============================================================================== tDCS GLM report -- scenario: unmerged_d0_10 ============================================================================== merge key: unmerged day window: 0..10 observations: 126 ============================================================================== DESCRIPTIVES ============================================================================== group n_subj n_sessions mean_success mean_rate max_day -------------------------------------------------------------------------- Electrode-Box-B2 3 33 70.0 0.555 10 Electrode-Box-A 1 11 58.9 0.499 10 Electrode-Box-A2 3 28 52.1 0.433 10 Naive 4 43 46.8 0.440 10 Right-Electrode 1 11 63.4 0.499 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 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 301.01 323.7 -142.51 285.01 Fixed effects coefficients (95% CIs): Name Estimate SE tStat DF {'(Intercept)' } 4.2892 0.10522 40.765 119 {'group_Electrode-Box-A' } -0.16759 0.20935 -0.80052 119 {'group_Electrode-Box-A2'} -0.14442 0.14887 -0.97013 119 {'group_Naive' } -0.44336 0.13882 -3.1938 119 {'group_Right-Electrode' } -0.094696 0.20909 -0.45289 119 {'day_c' } 0.20188 0.0052727 38.287 119 {'day_c2' } -0.024069 0.0015714 -15.317 119 pValue Lower Upper 9.1655e-72 4.0809 4.4976 0.425 -0.58213 0.24695 0.33395 -0.43919 0.15035 0.0017973 -0.71824 -0.16848 0.65145 -0.50872 0.31933 9.4346e-69 0.19144 0.21232 6.4425e-30 -0.02718 -0.020957 Random effects covariance parameters: Group: subject (12 Levels) Name1 Name2 Type Estimate {'(Intercept)'} {'(Intercept)'} {'std'} 0.17716 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 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 366.74 389.3 -175.37 350.74 Fixed effects coefficients (95% CIs): Name Estimate SE tStat DF {'(Intercept)' } 0.21772 0.13736 1.585 117 {'group_Electrode-Box-A' } -0.27791 0.2726 -1.0195 117 {'group_Electrode-Box-A2'} -0.37423 0.19356 -1.9334 117 {'group_Naive' } -0.64393 0.18075 -3.5625 117 {'group_Right-Electrode' } -0.25889 0.27218 -0.95118 117 {'day_c' } 0.21668 0.0069264 31.283 117 {'day_c2' } -0.013737 0.0021988 -6.2475 117 pValue Lower Upper 0.11567 -0.054325 0.48976 0.31008 -0.81779 0.26196 0.0556 -0.75756 0.0091015 0.0005325 -1.0019 -0.28596 0.34348 -0.79792 0.28014 1.1453e-58 0.20296 0.2304 6.9755e-09 -0.018092 -0.0093824 Random effects covariance parameters: Group: subject (12 Levels) Name1 Name2 Type Estimate {'(Intercept)'} {'(Intercept)'} {'std'} 0.22892 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 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 305.19 339.23 -140.6 281.19 Fixed effects coefficients (95% CIs): Name Estimate SE tStat {'(Intercept)' } 4.3338 0.10278 42.165 {'group_Electrode-Box-A' } -0.23805 0.20569 -1.1574 {'group_Electrode-Box-A2' } -0.17701 0.14533 -1.218 {'group_Naive' } -0.54258 0.13655 -3.9736 {'group_Right-Electrode' } -0.15185 0.20519 -0.74005 {'day_c' } 0.17638 0.0080904 21.802 {'day_c2' } -0.024639 0.0015803 -15.591 {'group_Electrode-Box-A:day_c' } 0.044079 0.016893 2.6093 {'group_Electrode-Box-A2:day_c'} 0.011922 0.012896 0.92443 {'group_Naive:day_c' } 0.059567 0.011689 5.0961 {'group_Right-Electrode:day_c' } 0.036369 0.016336 2.2263 DF pValue Lower Upper 115 8.6925e-72 4.1302 4.5374 115 0.24953 -0.64548 0.16937 115 0.22572 -0.46489 0.11086 115 0.00012391 -0.81305 -0.27211 115 0.46078 -0.5583 0.25459 115 1.1738e-42 0.16036 0.19241 115 3.8845e-30 -0.027769 -0.021509 115 0.010278 0.010617 0.07754 115 0.3572 -0.013623 0.037467 115 1.3744e-06 0.036414 0.08272 115 0.027945 0.00401 0.068729 Random effects covariance parameters: Group: subject (12 Levels) Name1 Name2 Type Estimate {'(Intercept)'} {'(Intercept)'} {'std'} 0.17214 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=9.52, Box-A2 mean=8.96 Welch two-sided p=0.643, Mann-Whitney p=0.700 (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=115) 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 = 1.16x Box-A2 (one-sided p=0.1660) -> not supported [rate/level ] Box-B2 = 1.45x Box-A2 (one-sided p=0.0266) -> 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=0.0414, Mann-Whitney one-sided (B2>A2) p=0.0500 rate (per-subject pooled success/total): Welch two-sided p=0.0702, 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: 0.98x p=0.912 vs Box-B2: 0.85x p=0.425 -> AMBIGUOUS (nearer Electrode-Box-A2) [rate/level ] vs Box-A2: 1.10x p=0.725 vs Box-B2: 0.76x p=0.310 -> AMBIGUOUS (nearer Electrode-Box-A2) Right-Electrode: [count/level] vs Box-A2: 1.05x p=0.813 vs Box-B2: 0.91x p=0.651 -> AMBIGUOUS (nearer Electrode-Box-A2) [rate/level ] vs Box-A2: 1.12x p=0.673 vs Box-B2: 0.77x p=0.343 -> AMBIGUOUS (nearer Electrode-Box-A2) 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.