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.
