compare.model: Model Comparison Tool

Description

Compares two nested latent class/profile models using multiple fit indices, likelihood ratio tests, and classification metrics.

Usage

compare.model(object1, object2, n.Bootstrap = 0)

Value

An object of class compare.model containing:

npar: Named vector with number of free parameters for each model
entropy: Named vector with entropy values (classification accuracy measure) for each model
AvePP: List containing average posterior probabilities per latent class/profile
fit.index: List of get.fit.index objects for both models
BF: Bayes Factor for model comparison (based on SIC)
LRT.obj: Likelihood ratio test (LRT) results
LRT.VLMR.obj: Vuong-Lo-Mendell-Rubin (VLMR) adjusted LRT results
LRT.Bootstrap.obj: Bootstrap LRT results (if n.Bootstrap > 0)
call: The matched function call
arguments: List containing the original arguments passed to the function

Arguments

object1: An object of class LCA or LPA, representing the first latent class/profile model.
object2: An object of class LCA or LPA, representing the second latent class/profile model. Must be of the same type as object1.
n.Bootstrap: Integer specifying the number of bootstrap replications for the parametric bootstrap likelihood ratio test (BLRT). Default is 0 (no bootstrap test performed).

Details

This function performs comprehensive model comparison between two nested LCA/LPA models. Key features include:

Automatically orders models by parameter count (smaller model first)
Computes multiple fit indices via get.fit.index
Calculates classification quality metrics (entropy, average posterior probabilities)
Performs three types of likelihood ratio tests:
- Standard LRT, see LRT.test
- VLMR adjusted LRT, see LRT.test.VLMR
- Parametric bootstrap LRT (computationally intensive but robust), see LRT.test.Bootstrap
Computes Bayes Factor using Sample-Size Adjusted BIC (SIC)

Important Requirements:

Both models must be of the same type (LCA or LPA)
Models must be nested (one model is a constrained version of the other)
n.Bootstrap > 0 requires significant computational resources

Examples

Run this code

library(LCPA)
set.seed(123)

data.obj <- sim.LPA(N = 500, I = 5, L = 3, constraint = "V0")
response <- data.obj$response

# need Mplus
if (FALSE) {
# Compare 3-class vs 4-class LPA models
object1 <- LPA(response, L = 3, method = "Mplus", constraint = "V0")
object2 <- LPA(response, L = 4, method = "Mplus", constraint = "V0")

compare.model.obj <- compare.model(object1, object2)

print(compare.model.obj)
}