Variance test in multilevel model

2023 4 8
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更新时间：2025 1 22
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How to perform a liklihood ratio test to compaire two modeles one with random effect (a model using fitglme() ) and the other without random effect (a model using fitglm() )

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Shantanu Dixit
Shantanu Dixit 2025-1-22
编辑：Shantanu Dixit 2025-1-22

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Hi Bezalam,
Assuming you have two models (a model using 'fitglme' and another using 'fitglm'). You can perform a likelihood ratio test to compare the two models as follows:
  • Compute the log-likelihood of both the models using the 'LogLikelihood' property.
  • Derive the test-statistic as '-2* (difference of log likelihood of both the models)'
  • Compute the degrees of freedom using the 'NumEstimatedCoefficients' property.
  • Compute the p-value using 'chi2cdf' to compare the two models.
% Assuming model_glm and model_glme as the two models
logL_glm = model_glm.LogLikelihood;
logL_glme = model_glme.LogLikelihood;
test_statistic = -2 * (logL_glm - logL_glme);
% Degrees of freedom are computed as the difference in the number of estimated parameters.
df = model_glme.NumEstimatedCoefficients - model_glm.NumEstimatedCoefficients;
p_value = 1 - chi2cdf(test_statistic, df);
fprintf('Test Statistic: %.2f\n', test_statistic);
fprintf('Degrees of Freedom: %d\n', df);
fprintf('p-value: %.4f\n', p_value);
You can refer to the useful MathWorks documentation on Generalized Linear Models:
Hope this helps!

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