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This is a common question, but I couldn't find a question / answer on Cross Validated dealing with the same problem. In short, is 1000 intercepts too many intercepts, that is, can individual be a random intercept var?

The Data
I have a longitudinal data-set with 3 time points and two groups. Time-point 1 is baseline for both groups, so t1 = no treatment for both groups.
Treatment group has 1000 individuals, control group has c.a. 300 individuals. As is expected, some individuals only answer on one time-point, others answer on two or on all three time-points.

respondent time.p group q1           q2
a          1      t     agree        1
a          2      t     neither nor  2
a          3      t     disagree     6 
b          1      c     neither nor  9
b          2      c     neither nor  5
b          3      c     disagree     1
c          1      t     agree        3
c          3      t     agree        5
d          2      c     disagree     8

The Question

  • Should I use mixed effects model for this problem?
  • If yes, is it correct to have respondent as random intercept (so c.a. 1000 intercepts)?
  • Do I have too few time-points?

I have both ordinal and continuous response vars. I'm using R, so I was going to use lme4 for the continuous response var and package ordinal for the likert.

My Syntax

# syntax for the ordinal var.
# levels = Strongly agree, Somewhat agree, Neither nor, 
#          Somewhat disagree, Strongly disagree
library(ordinal)
clmm2(q1 ~ group * time.p, 
      random = respondent, 
      Hess = TRUE, 
      nAGQ = 10, 
      data = Df)

# syntax for the continuous var.
library(lme4)
library(lmerTest)
lmer(q2 ~ group + time.p + 
     (1 | respondent),
     data = Df)

By the way, for all models I run I get convergent warning.

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Yes, you can use a random intercepts model to account for the correlations in the repeated measurements of each respondent. Even though you have 1000 respondents the intercepts, you include for them are assigned a normal distribution, and for this reason, the actual number of parameters is much less than 1000.

Regarding the convergence problems, you could also give a try in the GLMMadaptive package. For ordinal data you can fit the continuation ratio model; for more info, check here.

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    $\begingroup$ Thanks so much for the very quick reply. I did not know GLMMadaptive could be used on ordinal data. I've used it on binary response var with good results. I will try it to get rid of the convergent warning and shorten the computation time. $\endgroup$ – Helgi Guðmundsson Apr 11 at 19:25

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