[R-lang] Removing the correlation parameter

[Zhenguang Cai]

Hi all,

Barr et al. (2013) recommended a design-driven (i.e., maximal random 
structure) approach for LME. However, as some of you may have 
experienced, LME with maximal random structure on categorical data would 
often result in non-convergence. Barr et al. recommended, in these 
cases, removing the correlation parameter (i.e., correlation between a 
random intercept and the corresponding random slope). However, I found 
that Barr et al. (e.g., p.262, Table 1) and Baayen et al. (2008, p.395) 
used different R scripts to do this. I wonder which is the correct way 
to do. I use my own example below.

Barr et al: (But still correlations between levels of the fixed 
predictor in the results)
Generalized linear mixed model fit by the Laplace approximation
Formula: ResponseC ~ Prime + (1 | Subject) + (0 + Prime | Subject) + (1 
|      Item) + (0 + Prime | Item)
    Data: E1
    AIC   BIC logLik deviance
  798.3 876.1 -382.1    764.3
Random effects:
  Groups  Name        Variance   Std.Dev.   Corr
  Subject PrimeC      1.2124e+00 1.1011e+00
          PrimeE      1.4114e+00 1.1880e+00 0.583
          PrimeF      1.2177e+00 1.1035e+00 0.737  0.979
  Subject (Intercept) 1.7926e-02 1.3389e-01
  Item    PrimeC      2.1542e-09 4.6413e-05
          PrimeE      4.6549e-02 2.1575e-01 -0.001
          PrimeF      3.3489e-03 5.7870e-02  0.000  1.000
  Item    (Intercept) 2.7090e+00 1.6459e+00
Number of obs: 720, groups: Subject, 35; Item, 24

Fixed effects:
             Estimate Std. Error z value Pr(>|z|)
(Intercept)  -0.2973     0.4257  -0.698   0.4849
PrimeE        0.5507     0.3044   1.809   0.0705 .
PrimeF        1.3644     0.2787   4.896  9.8e-07 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
        (Intr) PrimeE
PrimeE -0.348
PrimeF -0.350  0.674


Baayen et al: (here the correlations are gone)
Formula: ResponseC ~ Prime + (1 | Subject) + (1 | Prime:Subject) + (1 
|      Item) + (1 | Prime:Item)
    Data: E1
    AIC   BIC logLik deviance
  781.7 813.7 -383.8    767.7
Random effects:
  Groups        Name        Variance Std.Dev.
  Prime:Subject (Intercept) 0.16358  0.40445
  Prime:Item    (Intercept) 0.00000  0.00000
  Subject       (Intercept) 1.02334  1.01160
  Item          (Intercept) 2.62534  1.62029
Number of obs: 720, groups: Prime:Subject, 105; Prime:Item, 72; Subject, 
35; Item, 24

Fixed effects:
             Estimate Std. Error z value Pr(>|z|)
(Intercept)  -0.2984     0.4196  -0.711   0.4769
PrimeE        0.5401     0.2595   2.081   0.0374 *
PrimeF        1.3539     0.2605   5.197 2.03e-07 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
        (Intr) PrimeE
PrimeE -0.334
PrimeF -0.336  0.54


Thanks,
Zhenguang Cai