Update on the study design and data: I am testing whether increased temperatures will affect dung burial by dung beetles. The beetle species that I have used makes balls of dung and buries each dung ball. So each dung ball is a separate data point. I am trying to predict whether the dung ball is buried or not (a binary outcome). The dung beetles and dung are kept in large climate controlled chambers, and each chamber is set to an offset (+0, +2 deg or +4 deg higher than ambient field temperature). Offset therefore is my treatment, and is a 3 level fixed effect. There are 27 chambers that were randomly assigned an offset (i.e. +0= 9 chambers +2 deg=9 chambers or +4 deg n= 9 chambers). I collected 165 dung balls across the 27 chambers, so my sample size is 165 (with 2 - 12 dung balls from each chamber). Because multiple dung balls came from the same chamber and are not independent, I want to control for that by including chamber as a random effect. The model runs fine with random intercepts that vary across Chambers, but I run into trouble when I include random slopes.
I am fitting a mixed effects model with a binary outcome. I have one fixed effect (Offset, a 3 level factor) and one random effect (chamber, with multiple data points coming from each chamber). I have included random intercepts that vary across chambers to account for the non-independence of data points that come from the same chamber. My code is as follows:
ball1=glmer(Buried~Offset+(1|Chamber), family=binomial, data=rubrusballs)
Output:
Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
Family: binomial ( logit )
Formula: Buried ~ Offset + (1 | Chamber)
Data: rubrusballs
AIC BIC logLik deviance df.resid
207.5 219.9 -99.8 199.5 161
Scaled residuals:
Min 1Q Median 3Q Max
-0.7884 -0.6049 -0.5695 1.2683 1.7559
Random effects:
Groups Name Variance Std.Dev.
Chamber (Intercept) 8.989e-18 2.998e-09
Number of obs: 165, groups: Chamber, 27
Fixed effects:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -1.0055 0.3018 -3.332 0.000862 ***
Offset2 -0.1205 0.4488 -0.268 0.788335
Offset3 0.5301 0.4019 1.319 0.187229
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Correlation of Fixed Effects:
(Intr) Offst2
Offset2 -0.672
Offset3 -0.751 0.505
I then added random slopes to my model to see if I could improve the fit of the model. My code for this second model was:
ball2=glmer(Buried~Offset+(Offset|Chamber), family=binomial, data=rubrusballs)
This second model gave me an error, as seen in the output below:
Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
Family: binomial ( logit )
Formula: Buried ~ Offset + (Offset | Chamber)
Data: rubrusballs
AIC BIC logLik deviance df.resid
215.3 243.3 -98.7 197.3 156
Scaled residuals:
Min 1Q Median 3Q Max
-0.9191 -0.6282 -0.6052 1.2697 2.1458
Random effects:
Groups Name Variance Std.Dev. Corr
Chamber (Intercept) 2.535e-05 0.005035
Offset2 9.156e-01 0.956895 -0.52
Offset3 5.704e-05 0.007553 -0.90 0.17
Number of obs: 165, groups: Chamber, 27
Fixed effects:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -1.004476 0.003277 -306.56 <2e-16 ***
Offset2 -0.458192 0.003277 -139.83 <2e-16 ***
Offset3 0.526834 0.265622 1.98 0.0473 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Correlation of Fixed Effects:
(Intr) Offst2
Offset2 -0.250
Offset3 -0.012 0.003
convergence code: 0
Model failed to converge with max|grad| = 0.0230258 (tol = 0.001, component 1)
I have had a similar problem with a previous data set (here), so apologies for posting a similar question. This is a different error message from last time however. I have tried a few different optimizers and these have not resolved the issue. Last time, it was suggested that the model showed a singular fit and could be reduced to include only random intercepts. I would appreciate if someone could have a look at the output of the 2nd model and offer any solutions to get the model to converge, or by looking at the output, do I even need to include random slopes?
Another question while I am here. To assess if I even need to include random intercepts/slopes, I would like to compare model fit between a glm (no random effects) and a glmer model (random effects) using the log likelihoods. However as I understand it, I can only comapre models this way if they were estimated using maximum likelihood (ML). Im pretty sure that glmer uses ML, but what about glms? Are they estimated using ML and therefore can I compare the fit of glm and glmer models?
