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biostats.R
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biostats.R
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all.subsets.gam <-
function(y,x.smooth,x.parametric=NULL,
family=binomial(link=logit),maxp=5,select='all',delta=7,rank=10,...){
owarn<-options("warn")
on.exit(options(warn=owarn$warn))
options(warn=-1)
require(mgcv,MuMIn)
#binary function copied from wle library
binary<-function(x,dim){
if(x==0){
pos<-1
}
else{
pos<-floor(log(x,2))+1
}
if(!missing(dim)){
if(pos<=dim){
pos<-dim
}
else{
warning("the value of `dim` is too small")
}
}
bin<-rep(0,pos)
dicotomy<-rep(FALSE,pos)
for(i in pos:1){
bin[i]<-floor(x/2^(i-1))
dicotomy[i]<-bin[i]==1
x<-x-((2^(i-1))*bin[i])
}
return(dicotomy)
}
if(is.null(x.parametric)){
x<-x.smooth
}
else{
x<-cbind(x.smooth,x.parametric)
}
p<-ncol(x)
m<-(2^p)-1
N<-nrow(x)
terms<-NULL
model<-NULL
id<-NULL
AIC<-NULL
K<-NULL
AICc<-NULL
adjR2<-NULL
D2<-NULL
for(i in 1:m){
bin<-binary(i,p)
if(sum(bin)<=maxp){
x.names<-names(x)[bin]
if(is.null(x.parametric)){
x.subset<-subset(x,select=x.names)
formula<-as.formula(paste('y~',paste(paste("s(",names(x.subset),")",sep=""),
sep="",collapse="+"),sep=""))
}
else{
sv.smooth<-x.names %in% names(x.smooth)
x.smooth.names<-x.names[sv.smooth]
x.smooth.subset<-subset(x,select=x.smooth.names)
sv.parametric<-x.names %in% names(x.parametric)
x.parametric.names<-x.names[sv.parametric]
x.parametric.subset<-subset(x,select=x.parametric.names)
x.subset<-cbind(x.smooth.subset,x.parametric.subset)
if(sum(sv.smooth)==0){
formula<-as.formula(paste('y~',paste(x.parametric.names,
sep='',collapse='+'),sep=''))
}
else if(sum(sv.parametric)==0){
formula<-as.formula(paste('y~',paste(paste('s(',x.smooth.names,')',sep=''),
sep='',collapse='+'),sep=''))
}
else{
formula<-as.formula(paste('y~',paste(c(x.parametric.names,
paste('s(',x.smooth.names,')',sep='')),
sep='',collapse='+'),sep=''))
}
}
model.gam<-gam(formula,family=family,data=x.subset,...)
#save terms
temp<-as.data.frame(x.names)
names(temp)<-'Term'
temp$id<-i
terms<-rbind(terms,temp)
#save model aic stats
model<-rbind(model,paste(x.names,collapse='+'))
id<-rbind(id,i)
AIC<-round(model.gam$aic,3)
t.AICc<-round(AICc(model.gam),3)
AICc<-rbind(AICc,t.AICc)
K<-model.gam$rank
AICc<-rbind(AICc,round(AIC+(2*K*(K+1)/(N-K-1)),3))
#save R-sq(adj) and deviance explained
adjr2<-summary(model.gam)$r.sq
adjR2<-rbind(adjR2,round(adjr2,3))
d2<-summary(model.gam)$dev.expl
D2<-rbind(D2,round(d2,3))
}
}
#create model AIC table
AIC.stats<-as.data.frame(cbind(id,model,adjR2,D2,as.data.frame(AICc)))
names(AIC.stats)<-c('id','Model','adjR2','D2','AICc')
AIC.stats<-AIC.stats[order(AIC.stats$AICc),]
AIC.stats$Delta<-AIC.stats$AICc-min(AIC.stats$AICc)
wgt<-exp(-0.5*AIC.stats$Delta)
AIC.stats$Wgt<-round(wgt/sum(wgt),3)
AIC.stats$Rank<-seq(1,nrow(AIC.stats))
if(select=='delta'){
AIC.stats<-AIC.stats[AIC.stats$Delta<=delta,]
}
else if(select=='rank'){
AIC.stats<-AIC.stats[AIC.stats$Rank<=rank,]
}
#create coefficients table
sv<-NULL
for(i in 1:nrow(terms)){
sv<-c(sv,any(terms$id[i]==AIC.stats$id))
}
terms<-terms[sv,]
