[R-sig-eco] modelling zero inflated continuous data using a two stage model in glmmpql - question about implementing the delta method

[Philip Harrison]

Update,

So it seems predictions for the delta method ARE as simple as the  
probabily*estimates, which for the example can pretty easily computed  
using the predict function (ive added my coding below)

However does anyone know how to compute confidence intervals with this  
delta method? Im guessing its not as straightforward as the product of  
the confidence intervals for the two models which are easily computed?

Any help would be greatly appreciated?

Cheers

Phil





Code

#### generate a grid for prediction which is object "predition grid"


library(AICmodavg)

#generate probability predictions form the binomial model

predoBin<-predictSE.lme(BinaryMod,predictiongrid,level=0,print.matrix=TRUE,se.fit=TRUE)

predsBinG<-cbind(predictiongrid,predoBin)

predsBinG$Probality<-plogis(predsBinG$fit)
predsBinG$CIH.bin<-plogis(predsBinG$fit+(1.96*predsBinG$fit$se.fit))
predsBinG$CIL.bin<-plogis(predsBinG$fit-(1.96*predsBinG$fit$se.fit))


###give the binomial model predictions an identifier


####generate (and backtransform from the cuberoot) predictions from  
the  positive model

predoPos<-predictSE.lme(PositveMod,predictiongrid,level=0,print.matrix=TRUE,se.fit=TRUE)
predsPosG<-cbind(PositiveModel,predoPos)
predsPosG$PosWij<-(predsPosG$fit)^3
predsBinG$CIH<-(predsPosG$PosWij+(1.96*predsPosG$se.fit))^3
predsBinG$CIL<-(predsPosG$PosWij-(1.96*predsPosG$se.fit))^3


DeltaMaker<-cbind(predBinG,predsPosG)

#########get the conditional estimates

DeltaMaker$ConditionalWij<-DeltaMaker$Probability*DeltaMaker$PosWij


####theorectical CI estimation (this is likely wrong???need to  
bootstrap or something?)


DeltaMaker$ConditionalWijCIH<-DeltaMaker$CIH.bin*DeltaMaker$CIH

DeltaMaker$ConditionalWijCIL<-DeltaMaker$CIL.bin*DeltaMaker$CIL

####im thinking maybe only using the CIs from the positive model might  
make sense?

DeltaMaker$ConditionalWijCIH<-DeltaMaker$Probability*DeltaMaker$CIH

DeltaMaker$ConditionalWijCIL<-DeltaMaker$Probability*DeltaMaker$CIL

























Quoting Philip Harrison <pharriso at uwaterloo.ca>:

> Dear R-sig-ecology group,
>
> I have some telemetry data with a zero-inflated (semi-continuous)  
> response, which I modelled using a two stage process using  
> glmmpql/nmle. I chose nlme/glmmpql because a temporal correlation  
> structure is very important for my telemetry data and I can live  
> with pql estimation and no AICs if it means I can avoid winBUGS!.
>
> I am pretty happy with my models and I don’t want to use  
> ZIPglmms,ZINBglmms or ZAPglmms as the response is a pretty normal  
> continuous variable and not a count.
>
> So now, if possible I would like to combine the results of the two  
> models to make predictions about resource selection (with Confidence  
> intervals) for each of the levels of my fixed effects, using the  
> ‘delta’ approach, mentioned a few times on r-sig-eco including here
>
> https://stat.ethz.ch/pipermail/r-sig-ecology/2011-May/002159.html
>
> I found quite a few papers about the delta approach (typically using  
> abundance estimates as the response), but I am having trouble  
> translating the method into code (I’ve added refs at the end of the  
> message). I have seen papers where they appear to just multiply the  
> predictions from the positive model by the probability from the  
> first model (although the papers in question use Bayesian techniques  
> multiplying the posterior modes) Can I do the same with the  
> predictions from my frequentist approach, somehow that seems over  
> simplistic?
>
> Also the response for the positive part of my model normalizes  
> nicely with a cube root transformation and many of the papers use  
> log-normal positive responses- I’m assuming this doesn’t make any  
> difference as long as I leave the back transformation until the very  
> end?
>
> Any help would be much appreciated. See below for model details
>
> ###############################################################################
> Models- First I model the probability of a non zero value, (i.e.  
> presence/absence) then model the continuous part i.e. the strength  
> of selection in the event of a positive selection event.  Sorry I  
> don’t have a real example dataset; however in this case I just need  
> to find out how to extract the relevant stuff from lme/glmmpql output.
>
> Wij – this is my resource selection response variable  (Wij=  
> proportion of time spent in habitat/proportion of habitat  
> available). This response varies from 0 (i.e. habitat was available  
> but not used) continuously through 1 (neither selected nor avoided)  
> and continuously >1 (positive selection) up to a theoretical infinity.
>
> Seas; a categorical 4 level variable
> Sequence; a variable created based on detection date used for the  
> correlation structure.
> Habitat: a categorical habitat variable
>
> Xdata$WijBin<-ifelse(Xdata$Wij>0,1,0)
> XdataUsed<- Xdata[Xdata$WijBIN0==1,]
>
> BinaryMod<-glmmpql(BinaryVariable~Seas+Habitat+Seas*Habitat,random=~1|FishID,cor=corCAR1(form=~Sequence),data=Xdata,family=”binomial”)
>
> PositiveModel <-lme((Wij)^(1/3)~  
> Seas+Habitat+Seas*Habitat,random=~1|FishID/TemperatureCategory,cor=corCAR1(form=~Sequence),data=XdataUsed)
>
>
>
> #########################
> Refs
>
> Pennington, Michael. "Efficient estimators of abundance, for fish  
> and plankton surveys." Biometrics (1983): 281-286.
>
> Stefánsson, Gunnar. "Analysis of groundfish survey abundance data:  
> combining the GLM and delta approaches." ICES Journal of Marine  
> Science: Journal du Conseil 53.3 (1996): 577-588.
>
> Anlauf-Dunn, Kara J., et al. "Habitat connectivity, complexity, and  
> quality: predicting adult coho salmon occupancy and abundance."  
> Canadian Journal of Fisheries and Aquatic Sciences 71.12 (2014):  
> 1864-1876.
>
>
>
>
> Phil Harrison
> PhD student (Fisheries Ecology)
> Department of Biology
> University of Waterloo
> 200 University Avenue West
> Waterloo, Ontario, Canada
> N2L 3G1
>
> _______________________________________________
> R-sig-ecology mailing list
> R-sig-ecology at r-project.org
> https://stat.ethz.ch/mailman/listinfo/r-sig-ecology
>



Philip Harrison MSc
PhD student (Fisheries Ecology)
Department of Biology
University of Waterloo
200 University Avenue West
Waterloo, Ontario, Canada
N2L 3G1
Cell:226-808-2309
Email:pharriso at uwaterloo.ca