[R-sig-ME] Nested model variance/parameter value

[N o s t a l g i a]

Hi John,

Treating answers (Q) as a random effect nested within an individual 
sounds like an interesting idea. As Qs are not part of my main 
interest, that would pose no problem to me. I guess it would be like:

model4 <- lmer(hon ~ sex * age * Question + schooling + 
(1|intv/ID/Question)

Or should I drop it from the interaction of the fixed effect?

- Ken


On 2021/12/11 10:03, John Maindonald wrote:
> My guess is that you should not be treating answers from different
> questions as independent.  They are nested within individuals, and
> a main effect is not sufficient to account for systematic differences.
> There are shades of the story I heard of an experimenter whose blocks
> were made up of plots that moved successively away from the river.
> What do you get if you analyse a summary measure for the questionnaire
> or individual questions?
> 
> John Maindonaldemail: john.maindonald using anu.edu.au 
> <mailto:john.maindonald using anu.edu.au>
> 
> 
>> On 11/12/2021, at 00:29, N o s t a l g i a <kenjiro using shoin.ac.jp 
>> <mailto:kenjiro using shoin.ac.jp>> wrote:
>>
>> I am a novice in mixed models, and I am trying to fit a model to a 
>> survey data with an interval-scale dependent variable (hon), four 
>> fixed-effect variables (sex, age, schooling, and questions) and two 
>> random effects. The random effects are interviewer (intv) and 
>> interviewee (ID), and as such, they are in a nested relationship. 
>> Sex, age and questions are found to be in an interacting relationship.
>>
>> A major question I am asking here is whether the interviewer effect 
>> is significant or not, so I tried the following intercept-only 
>> models, with model 1 using the nested model, model 2 only the 
>> interviewer effect, and model 3 only the interviewee effect:
>>
>> model1 <- lmer(hon ~ sex * age * Question + schooling + (1|intv/ID)
>> model2 <- lmer(hon ~ sex * age * Question + schooling + (1|intv)
>> model3 <- lmer(hon ~ sex * age * Question + schooling + (1|ID)
>>
>> The output from each model says the following:
>>
>> model 1:
>> Random effects:
>> Groups   Name        Variance Std.Dev.
>> ID:intv  (Intercept) 0.03988  0.1997
>> intv     (Intercept) 0.00000  0.0000
>> Residual             0.16847  0.4105
>> Number of obs: 3283, groups:  ID:intv, 305; intv, 28
>>
>> model 2:
>> Random effects:
>> Groups   Name        Variance Std.Dev.
>> intv     (Intercept) 0.002348 0.04846
>> Residual             0.205998 0.45387
>> Number of obs: 3283, groups:  intv, 28
>>
>> model 3:
>> Random effects:
>> Groups   Name        Variance Std.Dev.
>> ID       (Intercept) 0.04107  0.2027
>> Residual             0.16894  0.4110
>> Number of obs: 3294, groups:  ID, 306
>>
>> The respective Log likelihood and AIC values are:
>>
>> model1AIC = 4249.232  LL = -2076.616 (df=48)
>> model2AIC = 4539.69   LL = -2222.845 (df=47)
>> model3AIC = 4274.99   LL = -2090.495 (df=47)
>>
>> Since I got an error message saying "models were not all fitted to 
>> the same size of dataset" while running anova(), I compared the AICs 
>> and concluded that model2 is the best model of the three.
>>
>> Here I have three questions:
>>
>> 1. Why is the variance for the interviewer effect(intv) zero? Is it 
>> necessarily so because of the nested model, or is it simply because 
>> that there is no interviewer effect?
>>
>> 2. If intv is really zero, why does not the model 3 give a better AIC?
>>
>> 3. Am I allowed to compare the three models with AIC as I did above? 
>> Or should I use LL?
>>
>> Thanks in advance,
>>
>> Kenjiro Matsuda
>>
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