============================================================================== tDCS GLM report -- scenario: mergeNaive_full ============================================================================== merge key: mergeNaive 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-A 1 15 70.7 0.557 14 Electrode-Box-A2 7 107 58.4 0.479 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 569.28 588.6 -278.64 557.28 Fixed effects coefficients (95% CIs): Name Estimate SE tStat {'(Intercept)' } 4.5235 0.074032 61.102 {'group_Electrode-Box-A' } -0.12346 0.16529 -0.74694 {'group_Electrode-Box-A2'} -0.26481 0.093039 -2.8462 {'day_c' } 0.10065 0.0023081 43.608 {'day_c2' } -0.0064638 0.00024915 -25.944 DF pValue Lower Upper 180 2.6809e-122 4.3774 4.6696 180 0.45607 -0.44962 0.2027 180 0.0049387 -0.44839 -0.081217 180 1.2924e-97 0.096096 0.10521 180 1.0244e-62 -0.0069555 -0.0059722 Random effects covariance parameters: Group: subject (12 Levels) Name1 Name2 Type Estimate {'(Intercept)'} {'(Intercept)'} {'std'} 0.14464 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 663.16 682.41 -325.58 651.16 Fixed effects coefficients (95% CIs): Name Estimate SE tStat {'(Intercept)' } 0.62291 0.11692 5.3275 {'group_Electrode-Box-A' } -0.21631 0.26048 -0.83042 {'group_Electrode-Box-A2'} -0.5314 0.14632 -3.6318 {'day_c' } 0.12505 0.003415 36.618 {'day_c2' } -0.0069489 0.00035361 -19.651 DF pValue Lower Upper 178 2.981e-07 0.39218 0.85365 178 0.40742 -0.73034 0.29772 178 0.00036793 -0.82014 -0.24265 178 8.6013e-85 0.11831 0.13179 178 1.8602e-46 -0.0076467 -0.0062511 Random effects covariance parameters: Group: subject (12 Levels) Name1 Name2 Type Estimate {'(Intercept)'} {'(Intercept)'} {'std'} 0.22797 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 561.97 587.73 -272.98 545.97 Fixed effects coefficients (95% CIs): Name Estimate SE tStat {'(Intercept)' } 4.5372 0.083001 54.664 {'group_Electrode-Box-A' } -0.13394 0.18535 -0.72264 {'group_Electrode-Box-A2' } -0.27771 0.10424 -2.6641 {'day_c' } 0.090249 0.0032246 27.988 {'day_c2' } -0.0066704 0.00025769 -25.885 {'group_Electrode-Box-A:day_c' } 0.010369 0.0086089 1.2044 {'group_Electrode-Box-A2:day_c'} 0.020125 0.0041158 4.8897 DF pValue Lower Upper 178 3.3741e-113 4.3734 4.701 178 0.47085 -0.4997 0.23182 178 0.0084289 -0.48341 -0.071999 178 4.2889e-67 0.083886 0.096613 178 3.0498e-62 -0.0071789 -0.0061619 178 0.23002 -0.0066197 0.027358 178 2.2462e-06 0.012003 0.028247 Random effects covariance parameters: Group: subject (12 Levels) Name1 Name2 Type Estimate {'(Intercept)'} {'(Intercept)'} {'std'} 0.16287 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=6.25 Welch two-sided p=0.689, Mann-Whitney p=0.527 (nB=4, nA=7) -> 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 = 1.30x Box-A2 (one-sided p=0.0022) -> SUPPORTED [rate/level ] Box-B2 = 1.70x Box-A2 (one-sided p=0.0001) -> SUPPORTED Per-animal (Box-B2 n=4 vs Box-A2 n=7), pure stats (no GLME): count (per-subject mean success): Welch two-sided p=0.0158, Mann-Whitney one-sided (B2>A2) p=0.0030 rate (per-subject pooled success/total): Welch two-sided p=0.0207, Mann-Whitney one-sided (B2>A2) p=0.0030 (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.