How can I obtain the variability of different values of a categorical variable by separating into strata?

Hello, I am replicating the results of a study using the following linear mixed-effects model:

The code is:

lme = fitlme(Tabla_datos, 'logxi ~ logH  + Material + Material:logH + (1|key)', ...
             'FitMethod', 'REML');

With this code, I was able to obtain the data for all fixed effects in the following table (highlighted in blue).

However, I still haven’t been able to achieve the results for variability by material (values highlighted in yellow in the table). I understand that MATLAB assumes a common sigma for all random effects, which is why I want to calculate this variability for the different categories (in this case: materials), treating each material as an independent stratum with its own variability.

Thank you in advance for your responses.

Answer 1

[Deep]

I believe your equation is missing the category variable "Material" as a random effect, adding which will allow you to capture variability specific to each material category. You can modify your model formula to include "Material" as a random effect like this:

lme = fitlme(Tabla_datos, 'logxi ~ logH + Material + Material:logH + (1|key) + (1|Material)', 'FitMethod', 'REML');

You can then use the "randomEffects" function to extract the random effects estimates from the linear mixed-effects model. The following code snippet helps filter and display the statistics related to each "Material" category, while filtering out the other random effects in your equation:

% Extract random effects from the linear mixed-effects model
[~, ~, stats] = randomEffects(lme);
% Filter the statistics only for the group "Material"
isMaterialStats = strcmp(stats.Group, 'Material');
materialStats = stats(isMaterialStats, :);
% Display the results
disp(materialStats);

For further details on the "randomEffects" function, you can refer to the documentation at https://www.mathworks.com/help/stats/linearmixedmodel.randomeffects.html.