============================================================================== tDCS GLM report -- scenario: mergeB2_full ============================================================================== merge key: mergeB2 day window: 0..26 observations: 185 ============================================================================== DESCRIPTIVES ============================================================================== group n_subj n_sessions mean_success mean_rate max_day -------------------------------------------------------------------------- Electrode-Box-B2 5 78 78.4 0.596 22 Electrode-Box-A2 3 31 55.4 0.448 13 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 565.84 585.16 -276.92 553.84 Fixed effects coefficients (95% CIs): Name Estimate SE tStat DF {'(Intercept)' } 4.4986 0.054066 83.206 180 {'group_Electrode-Box-A2'} -0.096187 0.09052 -1.0626 180 {'group_Naive' } -0.34448 0.080981 -4.2538 180 {'day_c' } 0.10082 0.0023113 43.621 180 {'day_c2' } -0.00647 0.00024877 -26.008 180 pValue Lower Upper 1.3263e-145 4.3919 4.6053 0.28939 -0.2748 0.08243 3.3739e-05 -0.50427 -0.18468 1.2306e-97 0.096261 0.10538 7.2052e-63 -0.0069609 -0.0059791 Random effects covariance parameters: Group: subject (12 Levels) Name1 Name2 Type Estimate {'(Intercept)'} {'(Intercept)'} {'std'} 0.1166 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 661.88 681.14 -324.94 649.88 Fixed effects coefficients (95% CIs): Name Estimate SE tStat DF {'(Intercept)' } 0.57975 0.098046 5.913 178 {'group_Electrode-Box-A2'} -0.33262 0.16122 -2.0631 178 {'group_Naive' } -0.60174 0.14641 -4.1098 178 {'day_c' } 0.12534 0.0034238 36.607 178 {'day_c2' } -0.0069519 0.00035349 -19.666 178 pValue Lower Upper 1.6792e-08 0.38627 0.77323 0.040554 -0.65077 -0.014466 6.0348e-05 -0.89067 -0.31281 9.0274e-85 0.11858 0.13209 1.6927e-46 -0.0076494 -0.0062543 Random effects covariance parameters: Group: subject (12 Levels) Name1 Name2 Type Estimate {'(Intercept)'} {'(Intercept)'} {'std'} 0.21289 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 560.22 585.99 -272.11 544.22 Fixed effects coefficients (95% CIs): Name Estimate SE tStat {'(Intercept)' } 4.516 0.055699 81.079 {'group_Electrode-Box-A2' } -0.11558 0.094376 -1.2247 {'group_Naive' } -0.38342 0.083677 -4.5821 {'day_c' } 0.092386 0.0030001 30.794 {'day_c2' } -0.006943 0.00027446 -25.297 {'group_Electrode-Box-A2:day_c'} 0.0036285 0.0081693 0.44417 {'group_Naive:day_c' } 0.022361 0.0042611 5.2476 DF pValue Lower Upper 178 1.781e-142 4.4061 4.6259 178 0.22231 -0.30182 0.070658 178 8.6367e-06 -0.54854 -0.21829 178 3.1867e-73 0.086466 0.098307 178 7.6668e-61 -0.0074846 -0.0064014 178 0.65746 -0.012493 0.01975 178 4.3478e-07 0.013952 0.03077 Random effects covariance parameters: Group: subject (12 Levels) Name1 Name2 Type Estimate {'(Intercept)'} {'(Intercept)'} {'std'} 0.12017 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=6.98, Box-A2 mean=8.19 Welch two-sided p=0.508, Mann-Whitney p=0.786 (nB=5, nA=3) -> 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 = 1.10x Box-A2 (one-sided p=0.1440) -> not supported [rate/level ] Box-B2 = 1.39x Box-A2 (one-sided p=0.0196) -> SUPPORTED Per-animal (Box-B2 n=5 vs Box-A2 n=3), pure stats (no GLME): count (per-subject mean success): Welch two-sided p=0.0204, Mann-Whitney one-sided (B2>A2) p=0.0179 rate (per-subject pooled success/total): Welch two-sided p=0.0440, Mann-Whitney one-sided (B2>A2) p=0.0179 (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.