Variance test in multilevel model

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() )

Answer 1

[Shantanu Dixit]

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:

• 'GeneralizedLinearModel': https://www.mathworks.com/help/stats/generalizedlinearmodel.html
• 'GeneralizedLinearMixedModel': https://www.mathworks.com/help/stats/generalizedlinearmixedmodel-class.html
• 'chi2cdf': https://www.mathworks.com/help/stats/chi2cdf.html
• 'LogLikelihood': https://www.mathworks.com/help/stats/generalizedlinearmixedmodel-class.html#bubtdtx-LogLikelihood
• 'NumEstimatedCoefficients': https://www.mathworks.com/help/stats/generalizedlinearmixedmodel-class.html#bubtdtx-NumEstimatedCoefficients

Hope this helps!