Visualizing mixed model results One of the problems I've always had with mixed models is figuring out data visualizations - of the kind that could end up on a paper or poster - once one has the results.
Right now, I'm working on a Poisson mixed effects model with a formula that looks something like the following:
 a <- glmer(counts ~ X + Y + Time + (Y + Time | Site) + offset(log(people))
With something fitted in glm() one could easily use the predict() to get predictions for a new data set, and build something off of that. But with output like this - how would you construct something like a plot of the rate over time with the shifts from X (and likely with a set value of Y)? I think one could predict the fit well enough just from the Fixed effects estimates, but what about the 95% CI?
Is there anything else someone can think of that help visualize results? The results of the model are below:
Random effects:
 Groups     Name        Variance   Std.Dev.  Corr          
 Site       (Intercept) 5.3678e-01 0.7326513               
            time        2.4173e-05 0.0049167  0.250        
            Y           4.9378e-05 0.0070270 -0.911  0.172 

Fixed effects:
              Estimate Std. Error z value Pr(>|z|)    
(Intercept) -8.1679391  0.1479849  -55.19  < 2e-16
X            0.4130639  0.1013899    4.07 4.62e-05
time         0.0009053  0.0012980    0.70    0.486    
Y            0.0187977  0.0023531    7.99 1.37e-15

Correlation of Fixed Effects:
         (Intr) Y    time
X      -0.178              
time    0.387 -0.305       
Y      -0.589  0.009  0.085

 A: Predicting counts using the fixed-effects part of your model means that you set to zero (i.e. their mean) the random effects. This means that you can "forget" about them and use standard machinery to calculate the predictions and the standard errors of the predictions (with which you can compute the confidence intervals).
This is an example using Stata, but I suppose it can be easily "translated" into R language:
webuse epilepsy, clear
xtmepoisson seizures treat visit || subject: visit
predict log_seiz, xb
gen pred_seiz = exp(log_seiz)
predict std_log_seiz, stdp
gen ub = exp(log_seiz+invnorm(.975)*std_log_seiz)
gen lb = exp(log_seiz-invnorm(.975)*std_log_seiz)

tw (line pred_seiz ub lb visit if treat == 0, sort lc(black black black) ///
 lp(l - -)), scheme(s1mono) legend(off) ytitle("Predicted Seizures") ///
 xtitle("Visit")

The graph refers to treat == 0 and it's intended to be an example (visit is not a really continuous variable, but it's just to get the idea). The dashed lines are 95% confidence intervals.

