compare_models: Compare Demand Models

In beezdemand: Behavioral Economic Easy Demand

Compare Demand Models

Description

Compare multiple demand models using information criteria and likelihood ratio tests (when applicable). Works with all beezdemand model classes.

Usage

compare_models(..., test = c("auto", "lrt", "none"))

Arguments

...	Two or more model objects of class beezdemand_hurdle, beezdemand_nlme, or beezdemand_fixed.
test	Character; type of statistical test. One of: "auto" (default): Use LRT if models are nested and comparable, otherwise IC-only. "lrt": Force likelihood ratio test (requires nested models from same backend). "none": Only report information criteria, no p-value.

Details

Models are compared using AIC and BIC. For models from the same statistical backend (e.g., two hurdle models or two NLME models), likelihood ratio tests can be performed if the models are nested.

When comparing models from different backends (e.g., hurdle vs NLME), only information criteria comparisons are possible since the likelihoods are not directly comparable for LRT purposes.

Backend Compatibility

Backend 1	Backend 2	LRT Possible?
hurdle	hurdle	Yes (if nested)
nlme	nlme	Yes (if nested)
fixed	fixed	No (no likelihood)
hurdle	nlme	No
hurdle	fixed	No
nlme	fixed	No

Value

An object of class beezdemand_model_comparison containing:

comparison

Data frame with model fit statistics

test_type

Type of test performed

lrt_results

LRT results if performed (NULL otherwise)

best_model

Index of best model by BIC

notes

Character vector of notes/warnings

nesting_verified

Logical; always FALSE since nesting is not automatically verified. Users must ensure models are properly nested for valid LRT interpretation.

Statistical Notes

The likelihood ratio test (LRT) assumes that:

1. The models are nested (the reduced model is a special case of the full model obtained by constraining parameters).

2. Both models are fit to identical data.

3. Under the null hypothesis, the LR statistic follows a chi-square distribution with degrees of freedom equal to the difference in the number of parameters.

Important caveat for mixed-effects models: When variance components are tested at the boundary (e.g., testing whether a random effect variance is zero), the standard chi-square distribution is not appropriate. The correct null distribution is a mixture of chi-squares (Stram & Lee, 1994). The p-values reported here use the standard chi-square approximation, which is conservative (p-values are too large) for boundary tests.

This function does not automatically verify that models are nested. Users should ensure models are properly nested before interpreting LRT p-values.

References

Stram, D. O., & Lee, J. W. (1994). Variance components testing in the longitudinal mixed effects model. Biometrics, 50(4), 1171-1177.

See Also

compare_hurdle_models() for the legacy hurdle-specific comparison

Examples

data(apt)
fit2 <- fit_demand_hurdle(apt, y_var = "y", x_var = "x", id_var = "id",
                          random_effects = c("zeros", "q0"))
fit3 <- fit_demand_hurdle(apt, y_var = "y", x_var = "x", id_var = "id",
                          random_effects = c("zeros", "q0", "alpha"))
compare_models(fit2, fit3)

beezdemand documentation built on March 3, 2026, 9:07 a.m.