[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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