Continuing with the new regression model. Now it's the discrete dataset.

> summary(model1 <- lmer(score ~ nstates_amp_and_mel_n:phase_order:phase  +  +                  #                    - nstates_amp_and_mel_n - phase_order + +                  (1 | id), data=all, REML=F))fixed-effect model matrix is rank deficient so dropping 4 columns / coefficientsfixed-effect model matrix is rank deficient so dropping 4 columns / coefficientsfixed-effect model matrix is rank deficient so dropping 4 columns / coefficientsfixed-effect model matrix is rank deficient so dropping 4 columns / coefficientsLinear mixed model fit by maximum likelihood  t-tests use  Satterthwaite approximations to degrees of freedom ['merModLmerTest']Formula: score ~ nstates_amp_and_mel_n:phase_order:phase + (1 | id)   Data: all
AIC BIC logLik deviance df.resid  -27.3 -7.6 21.6 -43.3 79
Scaled residuals:  Min 1Q Median 3Q Max -2.5413 -0.4029 0.1231 0.6630 1.5332
Random effects: Groups Name Variance Std.Dev. id (Intercept) 0.01462 0.1209  Residual 0.02550 0.1597 Number of obs: 87, groups: id, 29
Fixed effects: Estimate Std. Error df t value Pr(>|t|) (Intercept) 0.81876 0.03005 33.02000 27.250 <2e-16 ***nstates_amp_and_mel_n:phase_order1st:phase1to1 -0.05299 0.03164 69.37000 -1.675 0.0985 . nstates_amp_and_mel_n:phase_order2nd:phase1to2 0.07556 0.05615 79.25000 1.346 0.1823 nstates_amp_and_mel_n:phase_order3rd:phase1to2 0.04166 0.05101 73.45000 0.817 0.4167 nstates_amp_and_mel_n:phase_order2nd:phase2to2 0.11753 0.04640 75.37000 2.533 0.0134 * nstates_amp_and_mel_n:phase_order3rd:phase2to2 0.09553 0.04987 73.76000 1.916 0.0593 . ---Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Correlation of Fixed Effects: (Intr) n____:_1 n____:_2:1 n____:_3:1 n____:_2:2n____:_1:11 0.243 n____:_2:12 -0.082 0.064 n____:_3:12 -0.119 -0.042 0.009 n____:_2:22 -0.006 0.046 0.005 0.045 n____:_3:22 -0.222 -0.060 0.165 0.027 0.001 fit warnings:fixed-effect model matrix is rank deficient so dropping 4 columns / coefficients

And here's what the coefficients look like:

The most marked difference of this from the coefficients induced from the original dataset is that the second condition's behavior has changed, and is no longer so well compressed. There is a significant increase in number of states from the 2nd to the 3rd phase of the second condition, whereas this increase is non-significant between the same phases of the first condition.

So the discrete meanings reduced the efficiency of the 2:2 phase.

Finally, $$R^2 = 0.6129882$$.

Currently unrated