============================================================================== tDCS GLM report -- scenario: mergeA2_d0_10 ============================================================================== merge key: mergeA2 day window: 0..10 observations: 126 ============================================================================== DESCRIPTIVES ============================================================================== group n_subj n_sessions mean_success mean_rate max_day -------------------------------------------------------------------------- Electrode-Box-B2 4 44 68.3 0.541 10 Electrode-Box-A2 4 39 54.0 0.452 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 297.29 314.31 -142.65 285.29 Fixed effects coefficients (95% CIs): Name Estimate SE tStat DF {'(Intercept)' } 4.2656 0.092258 46.236 121 {'group_Electrode-Box-A2'} -0.12664 0.12996 -0.97447 121 {'group_Naive' } -0.41983 0.12988 -3.2324 121 {'day_c' } 0.20187 0.0052718 38.293 121 {'day_c2' } -0.024068 0.0015714 -15.317 121 pValue Lower Upper 9.3543e-79 4.083 4.4483 0.33177 -0.38392 0.13065 0.0015818 -0.67696 -0.1627 1.7547e-69 0.19144 0.21231 4.2028e-30 -0.027179 -0.020957 Random effects covariance parameters: Group: subject (12 Levels) Name1 Name2 Type Estimate {'(Intercept)'} {'(Intercept)'} {'std'} 0.17893 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 363.74 380.67 -175.87 351.74 Fixed effects coefficients (95% CIs): Name Estimate SE tStat DF {'(Intercept)' } 0.15282 0.1244 1.2285 119 {'group_Electrode-Box-A2'} -0.28467 0.17474 -1.6291 119 {'group_Naive' } -0.57945 0.17473 -3.3162 119 {'day_c' } 0.21677 0.0069268 31.294 119 {'day_c2' } -0.013732 0.0021989 -6.2451 119 pValue Lower Upper 0.22169 -0.0935 0.39915 0.10595 -0.63068 0.061343 0.0012101 -0.92543 -0.23346 2.8838e-59 0.20305 0.23048 6.7844e-09 -0.018086 -0.0093781 Random effects covariance parameters: Group: subject (12 Levels) Name1 Name2 Type Estimate {'(Intercept)'} {'(Intercept)'} {'std'} 0.23963 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 304.66 327.35 -144.33 288.66 Fixed effects coefficients (95% CIs): Name Estimate SE tStat {'(Intercept)' } 4.2968 0.091824 46.794 {'group_Electrode-Box-A2' } -0.15174 0.12947 -1.172 {'group_Naive' } -0.50686 0.13029 -3.8902 {'day_c' } 0.18436 0.0072535 25.417 {'day_c2' } -0.024459 0.001577 -15.509 {'group_Electrode-Box-A2:day_c'} 0.014228 0.010876 1.3082 {'group_Naive:day_c' } 0.051203 0.011091 4.6167 DF pValue Lower Upper 119 1.7772e-78 4.115 4.4786 119 0.24354 -0.4081 0.10462 119 0.00016554 -0.76486 -0.24887 119 6.5517e-50 0.17 0.19872 119 2.3835e-30 -0.027581 -0.021336 119 0.19332 -0.0073071 0.035763 119 9.9271e-06 0.029242 0.073164 Random effects covariance parameters: Group: subject (12 Levels) Name1 Name2 Type Estimate {'(Intercept)'} {'(Intercept)'} {'std'} 0.17742 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=9.71, Box-A2 mean=9.18 Welch two-sided p=0.556, Mann-Whitney p=0.686 (nB=4, nA=4) -> 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 = 1.14x Box-A2 (one-sided p=0.1649) -> not supported [rate/level ] Box-B2 = 1.33x Box-A2 (one-sided p=0.0517) -> not 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=0.0230, Mann-Whitney one-sided (B2>A2) p=0.0143 rate (per-subject pooled success/total): Welch two-sided p=0.0689, Mann-Whitney one-sided (B2>A2) p=0.0571 (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.