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Likelihood Ratio Test in R, The likelihood-ratio test in statistics compares the goodness of fit of two nested regression models based on the ratio of their likelihoods, specifically one obtained by maximisation over the entire parameter space and another obtained after imposing some constraint.
A nested model is simply a subset of the predictor variables in the overall regression model.
For instance, consider the following regression model with four predictor variables.
Y = β0 + β1×1 + β2×2 + β3×3 + β4×4 + ε
The following model, with only two of the original predictor variables, is an example of a nested model.
Y = β0 + β1×1 + β2×2 + ε
To see if these two models differ significantly, we can use a likelihood ratio test with the following null and alternative hypotheses.
H0: Both the full and nested models fit the data equally well. As a result, you should employ the nested model.
H1: The full model significantly outperforms the nested model in terms of data fit. As a result, you should use the entire model.
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