terms<-terms[order(terms$Term),]
#create variable importance table
z<-merge(terms,AIC.stats,by='id')
N<-aggregate(is.finite(z$Term),list(z$Term),sum)
names(N)<-c('Term','N')
AICc<-aggregate(z$Wgt,list(z$Term),sum)
names(AICc)<-c('Term','AICc')
varimp<-merge(N,AICc,by='Term')
#final clean up of tables
AIC.stats<-subset(AIC.stats,select=-id)
#save results to list
return(list(model.AIC=AIC.stats,variable.importance=varimp))
}
all.subsets.glm <-
function(y,x1=NULL,x2=NULL,x2.linear=FALSE,x.force=NULL,
paired.logit=FALSE,family=binomial(link=logit),offset=NULL,weights=NULL,
maxp=5,select='AIC',sensitivity=.95,delta.AIC=7,delta.FP=.1,delta.Kappa=.1,
rank=10,varimp=FALSE,gof='logLik',coef.table=FALSE,model.ave=FALSE,...){
owarn<-options("warn")
on.exit(options(warn=owarn$warn))
options(warn=-1)
#check on valid model parameterization
if(x2.linear==TRUE & is.null(x2)) stop('if x2.linear=TRUE, then x2 cannot be
null')
if(paired.logit==TRUE & !is.null(x2)) stop('quadratic terms not allowed in paired
logistic regression, so x2 must be null')
################################################################################
#internal functions
################################################################################
#binary function (copied from wle library)
binary<-function(x,dim){
if(x==0){
pos<-1
}
else{
pos<-floor(log(x,2))+1
}
if(!missing(dim)){
if(pos<=dim){
pos<-dim
}
else{
warning("the value of `dim` is too small")
}
}
bin<-rep(0,pos)
dicotomy<-rep(FALSE,pos)
for(i in pos:1){
bin[i]<-floor(x/2^(i-1))
dicotomy[i]<-bin[i]==1
x<-x-((2^(i-1))*bin[i])
}
return(dicotomy)
}
#Kappa function
cohen.kappa<-function(y){
N<-sum(y)
ccr<-sum(diag(y))/sum(y)
p<-apply(y,1,sum)/N
q<-apply(y,2,sum)/N
num<-ccr-sum(p*q)
den<-1-sum(p*q)
k<-num/den
k[k<0]<-0
return(k)
}
#Kappa optimization function
kappa.opt<-function(threshold){
obs<-out[,1]>0
if(threshold==0){
pred<-out[,2]>=threshold
}
else {
pred<-out[,2]>threshold
}
temp<-c(sum(pred&obs),sum(!pred&obs),sum(pred&!obs),sum(!pred&!obs))
temp<-as.table(matrix(temp,nrow=2))
cohen.kappa(temp)
}
################################################################################
#add quadratic terms to x2 and define svars, the selection variable vector
if(x2.linear==TRUE){
svars<-c(names(x1),names(x2)) #svar does not include quadratic terms
svars.sq<-paste(svars,'.sq',sep='') #all quadratic terms
svars.sq.x2<-paste(names(x2),'.sq',sep='') #x2 quadratic terms
}
if(!is.null(x2)){
nvars<-ncol(x2)
for(i in 1:nvars){
temp<-x2[,i]^2
x2<-cbind(x2,temp)
names(x2)[nvars+i]<-paste(names(x2[i]),'.sq',sep='')
}
}
if(x2.linear==FALSE){
svars<-c(names(x1),names(x2)) #svar includes quadratic terms
}
p<-length(svars)
#define fvars, the selection variable vector for the forced terms
fvars<-names(x.force)
if(is.null(x.force)) q<-0
else q<-ncol(x.force)
#calculate the final dimension of the storage objects
ns<-0 #number of subsets we will consider (if maxp == p this is equal to m)
nc<-0 #number of coefficients
f<-ifelse(x2.linear,2,1)
for(i in 1:min(maxp,p)){
a<-choose(p,i)
ns<-ns+a
nc<-nc+a*(i*f+1+q)
}
#create parameters and pre-allocate storage objects
