number of profiles (the held blocks then have different
shapes, so the null is not a restriction of the alternative), or when the
alternative does not estimate more free parameters than the null.
latents_failed_replicates is warned when some replicate fails
validation, and the p-value is NA.
latents_unsupported_bootstrap refuses person-centred fits, for which
this simulator has no group-baseline distribution.
latents_unsupported_prior refuses fits estimated with a prior: their
likelihoods are evaluated at posterior modes, not ML estimates.
latents_incomparable_models when the two models differ in their
observations, grouping, covariance structure, centering or missing-data
handling; latents_bad_data when the data have missing indicators and
the models were not fitted with missing = "fiml"; latents_bad_nesting
also when two covariate models use different covariates or slope
specifications (other than a one-group-class null).
Examples
set.seed(1)
example_data <- data.frame(
school = rep(seq_len(10), each = 10),
score = rnorm(100, rep(c(-2, 2), each = 50))
)
smaller <- multilpa(example_data, "score", "school", n_profiles = 1,
n_group_classes = 1, n_starts = 2, seed = 1)
larger <- multilpa(example_data, "score", "school", n_profiles = 2,
n_group_classes = 1, n_starts = 2, seed = 1)
# `iter` is small so the example runs quickly; use many more for inference.
comparison <- bootstrap_lrt(smaller, larger, iter = 9, n_starts = 1,
max_iter = 2000, tol = 1e-6, seed = 1)
comparison
#> Parametric bootstrap likelihood-ratio comparison
#> Null: 1 profile; alternative: 2 profiles
#> Observed statistic: 44.198110
#> p-value: 0.1 (Monte Carlo SE 0.0949) from 9 of 9 valid replicates