# [R-sig-ME] Orthogonal vs. Non-orthogonal contrasts

Yasuaki SHINOHARA y.shinohara at aoni.waseda.jp
Wed May 25 04:42:10 CEST 2016

```Dear all,

Hello, I am doing research of second language acquisition.
I am wondering about the glmer in R for my analyses. Could you please

I have the following logistic mixed effects model.
model<-glmer(corr ~ A + B + C + D + A:B + B:C + A:D +(1+A|subject) +
(1+A|item:speaker),family=binomial,data=mydata,control=glmerControl(optimizer="bobyqa",
optCtrl=list(maxfun=1000)))

I tested language learners (subjects) three time (pre-training,
mid-training, post-training) with the "item" produced by "speaker", so
Factor A is "testing block" which has three levels (i.e., pre, mid,
post).
Since each subject took the test three times, the random slopes for
the Factor A were also included as a random factor.

I made an orthogonal contrast for the Factor A (testing block) as
follows.
PreVsMid<-c(1,-1,0)
PreMidVsPost<-c(1,1,-2)
contrasts(mydata\$A)<-cbind(PreVsMid,PreMidVsPost)

The results from summary(model) function for this factor were as
follows.
pre vs. mid test: β = 0.22, SE = 0.05, z = 4.34, p < 0.001
pre & mid vs. post test: β = -0.21, SE = 0.04, z = -5.96, p < 0.001.

However, I thought it would be better if I made a non-orthogonal
contrast for this factor as "pre vs. mid" and "pre vs. post" to test
my hypothesis. So I made a new contrast for the Factor A as follows.
PreVsMid<-c(1,-1,0)
PreVsPost<-c(1,0,-1)
contrasts(mydata\$A)<-cbind(PreVsMid,PreVsPost)

The results from summary(model) function for this contrast were
pre vs. mid test: β = -0.01, SE = 0.04, z = -0.14, p > 0.05 (=0.89),
pre vs. post test: β = 0.42, SE = 0.07, z = 5.96, p < 0.001.

Although the first contrast (pre vs. mid) is the same for both models,
why the results of pre vs. mid contrast are so different (one is very
significant, but the other one is not significant)?

I really appreciate any help.

Best wishes,
Yasu

```