[R-lang] Re: Main effects of categorical predictors in lmer

[Finlayson, Ian]

Hi Hossein,

 

As far as I can see, neither model is correct. If B is a predictor with
three levels then the model should contain 6 fixed effects: An
intercept, A, B1 compared to B2, B1 compared to B3, B1 compared to B2
interacting with A, and B1 compared to B3 interacting with A.

 

What I suspect you've done is actually enter B as a continuous predictor
with a mean of zero (since you used scale()). You'll need to keep B as a
factor, but give it appropriate contrasts:

 

B <- factor(B) # Make sure it's a factor

contrasts(B) <- contr.sum(3) # Generate a 3 level contrast matrix using
sum coding; alternative contr.helmert(3) for Helmhert coding

 

Then build your models.

 

It's possible that it won't set the right level as a baseline (the
baseline will be whichever is a row of -1). If so then you'll need to
manually set up the matrix. For sum coding, something like:

 

contrasts(B) <- cbind(c(-1,0,1),c(-1,1,0)) # Assuming that B1 is the
first row in contrasts(B) - double check!

 

I'd also do something similar with A so that your estimates are
comparable (if you've centered 0 and 1, then it'll come out -.5 and .5,
rather than -1 and 1)

 

HTH,

 

Ian

 

 

 

 

From: ling-r-lang-l-bounces@mailman.ucsd.edu
[mailto:ling-r-lang-l-bounces@mailman.ucsd.edu] On Behalf Of hossein
karimi
Sent: 10 October 2011 15:05
To: ling-r-lang-l@mailman.ucsd.edu
Subject: [R-lang] Main effects of categorical predictors in lmer

 

Dear R users,

I'm using mixed effects models (lmer) to predict a binary dependent
variable as a function of 1.a categorical predictor (A)with 2 levels (A1
and A2) , 2. another categorical predictor (B) with three levels (B1, B2
and B3) and 3. The interaction between these two predictors. I have
tried two models but they return different results and I'm not sure
which one is correct. I'm interested in the main effect of B and the
interaction between A and B (because A alone has a significant effect in
both models). My problem is that there seem to be two sensible ways of
examining the main effect of B: 1. to helmert code and 2. to center.
But these two methods produce opposite results! I don't know which one I
should use. Here are the two models with some details and their outputs:

 

Model 1: 'A' is centered. 'B' is helmert coded ('B1'(baseline)=2,
'B2'=-1, 'B3'=-1) so that I can get a main effect of B by checking to
see whether baseline condition in B differs from the mean of B1 and B2 .
The lmer output returns a significant effect of B and no significant AxB
interaction. However, as is highlighted below (in pink), the correlation
between B and the 'AxB' interaction is high (-54%).  

 

> model.1<-lmer(response~A*B+(A+1|sub)+(1|item), mydata,
family="binomial")

> print(model.1)

Generalized linear mixed model fit by the Laplace approximation 

Formula: response ~ A * B+ (A + 1 | sub) + (1 | item) 

   Data: mydata

AIC   BIC logLik deviance

783 822.6 -383.5      767

Random effects:

Groups Name        Variance Std.Dev. Corr  

 item   (Intercept) 0.7293   0.85399        

 sub    (Intercept) 2.0871   1.44468        

        A          1.3812   1.17524  0.562 

Number of obs: 1038, groups: item, 42; sub, 36

 

Fixed effects:

                  Estimate Std. Error z value Pr(>|z|)    

(Intercept)        1.05261    0.30283   3.476 0.000509 ***

A                -3.91080    0.32239 -12.131  < 2e-16 ***

B                  0.36128    0.09751   3.705 0.000211 ***

A:B            -0.29638    0.18681  -1.586 0.112626    

---

Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

 

Correlation of Fixed Effects:

                        (Intr)   A      B

A                  0.155              

B                  0.160 -0.278       

A:B              -0.156  0.238 -0.540

 

Model 2: 'A' and 'B' are both centered. The lmer output returns no
significant effect of B but the A:B interaction is significant. The
correlations between predictors are generally lower and the correlation
between B and A:B is reduced to -26%. 

 

Generalized linear mixed model fit by the Laplace approximation 

Formula: resonse ~ A * B + (A + 1 | sub) + (1 | item) 

   Data: mydata 

   AIC   BIC logLik deviance

756.1 795.7 -370.1    740.1

Random effects:

Groups Name        Variance Std.Dev. Corr  

 item   (Intercept) 0.87028  0.93289        

 sub    (Intercept) 2.41707  1.55469        

        A         1.23669  1.11206  0.533 

Number of obs: 1038, groups: item, 42; sub, 36

 

Fixed effects:

                Estimate Std. Error z value Pr(>|z|)    

(Intercept)       1.1004     0.3239   3.398 0.000679 ***

A               -4.0941     0.3248 -12.605  < 2e-16 ***

B                -0.1461     0.1400  -1.043 0.296851    

A:B             1.7923     0.2818   6.360 2.01e-10 ***

---

Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

 

Correlation of Fixed Effects:

                       (Intr)      A        B

A                    0.138              

B                   -0.148  0.185       

A:B                0.106 -0.292 -0.265

 

I personally think Model 2 is better but the thing is that I have
centered a categorical predictor with three levels. In my searches in
the web, I have never seen a three-level predictor to be centered; they
were all two-level categorical predictors. 

I have used the scale() function to center the predictors (I first
converted them to numeric variables and then used the scale () function
to center them). As I mentioned, my problem is that I don't know how to
get a main effect of B as well as a main A:B interaction. On the one
hand, it seems logical to compare 'B1' (baseline) with the mean of the
other two B conditions to see if the B manipulation has a general
effect. On the other hand, I hear that one needs to center variables to
get a main effect. 

 

I would be grateful of you could please help me

 

Regards,

 

Hossein

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