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I have the following set of model-averaged fixed effects from a set of binomial GLMMs:

model parameters image

I would like to plot the predicted effect of "NBT", along with confidence bands, while holding all the other variables at their baseline levels. My attempt to do this in ggplot:

Xvars <- seq(from=0, to=100, by=0.1)  #NBT range is 0-100
  binomIntercept <- 1.317
  binomSlope <- -0.0076     
  binomSE <- 0.009    
Means <- logistic(binomIntercept + binomSlope*Xvars)              
loCI <- logistic(binomIntercept + (binomSlope - 1.96*binomSE)*Xvars)
upCI <- logistic(binomIntercept + (binomSlope + 1.96*binomSE)*Xvars)
df <- data.frame(Xvars,Means,loCI,upCI)
p <- ggplot(data=df, aes(x = Xvars, y = Means)) + 
geom_line() +          
geom_line(data=df, aes(x = Xvars, y = upCI),col='grey') +
geom_line(data=df, aes(x = Xvars, y = loCI), col='grey')
p

graph image

I'm assuming that the confidence bands are cone shaped because I'm not accounting for uncertainty in the estimate for the intercept. Maybe this is okay (?), but it does look different from every regression line I've ever seen with confidence intervals plotted.

Can someone please tell me how I should be writing my equations to get the correct confidence intervals, given the intercept, slope, and standard errors from my model output?

(I know I can use the predict function to do this in R, but would like to know how to do it by hand.)

Glen_b
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jay
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  • Can you please check your links (404 error)? You can use http://imgur.com to share images, or better copy-paste output as plain text for model results. – chl Dec 24 '13 at 13:19
  • Charlie gave a good general answer to this question at http://stats.stackexchange.com/questions/15423/how-to-compute-prediction-bands-for-non-linear-regression which might help set you on the right path. – whuber Dec 26 '13 at 17:10
  • thanks @whuber, that gives me a good starting point. Is taking me a while to digest his answer but should be able to figure it out from there. Cheers – jay Dec 28 '13 at 22:05

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