m<-(2^p)-1 #number of subsets (disregarding maxp)
if(is.null(x1)) N<-nrow(x2) #number of observations
else N<-nrow(x1)
coefficients<-data.frame(character(nc),numeric(nc),numeric(nc),numeric(nc),
numeric(nc),numeric(nc),stringsAsFactors=FALSE)
names(coefficients)<-c("Term","Estimate","Std. Error","z value","Pr(>|z|)","id")
model<-character(ns)
id<-numeric(ns)
AICc<-numeric(ns)
D2<-numeric(ns)
cutpoint<-numeric(ns)
if(select=='commission') FP<-numeric(ns)
if(select=='Kappa') Kappa<-numeric(ns)
#assemble all the data in one dataframe
if(is.null(x1) & !is.null(x2)) x<-x2
if(!is.null(x1) & is.null(x2)) x<-x1
if(!is.null(x1) & !is.null(x2)) x<-cbind(x1,x2)
if(is.null(x.force)) d<-cbind(data.frame(y=y),x)
else d<-cbind(data.frame(y=y),x,x.force)
#loop thru all subsets models
oi<-0 # output index
cr<-1 # the index of the first empty Coefficient table Row
for(i in 1:m){
bin<-binary(i,p)
if(sum(bin)> maxp) next
oi<-oi+1
#create a model formula
if(x2.linear==TRUE){
temp<-svars.sq[bin]
terms.sq<-temp[svars.sq[bin] %in% svars.sq.x2]
terms<-c(svars[bin],terms.sq,fvars)
}
else{
terms<-c(svars[bin],fvars)
}
if(paired.logit==TRUE){
formula<-as.formula(paste("y~",paste('-1+',paste(terms,collapse="+"),sep="")))
}
else{
formula<-as.formula(paste("y~",paste(terms,collapse="+"),sep=""))
}
#fit model
model.glm<-glm(formula,family=family,offset=offset,weights=weights,data=d)
#save coefficient stats
if(varimp==TRUE | coef.table==TRUE){
temp<-as.data.frame(summary(model.glm)$coefficients)
Term<-row.names(temp)
temp<-cbind(Term,temp,stringsAsFactors=FALSE)
temp$id<-i
coefficients[cr:(cr+nrow(temp)-1), ]<-temp[,]
cr<-cr+nrow(temp)
}
#save model aic stats (always)
model[oi]<-paste(terms,collapse='+')
id[oi]<-i
AIC<-round(model.glm$aic,3)
K<-model.glm$rank
AICc[oi]<-round(AIC+(2*K*(K+1)/(N-K-1)),3)
d2<-(model.glm$null.deviance-model.glm$deviance)/model.glm$null.deviance
D2[oi]<-round(d2,3)
#compute errors of commission
if(select=='commission'){
if(length(unique(y))>2) stop('y must be binary (0,1) for select=commission')
out<-as.data.frame(cbind(model.glm$y,model.glm$fitted.values))
names(out)<-c('observed','fitted')
cut<-quantile(out$fitted[out$observed==1],prob=1-sensitivity)
cutpoint[oi]<-cut
FP[oi]<-round(nrow(out[out$fitted>=cut & out$observed==0,])/
nrow(out[out$observed==0,]),3)
}
#compute Kappa
if(select=='Kappa'){
if(length(unique(y))>2) stop('y must be binary (0,1) response for select=Kappa')
out<-as.data.frame(cbind(model.glm$y,model.glm$fitted.values))
names(out)<-c('observed','fitted')
temp<-optimize(kappa.opt,interval=c(min(out$fitted),max(out$fitted)),maximum=TRUE)
cutpoint[oi]<-temp$maximum
Kappa[oi]<-round(temp$objective,3)
}
} # end for loop
#create model stats table
if(select=='commission'){
model.stats<-data.frame(id,model,D2,AICc,cutpoint,FP)
model.stats$deltaAICc<-round(model.stats$AICc-min(model.stats$AICc),3)
wgtAICc<-exp(-0.5*model.stats$deltaAICc)
model.stats$wgtAICc<-round(wgtAICc/sum(wgtAICc),3)
model.stats$deltaFP<-model.stats$FP-min(model.stats$FP)
model.stats<-model.stats[order(model.stats$FP),]
model.stats$rank<-seq(1,nrow(model.stats))
