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Model Selection for Growth Mixture Models

Source: R/gmm-select.R
gmm_select.Rd

Compares growth mixture models with different numbers of latent classes using multiple criteria including BIC, entropy, and the Bootstrap Likelihood Ratio Test (BLRT).

Usage

gmm_select(
  data,
  id,
  time,
  outcome,
  classes = 1:5,
  strata = NULL,
  cluster = NULL,
  weights = NULL,
  growth_model = "linear",
  criteria = c("BIC", "BLRT", "entropy"),
  blrt_samples = 100,
  blrt_alpha = 0.05,
  starts = 200,
  cores = 1,
  verbose = TRUE,
  ...
)

Arguments

data

Data frame in long format

id

Character string specifying individual ID variable name

time

Character string specifying time variable name

outcome

Character string specifying outcome variable name

classes

Integer vector specifying class solutions to test (e.g., 1:5)

strata

Character string specifying stratification variable (optional)

cluster

Character string specifying cluster/PSU variable (optional)

weights

Character string specifying sampling weights variable (optional)

growth_model

Character string: "linear" (default), "quadratic", etc.

criteria

Character vector of criteria to compute: "BIC" (default), "BLRT", "entropy", "AIC", "aBIC"

blrt_samples

Integer number of bootstrap samples for BLRT (default: 100)

blrt_alpha

Significance level for BLRT (default: 0.05)

starts

Integer number of random starts per model (default: 200)

cores

Integer number of CPU cores (default: 1)

verbose

Logical, print progress? (default: TRUE)

...

Additional arguments passed to gmm_survey()

Value

An S4 object of class SurveyMixrSelect containing:

comparison_table

Data frame comparing fit across class solutions

fitted_models

List of fitted SurveyMixr objects

blrt_results

Detailed BLRT results if requested

recommended_classes

Recommended number of classes

criteria

Criteria used for selection

Details

This function systematically compares mixture models with different numbers of latent classes. Multiple criteria are available:

Information Criteria:

  • BIC: Bayesian Information Criterion (lower is better)

  • AIC: Akaike Information Criterion (lower is better)

  • aBIC: Sample-size adjusted BIC (lower is better)

Classification Quality:

  • Entropy: Classification certainty (higher is better, >0.8 preferred)

Hypothesis Testing:

  • BLRT: Bootstrap Likelihood Ratio Test comparing K vs K-1 classes. Considered the gold standard for class enumeration. A significant p-value (< 0.05) indicates that K classes fit better than K-1 classes.

The BLRT implementation uses parametric bootstrap: data is generated under the K-1 class model, and the distribution of likelihood ratio statistics is computed empirically. This is computationally intensive but provides the most reliable test for class enumeration.

Practical Considerations:

  • Increase starts (500-1000) for final model selection

  • BLRT is computationally intensive; use fewer bootstrap samples for initial exploration

  • Smallest class should typically be >5

  • Consider substantive interpretability alongside statistical criteria

References

Nylund, K. L., Asparouhov, T., & Muthén, B. O. (2007). Deciding on the number of classes in latent class analysis and growth mixture modeling: A Monte Carlo simulation study. Structural Equation Modeling, 14(4), 535-569.

McLachlan, G. J., & Peel, D. (2000). Finite mixture models. John Wiley & Sons.

Examples

if (FALSE) { # \dontrun{
# Compare 1-5 class models
selection <- gmm_select(
  data = mcs_simulated,
  id = "id",
  time = "age",
  outcome = "selfcontrol",
  classes = 1:5,
  strata = "stratum",
  cluster = "psu",
  weights = "weight",
  criteria = c("BIC", "BLRT", "entropy"),
  blrt_samples = 100,
  starts = 200,
  cores = 4
)

# View comparison table
print(selection)

# Extract best model
best_fit <- selection@fitted_models[[3]]  # If 3 classes optimal
} # }