[R-lang] Re: Collinearity and how to decide what predictors to include

[Xiao He]

Hi Alex,

Thank you for the explanations. I have one more question regarding
centering. I attempted centering, but found that it did not remove two
predictors' correlations. Two examples are shown below. As you can see, the
correlation between aoa and ls is the same as that between caoa and cls,
namely, it is 0.527. I wonder if I did something wrong. Thank you in
advance!

For example:
before centering
> lmer(n1~aoa + ls + (1|subject) + (1|word), cpn, family="binomial")
Generalized linear mixed model fit by the Laplace approximation
Formula: n1 ~ aoa + ls + (1 | subject) + (1 | word)
   Data: cpn
   AIC BIC logLik deviance
 345.1 364 -167.6    335.1
Random effects:
 Groups  Name        Variance Std.Dev.
 word    (Intercept) 5.03699  2.24432
 subject (Intercept) 0.21577  0.46451
Number of obs: 321, groups: word, 24; subject, 15

Fixed effects:
            Estimate Std. Error z value Pr(>|z|)
(Intercept)  0.08425    0.93113   0.090    0.928
aoa         -0.02672    0.02599  -1.028    0.304
ls           0.01771    0.03361   0.527    0.598

Correlation of Fixed Effects:
    (Intr) aoa
aoa -0.761
ls  -0.706  *0.527*


After centering:
> lmer(n1~caoa + cls + (1|subject) + (1|word), cpn, family="binomial")
Generalized linear mixed model fit by the Laplace approximation
Formula: n1 ~ caoa + cls + (1 | subject) + (1 | word)
   Data: cpn
   AIC BIC logLik deviance
 345.1 364 -167.6    335.1
Random effects:
 Groups  Name        Variance Std.Dev.
 word    (Intercept) 5.03699  2.24432
 subject (Intercept) 0.21577  0.46451
Number of obs: 321, groups: word, 24; subject, 15

Fixed effects:
            Estimate Std. Error z value Pr(>|z|)
(Intercept) -0.22650    0.50370  -0.450    0.653
caoa        -0.02672    0.02599  -1.028    0.304
cls          0.01771    0.03361   0.527    0.598

Correlation of Fixed Effects:
     (Intr) caoa
caoa 0.004
cls  0.001  *0.527 *
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