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am trying to plot a Poisson model on scale of original response variable. My advisor would like me to plot mean +/- SE for egg production by bumble bees.

I don't understand the meaning of the 'SE' term when using "type="response"". On the scale of the linear predictor, the CI's and SE's are symmetric about the mean. When the data frame is manually exponentiated, the CI's become asymmetric and match the output for lsmeans with "type="response"". However there is only one column for the "SE". Why are there not 2 columns, to account for asymmetry when transforming the (mean+/-SE) from the log scale? Thanks for your help!

Evan Palmer-Young
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1 Answers1

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If the mean and SDest estimate on the log-transformed scale are meanEst and SDestwhen the predictions are made, then this will be 95% bounds for the "response" estimate:

exp( meanEst +c(-1,1)*1.96*SDest)

It will necessarily be asymmetric around exp(meanEst) on the untransformed, original data scale. Only need two values to generate those mean and 2 bounds estimates (which are symmetric on the regression scale.)

IRTFM
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  • Thanks, @42- . I see now that the original, symmetric SE"s and CI's become asymmetric through the exponentiation. Still not entirely sure how to interpret the lsmeans "SE" on the scale of the original response variable. The package author, R. Lenth, told me it was estimated using the "delta method". – Evan Palmer-Young Mar 06 '16 at 21:06
  • In a Poisson model the exponentiated estimate is usually interpreted as a rate ratio. But the estimate on the linear scale is then a difference of logged-rates for a one unit difference of a parameter. The SE is the std deviation of those estimates in the log scale – IRTFM Mar 06 '16 at 21:55