Likelihood Ratio Test for Nested mlmodel Objects

Performs a likelihood ratio test comparing two nested models fitted with the same estimator (e.g. ml_lm, ml_logit, ml_negbin, etc.).

Usage

lrtest(object_1, object_2, ...)

# S3 method for class 'mlmodel'
lrtest(object_1, object_2, ...)

Arguments

object_1: A fitted model object inheriting from "mlmodel". Typically the restricted (smaller) model.
object_2: A fitted model object inheriting from "mlmodel". Typically the unrestricted (larger) model. The order of object_1 and object_2 does not matter — the function automatically determines which is the restricted model.
...: Further arguments passed to methods (currently not used).

Value

An object of class "lrtest.mlmodel" with the test statistic, degrees of freedom, and p-value.

Details

The likelihood ratio test statistic is calculated as: $$LR = 2 \times (\log L_{\text{unrestricted}} - \log L_{\text{restricted}})$$

Under the null hypothesis that the restricted model is correct, LR follows a $\chi^2$ distribution with degrees of freedom equal to the difference in the number of parameters between the two models.

Important: The two models must be nested (the restricted model must be a special case of the unrestricted one) and fitted on exactly the same sample. The restricted model must have a lower (or equal) log-likelihood.

Author

Alfonso Sanchez-Penalver

Examples


# Linear model example
data(mroz)
mroz$incthou <- mroz$faminc / 1000

fit_small <- ml_lm(incthou ~ age + huswage, data = mroz)
fit_large <- ml_lm(incthou ~ age + I(age^2) + huswage + educ + unem, 
                   data = mroz)

lrtest(fit_small, fit_large)
#> ℹ `object_1` is the restricted model (nested in `object_2`).
#> Likelihood Ratio Test
#> --------------------------------------------
#> Chisq(3) = 61.194    Pr(>Chisq) = < 1e-8
#> --------------------------------------------
#> LogLik (restricted)   : -2669.275   (df = 4)
#> LogLik (unrestricted) : -2638.678   (df = 7)

# You can also reverse the order — the function detects the restricted model
lrtest(fit_large, fit_small)
#> ℹ `object_2` is the restricted model (nested in `object_1`).
#> Likelihood Ratio Test
#> --------------------------------------------
#> Chisq(3) = 61.194    Pr(>Chisq) = < 1e-8
#> --------------------------------------------
#> LogLik (restricted)   : -2669.275   (df = 7)
#> LogLik (unrestricted) : -2638.678   (df = 4)