[R-sig-ME] lmer/glmer standard error interpretation and visualization

[Ben Bolker]

Colin Wahl <biowahl at ...> writes:

> I am in the process of finalizing figures for my thesis on stream
> invertebrate distributions among watershed and riparian types. See
> below for additional information on the design. I'm having difficulty
> including standard errors from the lmer modeling as error bars in the
> figures. Here is the table I've created from the lmer output:
> estimates of %EPT and St Error are back transformed from logits and
> converted from fractions to percents. Estimates are also absolute (not
> relative to the intercept).
> 

 [snip]
 
> The st. errors are huge. I initially used standard error calculations
> in excel for error bars (stdev(x)/sqrt(n(x))), which look very
> reasonable, and are reflective of significant differences.
> 
> Does anyone have any advice to offer for visualizing these glmer
> results? Should I use the huge model St. Errors? My inclination is
> yes, because they are used to calculated significant differences, but
> 28 + or - 59.6 with a significant p value seems ridiculous.

  How did you back-calculate the standard errors?  It simply doesn't
make sense to compute plogis([standard error]) to get the standard
error on the response scale; you can either use the delta method as
one of the variants of predict.glm() does [i.e. multiply the standard
error by the *derivative* of the link function], or calculate the
confidence intervals on the link scale (i.e. estimate plus/minus CI)
and back-transform them (they will not in general be symmetric).

  This is not an lmer issue, this is a general issue with generalized
linear models, or any other model that works on a transformed scale
and for which one wants to backtransform the parameters.