============================================================================== tDCS GLM report -- scenario: mergeA2_full ============================================================================== merge key: mergeA2 day window: 0..26 observations: 185 ============================================================================== DESCRIPTIVES ============================================================================== group n_subj n_sessions mean_success mean_rate max_day -------------------------------------------------------------------------- Electrode-Box-B2 4 63 80.2 0.605 22 Electrode-Box-A2 4 46 60.4 0.484 14 Naive 4 76 59.6 0.492 26 ============================================================================== (A) LEVEL / COUNT -- Poisson GLMM (subject random intercept) ============================================================================== Generalized linear mixed-effects model fit by PL Model information: Number of observations 185 Fixed effects coefficients 5 Random effects coefficients 12 Covariance parameters 1 Distribution Poisson Link Log FitMethod MPL Formula: success ~ 1 + group + day_c + day_c2 + (1 | subject) Model fit statistics: AIC BIC LogLikelihood Deviance 564.95 584.27 -276.47 552.95 Fixed effects coefficients (95% CIs): Name Estimate SE tStat DF {'(Intercept)' } 4.5232 0.058089 77.867 180 {'group_Electrode-Box-A2'} -0.1219 0.083374 -1.4621 180 {'group_Naive' } -0.36897 0.082023 -4.4984 180 {'day_c' } 0.10078 0.002307 43.684 180 {'day_c2' } -0.0064744 0.00024857 -26.047 180 pValue Lower Upper 1.4699e-140 4.4086 4.6379 0.14547 -0.28641 0.042619 1.2247e-05 -0.53082 -0.20712 9.6816e-98 0.096227 0.10533 5.8173e-63 -0.0069649 -0.0059839 Random effects covariance parameters: Group: subject (12 Levels) Name1 Name2 Type Estimate {'(Intercept)'} {'(Intercept)'} {'std'} 0.11179 Group: Error Name Estimate {'sqrt(Dispersion)'} 1 ============================================================================== (B) LEVEL / RATE -- Binomial GLMM (subject random intercept) ============================================================================== Generalized linear mixed-effects model fit by PL Model information: Number of observations 183 Fixed effects coefficients 5 Random effects coefficients 12 Covariance parameters 1 Distribution Binomial Link Logit FitMethod MPL Formula: success ~ 1 + group + day_c + day_c2 + (1 | subject) Model fit statistics: AIC BIC LogLikelihood Deviance 661.66 680.91 -324.83 649.66 Fixed effects coefficients (95% CIs): Name Estimate SE tStat DF {'(Intercept)' } 0.62325 0.10794 5.7739 178 {'group_Electrode-Box-A2'} -0.33496 0.15306 -2.1884 178 {'group_Naive' } -0.64512 0.15201 -4.2441 178 {'day_c' } 0.12541 0.0034219 36.649 178 {'day_c2' } -0.0069611 0.00035344 -19.695 178 pValue Lower Upper 3.3843e-08 0.41024 0.83626 0.029941 -0.63701 -0.032914 3.5275e-05 -0.94509 -0.34516 7.5329e-85 0.11866 0.13216 1.4145e-46 -0.0076585 -0.0062636 Random effects covariance parameters: Group: subject (12 Levels) Name1 Name2 Type Estimate {'(Intercept)'} {'(Intercept)'} {'std'} 0.20951 Group: Error Name Estimate {'sqrt(Dispersion)'} 1 ============================================================================== (C) LEARNING RATE -- Poisson GLMM (group x day interaction) ============================================================================== Generalized linear mixed-effects model fit by PL Model information: Number of observations 185 Fixed effects coefficients 7 Random effects coefficients 12 Covariance parameters 1 Distribution Poisson Link Log FitMethod MPL Formula: success ~ 1 + day_c2 + group*day_c + (1 | subject) Model fit statistics: AIC BIC LogLikelihood Deviance 557.88 583.64 -270.94 541.88 Fixed effects coefficients (95% CIs): Name Estimate SE tStat {'(Intercept)' } 4.5419 0.060057 75.626 {'group_Electrode-Box-A2' } -0.13686 0.086298 -1.5859 {'group_Naive' } -0.41002 0.085075 -4.8196 {'day_c' } 0.090967 0.0032463 28.021 {'day_c2' } -0.0068957 0.0002769 -24.904 {'group_Electrode-Box-A2:day_c'} 0.0071293 0.0064228 1.11 {'group_Naive:day_c' } 0.023329 0.0043517 5.3609 DF pValue Lower Upper 178 3.0366e-137 4.4233 4.6604 178 0.11453 -0.30716 0.033436 178 3.0699e-06 -0.57791 -0.24214 178 3.6033e-67 0.084561 0.097373 178 6.7558e-60 -0.0074422 -0.0063493 178 0.2685 -0.0055454 0.019804 178 2.5437e-07 0.014742 0.031917 Random effects covariance parameters: Group: subject (12 Levels) Name1 Name2 Type Estimate {'(Intercept)'} {'(Intercept)'} {'std'} 0.11568 Group: Error Name Estimate {'sqrt(Dispersion)'} 1 Per-animal OLS slope test (Box-B2 vs Box-A2), cluster-honest: Per-subject OLS slope of success vs day: Box-B2 mean=6.92, Box-A2 mean=7.95 Welch two-sided p=0.531, Mann-Whitney p=0.886 (nB=4, nA=4) -> parallel learning (no slope difference detected) (Reference only: the GLMM group x day_c joint F-test gives p=0.0000, but with just observation-level DF (df2=178) it is ANTICONSERVATIVE for this few-subject design and is NOT the basis for the conclusion above.) ============================================================================== INTERPRETATION ============================================================================== Note: these are subject-level GLMMs (Laplace-approximated fitglme), not the Python reference's population-average GEE -- directions/magnitudes should agree, exact ratios and p-values will differ. Anchor check -- H2: Box-B2 BETTER than Box-A2 (the two anchors must differ) [count/level] Box-B2 = 1.13x Box-A2 (one-sided p=0.0719) -> not supported [rate/level ] Box-B2 = 1.40x Box-A2 (one-sided p=0.0143) -> SUPPORTED Per-animal (Box-B2 n=4 vs Box-A2 n=4), pure stats (no GLME): count (per-subject mean success): Welch two-sided p=0.0348, Mann-Whitney one-sided (B2>A2) p=0.0286 rate (per-subject pooled success/total): Welch two-sided p=0.0555, Mann-Whitney one-sided (B2>A2) p=0.0286 (No unknown groups -- they were merged into the anchors; only the H2 anchor contrast applies.) ============================================================================== CAVEATS ============================================================================== - Tiny groups: each arm has only n=3-4 subjects (Naive n=4; anchor arms n=3-5 depending on merge), and -- in unmerged scenarios -- each unknown condition (Electrode-Box-A, Right-Electrode) has only n=1 subject. Treat every group comparison here as preliminary. - Single-subject classification: for a 1-subject unknown, 'matches anchor X' means 'not statistically distinguishable from X', NOT proof of equivalence; inference with a single subject in a group is fragile. - Count vs rate: 'success' alone is a raw count; the rate model (success/attempts) is the fairer accuracy comparison when attempt counts differ between groups.