[R-sig-ME] Random structure more complex than fixed structure
Tibor Kiss
t|bor@k|@@ @end|ng |rom ruhr-un|-bochum@de
Mon Dec 20 19:56:16 CET 2021
Dear list members,
I have a model where I assume a more complex structure for the random effects than for the fixed effects. Schematically, the model looks like the following, it is a cumulative link mixed model (ordinal::clmm), because the response consists of a five point Likert scale (the same would apply to a binomial GLMM). You can find the output of the model for the fixed and random structures below.
model <-
clmm(ANSWER ~ ADVERBIAL + POSITION +
(0 + ADVERBIAL * POSITION | subjects) +
(0 + POSITION | items), # ADVERBIAL constant for items
data)
The reason for assuming random slopes with interaction, but no such interaction in the fixed effects are as follows:
1. I am interested in the by-subject variability for each condition. This is a 3 x 2 design, with three ADVERBIAL types, and two POSITIONs, and I assume that there is less by-subject variance in the second level of POSITION. Hence, I need an interaction to get simple effects for each combination of the two predictors.
2. If I compare this model with a simpler one, where I assume a random slope for POSITION only, then the more complex structure is indicated as significant in comparison to the simpler model (p < 0.01).
3. Also, an interaction of the fixed effects does not prove to be significant.
In addition, the output of the model makes perfect sense to me: for each pair of POSITION and ADVERBIAL the by-subject variance for POSITION 2 is lower than the one for POSITION 1, which I interpret as a stronger confidence in judgments for POSITION 2 across the participants of the experiment.
My question is: is it ok/justified to assume a random structure that is more complex than the fixed structure, if I want to find out about the by-subject variability for each condition in an experiment. Also: would there be a simpler way to do the same?
Thanks for your help.
With kind regards
Tibor
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## ADVERBIAL COM(O) -0.9571 0.3479 -2.751 0.00594 **
## ADVERBIAL ILOC -1.0353 0.3396 -3.049 0.00230 **
## POSITION 2 1.1916 0.1738 6.856 7.08e-12 ***
## ---
## Threshold coefficients:
## Estimate Std. Error z value
## 1|2 -4.5321 0.3557 -12.740
## 2|3 -2.0566 0.3301 -6.231
## 3|4 -1.3708 0.3278 -4.182
## 4|5 1.7521 0.3286 5.333
## Random effects:
## Groups Name Variance Std.Dev. Corr
## subjects ADVERBIAL INSTR 2.3987 1.5488
## ADVERBIAL COM(O) 2.3873 1.5451 0.748
## ADVERBIAL ILOC 2.1802 1.4766 0.898 0.561
## POSITION 2 0.8843 0.9404 -0.078 -0.109 -0.088
## ADVERBIAL COM(O):POSITION 2 0.7158 0.8460 0.240 -0.334 0.487 -0.178
## ADVERBIAL ILOC:POSITION 2 0.6667 0.8165 -0.430 0.083 -0.595 -0.386 -0.790
## items POSITION 1 0.5416 0.7359
## POSITION 2 0.6100 0.7810 0.781
## Number of groups: subjects 51, items 36
———————————————————
Prof. Dr. Tibor Kiss
Linguistic Data Science Lab
Ruhr-Universität Bochum
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