============================================================================== tDCS GLM report -- scenario: unmerged_full ============================================================================== merge key: unmerged day window: 0..26 observations: 185 ============================================================================== DESCRIPTIVES ============================================================================== group n_subj n_sessions mean_success mean_rate max_day -------------------------------------------------------------------------- Electrode-Box-B2 3 40 77.0 0.591 14 Electrode-Box-A 1 15 70.7 0.557 14 Electrode-Box-A2 3 31 55.4 0.448 13 Naive 4 76 59.6 0.492 26 Right-Electrode 1 23 85.8 0.627 22 ============================================================================== (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 7 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 567.38 593.14 -275.69 551.38 Fixed effects coefficients (95% CIs): Name Estimate SE tStat DF {'(Intercept)' } 4.5636 0.062818 72.648 178 {'group_Electrode-Box-A' } -0.16366 0.1251 -1.3082 178 {'group_Electrode-Box-A2'} -0.16301 0.090874 -1.7939 178 {'group_Naive' } -0.41017 0.083133 -4.9339 178 {'group_Right-Electrode' } -0.15781 0.12382 -1.2745 178 {'day_c' } 0.10084 0.0023114 43.629 178 {'day_c2' } -0.0064669 0.00024857 -26.016 178 pValue Lower Upper 3.0937e-134 4.4397 4.6876 0.19249 -0.41052 0.083214 0.074534 -0.34234 0.016314 1.8418e-06 -0.57422 -0.24612 0.20416 -0.40216 0.086543 5.5938e-97 0.096281 0.1054 1.4969e-62 -0.0069574 -0.0059764 Random effects covariance parameters: Group: subject (12 Levels) Name1 Name2 Type Estimate {'(Intercept)'} {'(Intercept)'} {'std'} 0.10379 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 7 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 664.34 690.01 -324.17 648.34 Fixed effects coefficients (95% CIs): Name Estimate SE tStat DF {'(Intercept)' } 0.67246 0.11921 5.6411 176 {'group_Electrode-Box-A' } -0.2656 0.23687 -1.1213 176 {'group_Electrode-Box-A2'} -0.42592 0.16928 -2.5161 176 {'group_Naive' } -0.69483 0.15707 -4.4236 176 {'group_Right-Electrode' } -0.19395 0.23547 -0.82369 176 {'day_c' } 0.12539 0.0034255 36.605 176 {'day_c2' } -0.0069542 0.0003534 -19.678 176 pValue Lower Upper 6.6327e-08 0.4372 0.90772 0.26369 -0.73306 0.20187 0.012762 -0.75999 -0.091839 1.6969e-05 -1.0048 -0.38484 0.41123 -0.65866 0.27075 3.2383e-84 0.11863 0.13215 2.5332e-46 -0.0076517 -0.0062568 Random effects covariance parameters: Group: subject (12 Levels) Name1 Name2 Type Estimate {'(Intercept)'} {'(Intercept)'} {'std'} 0.19922 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 11 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 566.35 604.99 -271.17 542.35 Fixed effects coefficients (95% CIs): Name Estimate SE tStat {'(Intercept)' } 4.5639 0.066952 68.167 {'group_Electrode-Box-A' } -0.1538 0.13339 -1.1531 {'group_Electrode-Box-A2' } -0.16353 0.097941 -1.6697 {'group_Naive' } -0.4286 0.088752 -4.8292 {'group_Right-Electrode' } -0.10141 0.13294 -0.76285 {'day_c' } 0.084832 0.0050395 16.833 {'day_c2' } -0.0071091 0.00030673 -23.177 {'group_Electrode-Box-A:day_c' } 0.015434 0.0094241 1.6377 {'group_Electrode-Box-A2:day_c'} 0.010314 0.0089464 1.1529 {'group_Naive:day_c' } 0.031147 0.0065742 4.7377 {'group_Right-Electrode:day_c' } 0.011613 0.007034 1.651 DF pValue Lower Upper 174 1.9324e-127 4.4318 4.6961 174 0.25047 -0.41707 0.10946 174 0.096774 -0.35684 0.029772 174 2.9893e-06 -0.60377 -0.25343 174 0.44659 -0.3638 0.16097 174 2.3384e-38 0.074885 0.094778 174 4.4285e-55 -0.0077145 -0.0065037 174 0.10329 -0.0031665 0.034034 174 0.25055 -0.0073435 0.027971 174 4.4703e-06 0.018171 0.044122 174 0.10054 -0.0022698 0.025496 Random effects covariance parameters: Group: subject (12 Levels) Name1 Name2 Type Estimate {'(Intercept)'} {'(Intercept)'} {'std'} 0.11116 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=7.96, Box-A2 mean=8.19 Welch two-sided p=0.896, Mann-Whitney p=1.000 (nB=3, 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=174) 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 = 1.18x Box-A2 (one-sided p=0.0364) -> SUPPORTED [rate/level ] Box-B2 = 1.53x Box-A2 (one-sided p=0.0059) -> SUPPORTED Per-animal (Box-B2 n=3 vs Box-A2 n=3), pure stats (no GLME): count (per-subject mean success): Welch two-sided p=0.0552, Mann-Whitney one-sided (B2>A2) p=0.0500 rate (per-subject pooled success/total): Welch two-sided p=0.0722, Mann-Whitney one-sided (B2>A2) p=0.0500 Classification -- is each UNKNOWN condition A2-like or B2-like? (ratio >1 = above that anchor; p = differs from that anchor) Electrode-Box-A: [count/level] vs Box-A2: 1.00x p=0.996 vs Box-B2: 0.85x p=0.192 -> AMBIGUOUS (nearer Electrode-Box-A2) [rate/level ] vs Box-A2: 1.17x p=0.501 vs Box-B2: 0.77x p=0.264 -> AMBIGUOUS (nearer Electrode-Box-A2) Right-Electrode: [count/level] vs Box-A2: 1.01x p=0.967 vs Box-B2: 0.85x p=0.204 -> AMBIGUOUS (nearer Electrode-Box-A2) [rate/level ] vs Box-A2: 1.26x p=0.328 vs Box-B2: 0.82x p=0.411 -> AMBIGUOUS (nearer Electrode-Box-B2) NOTE: each unknown has ONLY 1 subject. 'Matches' means 'not statistically distinguishable', weak evidence at n=1, not proof of equivalence. ============================================================================== 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.