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PAPER LME REPLICATION -- mergeNaive (full range)
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model: behavior ~ stim + day + stim:day + (1|rat)   [stim: Electrode-Box-B2=1 vs Electrode-Box-A2=0]
behavior = successful reaches (COUNT per session)
N = 11 rats, 170 sessions   (day raw; day 0 = paper "Day 1")
day coverage: stim(B2) 0..22, control(A2) 0..26
** WARNING: unequal day coverage -- the full-range stim:day interaction
   extrapolates the control group's line and is CONFOUNDED here (the paper's
   groups had equal coverage). See the _d0_13 fair-window and phased analyses. **

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FULL MODEL SUMMARY -- fitlme: behavior ~ stim + day + stim:day + (1|rat)
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Linear mixed-effects model fit by ML

Model information:
    Number of observations             170
    Fixed effects coefficients           4
    Random effects coefficients         11
    Covariance parameters                2

Formula:
    behavior ~ 1 + day*stim + (1 | rat)

Model fit statistics:
    AIC       BIC       LogLikelihood    Deviance
    1526.4    1545.2    -757.2           1514.4  

Fixed effects coefficients (95% CIs):
    Name                   Estimate    SE         tStat     DF     pValue    
    {'(Intercept)'}        30.553       4.7932    6.3742    166    1.7469e-09
    {'day'        }        3.5345      0.33399    10.583    166    2.5084e-20
    {'stim'       }        10.155       8.0021    1.2691    166        0.2062
    {'day:stim'   }        1.5835      0.58611    2.7018    166     0.0076138


    Lower      Upper 
     21.089    40.016
     2.8751    4.1939
    -5.6439    25.954
    0.42633    2.7407

Random effects covariance parameters (95% CIs):
Group: rat (11 Levels)
    Name1                  Name2                  Type           Estimate
    {'(Intercept)'}        {'(Intercept)'}        {'std'}        9.2449  


    Lower    Upper 
    5.388    15.863

Group: Error
    Name               Estimate    Lower     Upper 
    {'Res Std'}        19.866      17.802    22.168



effect                     t(df) / F(df1)     p (resid)    Satterthwaite: p (df)
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stim x day (interaction)   t(166)=  2.70 F(1)=  7.299  p=0.007614    p=0.007598 (df=170)
day (learning)             t(166)= 10.58 F(1)=111.990  p=2.508e-20    p=2.011e-20 (df=170)
stim (main, Day 1)         t(166)=  1.27 F(1)=  1.611  p=0.2062    p=0.217 (df=23)
interaction 95% CI: [+0.43, +2.74]

HONEST LME -- per-rat random slope (day|rat): interaction F(1,11.4)=0.92, p=0.3565
  Satterthwaite DF on the random-INTERCEPT model above stays ~= residual (the
  slope's error is at session level), so it does NOT fix pseudoreplication. A per-animal
  random slope collapses the interaction DF toward the animal count -- the honest test.

INTERPRETATION
  - stim x day interaction: SIGNIFICANT (p=0.0076, slope diff=+1.58) -> tDCS (Box-B2) improves FASTER -- benefit accumulates over training.
  - stim main effect on Day 1 (our day 0): n.s. (p=0.2062) -> groups are comparable on Day 1.

Paper (N=24): interaction t(227)=2.68, F(1)=7.12, p=0.008; day t(227)=9.64,
  F(1)=267.64, p=1.2e-18; stim t(227)=0.23, F(1)=0.053, p=0.81.