fix(matlab): report learning rate via per-animal slope test, not anticonservative GLMM F-test

fitglme coefTest only offers observation-level DF (df2~=178), which overstates
the group x day interaction significance for this few-subject design (p~=0 in
every scenario). Replace the reported learning-rate result with a cluster-honest
per-animal slope test (per-subject OLS slope of success vs day, Welch + MWU,
B2 vs A2) -- now correctly parallel in all 6 scenarios, matching the Python GEE.
The GLMM F-test is kept as a flagged reference only. Adds a regression test.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

analysis/matlab/tdcs_models.m

@@ -12,9 +12,18 @@ function R = tdcs_models(S, meta, cfg)
 %     R.learnGLME   GeneralizedLinearMixedModel, Poisson learning-rate
 %                   model with a group x day_c interaction:
 %                     success ~ group*day_c + day_c2 + (1|subject)
-%     R.learn       struct with the joint Wald test (via COEFTEST) that
+%     R.learn       learning-rate comparison, Box-B2 vs Box-A2. The reported
-%                   all group x day_c interaction terms are zero:
+%                   result is a PER-ANIMAL slope test (cluster-honest, like
-%                   .jointP, .jointF, .jointDF1, .jointDF2.
+%                   R.perAnimal): each subject's OLS slope of success on day,
+%                   then Welch t / two-sided Mann-Whitney across groups:
+%                   .slopeWelchP, .slopeMWUp, .nB, .nA, .meanSlopeB,
+%                   .meanSlopeA. The GLMM group x day_c joint F-test is also
+%                   kept for reference (.glmeJointP, .glmeJointF, .glmeJointDF1,
+%                   .glmeJointDF2) but is ANTICONSERVATIVE here: fitglme's
+%                   coefTest offers only observation-level DF, which overstates
+%                   significance for this few-subject design (it reads p~=0
+%                   even when the per-animal slopes are clearly parallel), so
+%                   it is NOT the basis for the conclusion.
 %     R.perAnimal   per-subject Box-B2 vs Box-A2 comparison (pure stats,
 %                   no GLME involved): .countWelchP, .countMWUp,
 %                   .rateWelchP, .rateMWUp, .nB, .nA. "count" = per-subject
@@ -51,10 +60,10 @@ R.rateGLME = fitglme(Sr, countFormula, 'Distribution', 'Binomial', ...
 
 learnFormula = 'success ~ group*day_c + day_c2 + (1|subject)';
 R.learnGLME = fitglme(S, learnFormula, 'Distribution', 'Poisson');
-R.learn = localJointInteractionTest(R.learnGLME);
 
 R.perAnimal = localPerAnimal(S, cfg);
 R.h2 = localH2(R.countGLME, R.rateGLME, cfg);
+R.learn = localLearn(R.learnGLME, S, cfg);
 
 if meta.isUnmerged
     R.classify = localClassifyAll(R.countGLME, R.rateGLME, cfg);
@@ -200,6 +209,34 @@ end
 end
 
 % -------------------------------------------------------------- learning
+function out = localLearn(learnGLME, S, cfg)
+%LOCALLEARN Learning-rate result: per-animal slope test (primary, cluster-
+%   honest) plus the GLMM interaction joint F-test (reference, anticonservative).
+bSlopes = localSubjectSlopes(S(S.group == cfg.anchorHigh, :));
+aSlopes = localSubjectSlopes(S(S.group == cfg.anchorLow, :));
+[~, slopeWelchP] = ttest2(bSlopes, aSlopes, 'Vartype', 'unequal');
+slopeMWUp = ranksum(bSlopes, aSlopes);   % two-sided: slope-diff direction unknown
+
+j = localJointInteractionTest(learnGLME);
+out = struct( ...
+    'slopeWelchP', slopeWelchP, 'slopeMWUp', slopeMWUp, ...
+    'nB', numel(bSlopes), 'nA', numel(aSlopes), ...
+    'meanSlopeB', mean(bSlopes), 'meanSlopeA', mean(aSlopes), ...
+    'glmeJointP', j.jointP, 'glmeJointF', j.jointF, ...
+    'glmeJointDF1', j.jointDF1, 'glmeJointDF2', j.jointDF2);
+end
+
+function slopes = localSubjectSlopes(T)
+%LOCALSUBJECTSLOPES Per-subject OLS slope of success on day.
+subj = unique(T.subject);
+slopes = zeros(numel(subj), 1);
+for i = 1:numel(subj)
+    rows = T.subject == subj(i);
+    coeffs = polyfit(T.day(rows), T.success(rows), 1);
+    slopes(i) = coeffs(1);
+end
+end
+
 function out = localJointInteractionTest(learnGLME)
 %LOCALJOINTINTERACTIONTEST Joint Wald test that all group x day_c
 %   interaction fixed effects are zero (do groups learn at different

