How to report and quantify the random effect in a logistic model?
To get the confidence intervals from the random effects, you need to either use profiling or bootstrapping. Variances -- like the random effects -- tend to have very skewed sampling distributions, so symmetric (Wald) confidence intervals based on standard errors don't make sense. I wouldn't back transform the RE estimates. They are meaningful in their own right as the variance between groups. For example, in your model, the random effect for CITY is just the variance of (1.5) between the intercepts for cities. I would just report the model summary as a table, but I guess you could also write something like "The standard deviation of distribution of the intercept between cities was 3.1" but that seems very awkward to me. For something like "proportion of variance explained", you're looking for something like a standardized effect size, but that is *very* difficult to define in a meaningful way for GLMs and LMMs and thus doubly so for GLMMs. Henrik Singmann has a nice way to explain the issue briefly to reviewers (https://afex.singmann.science/forums/topic/compute-effect-sizes-for-mixed-objects#post-295) and links to the larger GLMM FAQ question on that section. Best, Phillip
On 2/12/20 8:01 pm, Pi wrote:
Hello.
I'm fitting a logistic regression model with mixed effects using the
package glmmTMB. (Because the dataset is quite large and lme4 produces out
of memory errors, even increasing memory.limit).
I need help to interpret and report the output.
Family: binomial ( logit )
Formula: OUTPUT ~ SEX + YEAR + OTHER + (1|CITY/ID)
Data: mydata
AIC BIC logLik deviance df.resid
890000 891000 -450000 889000 1000000
Random effects:
Conditional model:
Groups Name Variance Std.Dev.
ID:CITY (Intercept) 10.0 3.1
CITY (Intercept) 1.5 1.2
Number of obs: 1000009, groups: ID:CITY, 200000; CITY, 20
Conditional model:
Estimate Std.Error z value Pr(>|z|)
(Intercept) 0.79 0.28 2.9 0.005
SEX1 -0.21 0.017 -12 <2e-16
YEAR 0.48 0.0048 100 <2e-16
OTHER -0.70 0.005 -130 <2e-16
Output from sjPlot:
Random Effects
?2 3.29
?00 ID:CITY 10.0
?00 CITY 1.5
ICC 0.78
How can I report the effect of CITY and its confidence interval?
I think most people would report the CI of the odds of the Intercept using
the variance to calculate
{ exp(Intercept-1.96*1.2) , exp(Intercept+1.96*1.2) }
but this doesn't take into account the standard error of the Intercept from
the conditional model, 0.28. How should I combine them?
(I think this is the estimated deviation for the Intercept excluding the
random effects).
Is it acceptable to ignore the Intercept value and just say...?
"The 95% CI for the odds ratio for the CITY is
{exp(-1.96\*1.2),exp(+1.96\*1.2)}"
or
"The odds of OUTPUT is multiplied by a number between exp(-1.96\*1.2) and
exp(+1.96\*1.2) due to the variability of CITY". I don't know how to
include here the 95%IC argument.
I have also tried to calculate the residuals with residuals(model) but it
produces an out of memory error.
Is there any way to do it approximately? or is there already some useful
information in the output?
I just need to say what proportion of the total variance (or of the
residuals) is explained by the variable CITY.
The ?2 value reported by sjPlot is the variance of the residuals.
What about the variance of ID:CITY (Intercept) 10.0? How should I report
it? How can I split it into variance due to ID and variance due to the
interaction of ID and CITY?
[[alternative HTML version deleted]]
_______________________________________________ R-sig-mixed-models at r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models