Hello, 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). Watershed ? ? Effect ? ? ? ? ? ? ? ? ?Estimate ?St. Error? z score ?p value Forested ? ? Intercept: F vs. 0 ? ? 28.23 ? 59.6 ? ? -2.346 ? ? 0.019* ? ? ? ? ? ? ?? ? ? Riparian: ?F vs. NF ? 16.017 ? 62.3 ? ? -1.436 ? 0.151 Cultivated ? ?Watershed: C vs. F ? ?1.351 ? 65.3 ? ? -5.297 ? ?<0.000* ? ? ? ? ? ? ? ? ? Riparian: ?F vs. NF ? ?1.555 ? 69.2 ? ? ?1.071 ? ?0.284 Developed ? Watershed: D vs. F ? ?0.175 ? 66.8 ? ? -7.714 ? <0.000* ? ? ? ? ? ? ?? ? ? Riparian: ?F vs. NF ? ?0.292 ? 70.9 ? ? ?1.391 ? 0.164 Grassland ? ?Watershed: G vs. F ? 28.94 ? 66.6 ? 0.05 ? ?0.960 ? ? ? ? ? ? ? ? ? Riparian: ?F vs. NF ? ? 1.967 ? ? 70.7 ? ? -2.595 ?? 0.009* 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. Thank you, Colin Wahl M.S. Candidate Dept. of Biology Western Washington University
lmer/glmer standard error interpretation and visualization
3 messages · Colin Wahl, 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).
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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.
Ben Bolker <bbolker at ...> writes:
Colin Wahl <biowahl at ...> writes: 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.
PS this is why epidemiologists spend so much time learning about odds ratios and log-odds -- you can back-transform from logit effects to odds-ratio effects, but once you get there there's just not any perfect way to transform back to a probability scale in a way that is completely general ... http://lesswrong.com/lw/8lr/logodds_or_logits/