[R-sig-ME] Orthogonal vs. Non-orthogonal contrasts
Thierry Onkelinx
thierry.onkelinx at inbo.be
Thu May 26 08:53:44 CEST 2016
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 op 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 op 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 op 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 op r-project.org mailing list
>>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>>>
>>>
>
> ************************************
> Yasuaki SHINOHARA, Ph.D.
> Assistant Professor
> Center for English Language Education (CELESE)
> Waseda University Faculty of Science and Engineering
> 3-4-1 Okubo, Shinjuku-ku, 169-8555, Tokyo JAPAN
> email: y.shinohara op aoni.waseda.jp
>
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