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

N o s t a l g i a kenj|ro @end|ng |rom @ho|n@@c@jp
Fri Dec 10 12:29:45 CET 2021

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:

model1	AIC = 4249.232  LL = -2076.616 (df=48)
model2	AIC = 4539.69   LL = -2222.845 (df=47)
model3	AIC = 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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