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PAPER LME REPLICATION -- mergeA2 (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 = 8 rats, 109 sessions   (day raw; day 0 = paper "Day 1")
day coverage: stim(B2) 0..22, control(A2) 0..14
** 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             109
    Fixed effects coefficients           4
    Random effects coefficients          8
    Covariance parameters                2

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

Model fit statistics:
    AIC       BIC       LogLikelihood    Deviance
    962.68    978.83    -475.34          950.68  

Fixed effects coefficients (95% CIs):
    Name                   Estimate    SE         tStat      DF     pValue    
    {'(Intercept)'}         20.701      4.9127     4.2138    105    5.3256e-05
    {'day'        }         6.8599     0.69872     9.8178    105    1.5726e-16
    {'stim'       }         22.092      6.4372     3.4319    105    0.00085848
    {'day:stim'   }        -2.1793     0.81821    -2.6635    105     0.0089525


    Lower      Upper   
      10.96      30.442
     5.4745      8.2453
     9.3279      34.855
    -3.8016    -0.55692

Random effects covariance parameters (95% CIs):
Group: rat (8 Levels)
    Name1                  Name2                  Type           Estimate  
    {'(Intercept)'}        {'(Intercept)'}        {'std'}        2.1043e-15


    Lower    Upper
    NaN      NaN  

Group: Error
    Name               Estimate    Lower     Upper 
    {'Res Std'}        18.954      16.597    21.644



effect                     t(df) / F(df1)     p (resid)    Satterthwaite: p (df)
----------------------------------------------------------------------------
stim x day (interaction)   t(105)= -2.66 F(1)=  7.094  p=0.008953    p=0.008906 (df=109)
day (learning)             t(105)=  9.82 F(1)= 96.388  p=1.573e-16    p=1.113e-16 (df=109)
stim (main, Day 1)         t(105)=  3.43 F(1)= 11.778  p=0.0008585    p=0.000848 (df=109)
interaction 95% CI: [-3.80, -0.56]

HONEST LME -- per-rat random slope (day|rat): interaction F(1,9.7)=0.11, p=0.746
  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=0.0090, slope diff=-2.18) -> tDCS (Box-B2) improves SLOWER -- groups converge.
  - stim main effect on Day 1 (our day 0): SIGNIFICANT (p=0.0009) -> groups already DIFFER 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.
