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

[Yasuaki SHINOHARA]

Dear Thierry,

Thank you very much for your reply.

I understood that the results of each main fixed factor (e.g., Factor 
A, B, C and D) are pointless, since the interaction factors affected 
the results of the main fixed factors. Actually, I manually coded the 
contrasts for all the fixed factors based on the hypothesis I wanted 
to test, as follows.

#Factor A (testing block)
PreVsMid<-c(1,-1,0)
PreVsPost<-c(-1,0,1)
contrasts(alldata$FactorA)<-cbind(PreVsMid,PreVsPost)
#Factor B (Trainer order)
IDVsDIS<-c(1,-1)
contrasts(alldata$FactorB)<-cbind(IDVsDIS)
#Factor C (Phonetic environment)
IniVsMid<-c(1,-1,0)
IniVsCls<-c(-1,0,1)
contrasts(alldata$FactorC)<-cbind(IniVsMid, IniVsCls)
#Factor D (Length of Experience, continuous variable)
alldata$FactorD<-as.numeric(alldata$FactorD)

What I really wanted to test is the interaction between Factor A and 
Factor B. Factor A has the two contrasts (i.e., PreVsMid (1,-1,0), 
PreVsPost(-1,0,1)), and Factor B has only one contrast (i.e., IDvsDIS 
(-1,1)) since there are only two levels in the Factor B. I tested 
whether there is a significant difference in the contrast of PreVsMid 
between the two levels of Factor B (IDvsDIS). Therefore, I did not use 
the dummy (simple effect) coding but used the effect coding.

As you suggested, I tried to figure out how to use the multcomp 
package. I found that the glht function in the packages allows me to 
test a variety of contrasts with a matrix. However, I felt that the 
contrasts I coded above are maybe enough to test my hypothesis, and I 
am wondering whether I should use the glht function for the contrasts.

Could you please let me know if there are any advantage of using the 
glht function?

I really appreciate your help.

Best wishes,
Yasu


On Thu, 26 May 2016 08:53:44 +0200
  Thierry Onkelinx <thierry.onkelinx at inbo.be> wrote:
> 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: 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
>>>>
>>>> _______________________________________________
>>>> R-sig-mixed-models at r-project.org mailing list
>>>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>>>>
>>>>