Hi Paul,
You are correct that a significant X*G interaction in your model (Y ~ CV1 + CV2 + X*G) indicates that the slope of Y versus X is not the same across your three groups, after accounting for the covariates. However, to determine which groups differ in slope (e.g., is the slope in Group 1 different from Group 2, etc.), you need to perform post-hoc tests on the interaction terms.
MATLAB’s fitlm encodes categorical variables using dummy variables, so the model coefficients represent the slope for the reference group and the differences in slope for the other groups relative to that reference. To compare slopes between any two groups, you can use the coefTest function to test linear combinations of the coefficients corresponding to the interaction terms. For example, to test whether the slope in Group 2 differs from Group 3, you would test whether the difference between their interaction coefficients is significantly different from zero. This approach allows you to perform all pairwise comparisons of slopes between groups, even with multiple covariates in the model.
% Fit the model (assuming mytable has variables: Y, X, G, CV1, CV2)
mymodel = fitlm(mytable, 'Y ~ CV1 + CV2 + X*G');
% Get coefficient names to identify indices
coefNames = mymodel.CoefficientNames;
% Find indices for interaction terms (adjust names if your groups are named differently)
idx_XG2 = find(strcmp(coefNames, 'X:G_2')); % e.g., Group 2
idx_XG3 = find(strcmp(coefNames, 'X:G_3')); % e.g., Group 3
% Test if slope in Group 2 differs from Group 3
c = zeros(1, numel(coefNames));
c(idx_XG2) = 1;
c(idx_XG3) = -1;
[p_BvsC, F, df1, df2] = coefTest(mymodel, c);
% Test if slope in Group 1 (reference) differs from Group 2
c2 = zeros(1, numel(coefNames));
c2(idx_XG2) = 1;
[p_AvsB, F, df1, df2] = coefTest(mymodel, c2);
% Test if slope in Group 1 (reference) differs from Group 3
c3 = zeros(1, numel(coefNames));
c3(idx_XG3) = 1;
[p_AvsC, F, df1, df2] = coefTest(mymodel, c3);
% Display results
fprintf('Group 1 vs Group 2 slope difference p-value: %.4f\n', p_AvsB);
fprintf('Group 1 vs Group 3 slope difference p-value: %.4f\n', p_AvsC);
fprintf('Group 2 vs Group 3 slope difference p-value: %.4f\n', p_BvsC);
