While R is certainly used for statistical simulations as you showed,
this list is really for questions about R programming, not statistics.
While they certainly overlap and someone may respond here, I suggest
you post this to stats.stackexchange.com or other statistics site that
is specifically for such issues.
Cheers,
Bert
Bert Gunter
Genentech Nonclinical Biostatistics
(650) 467-7374
"Data is not information. Information is not knowledge. And knowledge
is certainly not wisdom."
H. Gilbert Welch
On Thu, May 1, 2014 at 7:00 AM, Wall, Wade A ERDC-RDE-CERL-IL
<wade.a.w...@usace.army.mil> wrote:
> Hi all,
>
> I am trying to run a power analysis using simulated data to compare the power
> of a glm versus a binomial proportion test to detect differences in
> proportions. For example, suppose you have some proportion that decreases by
> some amount over X number of time steps.
> .4,.39,.38,.37 . . . . .01 and simulate data over those time steps based on
> the decrease. Does a glm approach (differences in slope) "outperform" an
> approach whereby you simply look at proportional differences. I ran
> simulations and basically summed up the number of times p<.05 divided by the
> number of trials. I was expecting that a glm approach would have more power
> because it would be utilizing all the data across multiple time steps,
> whereas a binomial proportion test is only comparing two populations ( the
> beginning and the end points).
>
> However the results indicated that a binomial proportion test had more power
> relative to a glm at fewer time steps and that, depending on the simulated
> decrease in proportions, the relationship between glm power and binomial
> proportion test power changed. Interestingly, a greater decreases, a binomial
> proportion test seems have greater power compared to a glm, which to me is
> counterintuitive since the slope should be greater.
>
> I am attaching the code below my questions in case anyone is interested.
>
> My questions are:
>
>
> (1) Am I interpreting the results and p-values correctly?
>
> (2) If I am interested in trends, does glm results really have lower power
> and, if so, is there a way to combine the two tests?
>
> I know that I am ignoring a lot of issues such as autocorrelation, but I am
> really just trying to understand the output.
>
> Any suggestions or insights would be appreciated.
>
> ##### Attempt at using glm model ######
> ltProb <- 0.4 ## longterm average of nest survival
> probability
> change <- c(.01,.03,.05)
> yrs <- seq(1,20, by=1) ##
> Years of inquiry, probability of detecting a yearly change nest survival
> samplesize <- 50 ## Reasonable
> sample size range
> reps <- 1000
> ## of simulations per
> SurvProb <- ltProb
> ## initiating survival probablity for later use, nuisance
> power <- matrix(nrow=length(change)*length(yrs)*length(samplesize), ncol=5)
> ## creating a matrix to hold data
>
> scenario <- 0
> ## initializing scenarios which will be a placeholder later on
> for (a in 1:length(change)){
> ## loop through yearly pop change scenarios
> for (c in 1:length(samplesize)){
> ## loop through sample size scenarios
> for (b in 1:length(yrs)){
> ## loop through years sceanarios
> scenario=scenario+1
> power[scenario,1] <- change[a]
>
> ## filling
> matrix with pop change used
> power[scenario,2]<-ltProb*((1-change[a])**yrs[b])
> power[scenario,3] <- yrs[b]
>
> ## filling matrix with
> number of years used
> power[scenario,4] <- samplesize[c]
>
> ## filling
> matrix with sample size used
> }
> }
> }
> colnames(power) <- c("PopChange", "Proportion2","yrs", "Sample_Size", "Power")
> power=as.data.frame(power)
> power$Sample_Size=as.numeric(power$Sample_Size)
>
> scenario=levels(as.factor(power$PopChange)) ## To subset power
> ps = levels(as.factor(power$Sample_Size))
> results <- matrix(nrow=0, ncol=5) ## final matrix
> results=as.data.frame(results)
> reps=1000 ## set number of reps
>
> for (k in 1:length(scenario)){
> for (m in 1:length(ps)){
> sub=power[(power$PopChange==scenario[k]) & power$Sample_Size==ps[m],] ##
> Subset by scenario and sample size
> probs = matrix(nrow=1000,ncol=16) ## this is matrix for probabilities.
> dat=matrix(nrow=0,ncol=3,NA)
> dat=as.data.frame(dat)
> for (l in 1:reps){ ##This should be for the replicates
> dat=matrix(nrow=0,ncol=3,NA)
> dat=as.data.frame(dat)
> print(l)
> for (j in 1:nrow(sub)){
> tmp=rbinom(n=sub$Sample_Size[j],size=1,prob=sub[j,2])
>
> tmp.dat=cbind(tmp,rep(sub$yrs[j],sub$Sample_Size[j]),rep(sub$Proportion2[j],sub$Sample_Size[j]))
> dat=rbind(dat,tmp.dat)
> if (sub$yrs[j]>4){
> x=(glm(dat[,1]~dat[,2],family=binomial))
> probs[l,j-4]=ifelse(summary(x)$coefficients[2,4]<.05,1,0)
> }
> }
> }
> sub$Power[5:20]=apply(probs,2,sum)/nrow(probs)
> results=rbind(results,sub)
> }
> }
>
> tmp=results[!is.na(results$Power),] ### remove NAs
> tmp$SampleSize_Decline=paste(tmp$Sample_Size,tmp$PopChange,sep=":")
> tmp$SampleSize_Decline=as.factor(tmp$SampleSize_Decline)
>
> ### Now do the same using prop.test #####
> tmp$PropPower = NA
> for (i in 1:nrow(tmp)){
> print(i)
> x=0
> for (j in 1:1000){
> a = rbinom(tmp$Sample_Size[i],1,prob = (tmp$Proportion2[i]))
> b=binom.test(sum(a),length(a),p=.4,conf.level=.95,alternative="less")
> if (b$p.value < .05) {x=x+1}
> }
> tmp$PropPower[i] = x/1000
> }
>
> ##### graph results
> d=unique(tmp$PopChange)
> for (i in 1:length(d)){
> par(mfcol = c(1,2))
> sub = tmp[tmp$PopChange == d[i],]
> plot(sub$yrs,sub$Power,col="red", main = d[i], xlab = "Number of
> years",ylab="Power")
> points(sub$yrs,sub$PropPower,col="black")
> plot(sub$PropPower,sub$Power,xlab="Binomial Proportion Power", ylab="GLM
> Power",main=d[i])
> abline(0,1)
> readline("Press <return to continue")
> }
>
>
> ##### End Code #####
>
>
>
> Wade A. Wall
> US Army ERDC-CERL
> P.O. Box 9005
> Champaign, IL 61826-9005
> 1-217-373-4420
> wade.a.w...@usace.army.mil<mailto:wade.a.w...@usace.army.mil>
>
>
>
>
> [[alternative HTML version deleted]]
>
> ______________________________________________
> R-help@r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
______________________________________________
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
