============================================================================== tDCS GLM report -- scenario: mergeB2_d0_10 ============================================================================== merge key: mergeB2 day window: 0..10 observations: 126 ============================================================================== DESCRIPTIVES ============================================================================== group n_subj n_sessions mean_success mean_rate max_day -------------------------------------------------------------------------- Electrode-Box-B2 5 55 66.4 0.533 10 Electrode-Box-A2 3 28 52.1 0.433 10 Naive 4 43 46.8 0.440 10 ============================================================================== (A) LEVEL / COUNT -- Poisson GLMM (subject random intercept) ============================================================================== Generalized linear mixed-effects model fit by PL Model information: Number of observations 126 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 297.84 314.85 -142.92 285.84 Fixed effects coefficients (95% CIs): Name Estimate SE tStat DF {'(Intercept)' } 4.2369 0.08452 50.129 121 {'group_Electrode-Box-A2'} -0.091837 0.13759 -0.66748 121 {'group_Naive' } -0.39133 0.12596 -3.1068 121 {'day_c' } 0.2019 0.0052735 38.287 121 {'day_c2' } -0.024069 0.0015714 -15.317 121 pValue Lower Upper 8.553e-83 4.0696 4.4042 0.50574 -0.36423 0.18055 0.0023571 -0.64071 -0.14196 1.787e-69 0.19146 0.21235 4.1977e-30 -0.02718 -0.020958 Random effects covariance parameters: Group: subject (12 Levels) Name1 Name2 Type Estimate {'(Intercept)'} {'(Intercept)'} {'std'} 0.18296 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 124 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 364.15 381.07 -176.07 352.15 Fixed effects coefficients (95% CIs): Name Estimate SE tStat DF {'(Intercept)' } 0.11026 0.11374 0.96938 119 {'group_Electrode-Box-A2'} -0.26616 0.18448 -1.4427 119 {'group_Naive' } -0.53698 0.16912 -3.1751 119 {'day_c' } 0.21673 0.0069278 31.283 119 {'day_c2' } -0.013726 0.0021988 -6.2424 119 pValue Lower Upper 0.33432 -0.11496 0.33548 0.15172 -0.63144 0.09913 0.0019073 -0.87186 -0.2021 2.9856e-59 0.20301 0.23044 6.8729e-09 -0.01808 -0.009372 Random effects covariance parameters: Group: subject (12 Levels) Name1 Name2 Type Estimate {'(Intercept)'} {'(Intercept)'} {'std'} 0.24468 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 126 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 304.98 327.67 -144.49 288.98 Fixed effects coefficients (95% CIs): Name Estimate SE tStat {'(Intercept)' } 4.2592 0.082682 51.513 {'group_Electrode-Box-A2' } -0.10296 0.13455 -0.76522 {'group_Naive' } -0.46886 0.1243 -3.7722 {'day_c' } 0.1907 0.0067258 28.354 {'day_c2' } -0.02454 0.0015791 -15.541 {'group_Electrode-Box-A2:day_c'} -0.0023862 0.012062 -0.19783 {'group_Naive:day_c' } 0.045036 0.010729 4.1975 DF pValue Lower Upper 119 3.2785e-83 4.0955 4.423 119 0.44566 -0.36937 0.16346 119 0.00025365 -0.71498 -0.22275 119 9.114e-55 0.17738 0.20402 119 2.0273e-30 -0.027667 -0.021413 119 0.84352 -0.02627 0.021498 119 5.2317e-05 0.023791 0.066281 Random effects covariance parameters: Group: subject (12 Levels) Name1 Name2 Type Estimate {'(Intercept)'} {'(Intercept)'} {'std'} 0.17816 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=9.74, Box-A2 mean=8.96 Welch two-sided p=0.517, Mann-Whitney p=0.571 (nB=5, nA=3) -> parallel learning (no slope difference detected) (Reference only: the GLMM group x day_c joint F-test gives p=0.0001, but with just observation-level DF (df2=119) 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=0.2522) -> not supported [rate/level ] Box-B2 = 1.30x Box-A2 (one-sided p=0.0745) -> not 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=0.0228, Mann-Whitney one-sided (B2>A2) p=0.0179 rate (per-subject pooled success/total): Welch two-sided p=0.0943, Mann-Whitney one-sided (B2>A2) p=0.0714 (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.