analysis/matlab/tdcs_report.m

@@ -87,11 +87,19 @@ s = [s localCleanDisp(R.countGLME) sprintf('\n')];
 s = [s localHeader('(B) LEVEL / RATE -- Binomial GLMM (subject random intercept)')];
 s = [s localCleanDisp(R.rateGLME) sprintf('\n')];
 
-s = [s localHeader('(C) LEARNING RATE -- joint test (all group x day_c interactions = 0)')];
+s = [s localHeader('(C) LEARNING RATE -- per-animal slope test (Box-B2 vs Box-A2)')];
-s = [s sprintf('F=%.3f, df1=%d, df2=%.2f, p=%.4f\n', ...
+if R.learn.slopeMWUp < 0.05
-    R.learn.jointF, R.learn.jointDF1, R.learn.jointDF2, R.learn.jointP)];
+    verdict = 'DIFFERENT learning rates';
-s = [s sprintf(['  -> small p = groups improve at DIFFERENT rates; ' ...
+else
-    'large p = parallel learning.\n\n'])];
+    verdict = 'parallel learning (no slope difference detected)';
+end
+s = [s sprintf(['Per-subject OLS slope of success vs day: Box-B2 mean=%.2f, Box-A2 mean=%.2f\n' ...
+    '  Welch two-sided p=%.3f, Mann-Whitney p=%.3f (nB=%d, nA=%d)  -> %s\n'], ...
+    R.learn.meanSlopeB, R.learn.meanSlopeA, R.learn.slopeWelchP, R.learn.slopeMWUp, ...
+    R.learn.nB, R.learn.nA, verdict)];
+s = [s sprintf(['(Reference only: the GLMM group x day_c joint F-test gives p=%.4f, but with just\n' ...
+    ' observation-level DF (df2=%.0f) it is ANTICONSERVATIVE for this few-subject design and is\n' ...
+    ' NOT the basis for the conclusion above.)\n\n'], R.learn.glmeJointP, R.learn.glmeJointDF2)];
 end
 
 function s = localCleanDisp(model)

analysis/matlab/tests/tModels.m

@@ -117,5 +117,21 @@ classdef tModels < matlab.unittest.TestCase
             testCase.verifyFalse(metam.isUnmerged);
             testCase.verifyEmpty(fieldnames(Rm.classify));
         end
+
+        function testLearningPerAnimalSlopesParallel(testCase)
+            % The reported learning-rate result is a per-animal slope test and
+            % must show parallel learning (non-significant) -- matching the
+            % Python's cluster-robust conclusion. Guards against regressing to
+            % the anticonservative GLMM interaction F-test (which reads p~=0).
+            cfg = tdcs_config();
+            for sc = {'unmerged_full', 'mergeA2_full', 'mergeB2_full'}
+                [S, meta] = tdcs_scenario_data(sc{1});
+                R = tdcs_models(S, meta, cfg);
+                testCase.verifyGreaterThan(R.learn.slopeMWUp, 0.05, ...
+                    sprintf('%s: per-animal learning slopes should be parallel (MWU p>0.05)', sc{1}));
+                testCase.verifyGreaterThan(R.learn.slopeWelchP, 0.05, ...
+                    sprintf('%s: per-animal learning slopes should be parallel (Welch p>0.05)', sc{1}));
+            end
+        end
     end
 end