Orthogonal vs. Non-orthogonal contrasts

Dear Yasu,

The contrast x = c(1, -1, 0) is equivalent to beta_x * 1 * a_1 + 
beta_x *
(-1) * a_2 + beta_x * 0 * a_3.
Likewise contrast y = c(.5, -.5, 0) is equivalent to beta_y * 0.5 * 
a_1 +
beta_y * (-0.5) * a_2 + beta_y * 0 * a_3.

Since both model the same thing beta_x * 1 * a_1 + beta_x * (-1) * 
a_2 +
beta_x * 0 * a_3 = beta_y * 0.5 * a_1 + beta_y * (-0.5) * a_2 + 
beta_y * 0
* a_3.
Some simple math will show that beta_x = 2 * beta_y

Your contrasts are correct but pointless given your model. They are 
only
meaningful in case FactorA is only a main effect. You included 
FactorA in
some interactions as well. So you'll need to define contrasts on the 
full
set of fixed parameters to get some sensible results. You can do 
that with
the multcomp package. I would also suggest that you find some local
statistician to help you define the contrasts relevant for your 
model.

Best regards,


ir. Thierry Onkelinx
Instituut voor natuur- en bosonderzoek / Research Institute for 
Nature and
Forest
team Biometrie & Kwaliteitszorg / team Biometrics & Quality 
Assurance
Kliniekstraat 25
1070 Anderlecht
Belgium

To call in the statistician after the experiment is done may be no 
more
than asking him to perform a post-mortem examination: he may be able 
to say
what the experiment died of. ~ Sir Ronald Aylmer Fisher
The plural of anecdote is not data. ~ Roger Brinner
The combination of some data and an aching desire for an answer does 
not
ensure that a reasonable answer can be extracted from a given body 
of data.
~ John Tukey

2016-05-26 6:31 GMT+02:00 Yasuaki SHINOHARA 
<y.shinohara at aoni.waseda.jp>:

Dear Thierry,

Thank you very much for your reply.
I understood why. The interaction of blockPreVsMid:FactorD turned
significant in the model which contrasted the testing block factor 
as
PreVsMid and PreVsPost (i.e.,cbind(c(1,-1,0),c(-1,0,1))), although 
the
interaction was not significant in the model with the testing block
contrasted as PreVsMid and PreMidVsPost (i.e., 
cbind(c(1,-1,0),c(1,1,-2))).

Could I ask another question?
What is the difference in making a contrast of PreVsMid as c(1,-1,0) 
and
as c(0.5, -0.5, 0)?
It seems that the beta and SE are double if I code the contrasts 
with
(0.5, -0.5, 0). I hope it does not matter.

Also, I coded "contrasts(data$FactorA)<-cbind(c(1,-1,0),c(-1,0,1))" 
to
test the differences between the mean of level 1 vs. the mean of 
level 2
and between the mean of level 1 and the mean of level 3. Is this 
correct?
Some website says something different from what I understood (e.g., 
the
first Answer of
http://stats.stackexchange.com/questions/44527/contrast-for-hypothesis-test-in-r-lmer
).

My model includes both categorical and numeric variable, and all
categorical variables were coded manually.

Best wishes,
Yasu


On Wed, 25 May 2016 09:44:14 +0200
 Thierry Onkelinx <thierry.onkelinx at inbo.be> wrote:

Dear Yasu,

A is part of two interactions. Hence you cannot interpret this main 
effect
without the interactions. Note that changing the contrast will also 
effect
the interactions.

Best regards,

ir. Thierry Onkelinx
Instituut voor natuur- en bosonderzoek / Research Institute for 
Nature and
Forest
team Biometrie & Kwaliteitszorg / team Biometrics & Quality 
Assurance
Kliniekstraat 25
1070 Anderlecht
Belgium

To call in the statistician after the experiment is done may be no 
more
than asking him to perform a post-mortem examination: he may be able 
to
say
what the experiment died of. ~ Sir Ronald Aylmer Fisher
The plural of anecdote is not data. ~ Roger Brinner
The combination of some data and an aching desire for an answer does 
not
ensure that a reasonable answer can be extracted from a given body 
of
data.
~ John Tukey

2016-05-25 4:42 GMT+02:00 Yasuaki SHINOHARA 
<y.shinohara at aoni.waseda.jp>:

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
answer my question?

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: ? = 0.22, SE = 0.05, z = 4.34, p < 0.001
pre & mid vs. post test: ? = -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: ? = -0.01, SE = 0.04, z = -0.14, p > 0.05 (=0.89),
pre vs. post test: ? = 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