model.stats<-model.stats[model.stats$deltaFP<=delta.FP & model.stats$rank<=rank,]
model.stats<-model.stats[,c(1,2,3,4,7,8,5,6,9,10)]
}
else if(select=='Kappa'){
model.stats<-data.frame(id,model,D2,AICc,cutpoint,Kappa)
model.stats$deltaAICc<-round(model.stats$AICc-min(model.stats$AICc),3)
wgtAICc<-exp(-0.5*model.stats$deltaAICc)
model.stats$wgtAICc<-round(wgtAICc/sum(wgtAICc),3)
model.stats$deltaKappa<-max(model.stats$Kappa)-model.stats$Kappa
model.stats<-model.stats[order(model.stats$Kappa,decreasing=TRUE),]
model.stats$rank<-seq(1,nrow(model.stats))
model.stats<-model.stats[model.stats$deltaKappa<=delta.Kappa & model.stats$rank<=rank,]
model.stats<-model.stats[,c(1,2,3,4,7,8,5,6,9,10)]
}
else{
model.stats<-data.frame(id,model,D2,AICc)
model.stats$deltaAICc<-model.stats$AICc-min(model.stats$AICc)
wgtAICc<-exp(-0.5*model.stats$deltaAICc)
model.stats$wgtAICc<-round(wgtAICc/sum(wgtAICc),3)
model.stats<-model.stats[order(model.stats$AICc),]
model.stats$rank<-seq(1,nrow(model.stats))
model.stats<-model.stats[model.stats$deltaAICc<=delta.AIC & model.stats$rank<=rank,]
rownames(model.stats) <- 1:nrow(model.stats)
}
#create coefficients table
if(coef.table==TRUE){
sv<-coefficients$id %in% model.stats$id
coefficients<-coefficients[sv,]
coefficients<-coefficients[order(coefficients$Term),]
#coefficients<-coefficients[coefficients$Term!='(Intercept)',]
coefficients<-coefficients[,c(6,1:5)]
rownames(coefficients)<-1:nrow(coefficients)
}
#create variable importance table
if(varimp==TRUE){
z<-merge(coefficients,model.stats,by='id')
z$Term<-gsub('.sq','',x=z$Term)
z<-z[!duplicated(z[,1:2]),]
N<-aggregate(rep(1, nrow(z)),list(z$Term),sum)
names(N)<-c('Term','N')
AICc<-aggregate(z$wgtAICc,list(z$Term),sum)
names(AICc)<-c('Term','AICc')
varimport.AICc<-merge(N,AICc,by='Term')
if(p<=12 & paired.logit==FALSE){
require(hier.part)
if(!is.null(x.force)) x<-cbind(x,x.force)
HP<-round(hier.part(y,x,family=family,gof=gof,
barplot=FALSE)$I.perc/100,3)
HP$Term<-row.names(HP)
names(HP)<-c('HP','Term')
varimport.HP<-HP[,c(2,1)]
}
else{varimport.HP=NULL}
}
#create model averaging table
if(model.ave==TRUE){
require(MuMIn)
form.list<-list(nrow(model.stats))
for(i in 1:nrow(model.stats)){
if(paired.logit==TRUE){
glm.form<-as.formula(paste('y~ -1 +',model.stats$model[i],sep=''))
}
else{
glm.form<-as.formula(paste('y~',model.stats$model[i],sep=''))
}
form.list[[i]]<-glm(glm.form,data=d,family='binomial')
}
temp<-summary(model.avg(form.list))
subset.model.ave.results<-as.data.frame(temp$coefmat.subset)
full.model.ave.results<-as.data.frame(temp$coefmat.full)
}
#save results to list
if(coef.table==TRUE & varimp==TRUE & model.ave==TRUE)
return(list(model.statistics=model.stats,coefficients=coefficients,
variable.importance.AICc=varimport.AICc,variable.importance.HP=varimport.HP,
subset.averaged.coefficients=subset.model.ave.results,
full.averaged.coefficients=full.model.ave.results))
if(coef.table==TRUE & varimp==FALSE & model.ave==TRUE)
return(list(model.statistics=model.stats,coefficients=coefficients,
subset.averaged.coefficients=subset.model.ave.results,
full.averaged.coefficients=full.model.ave.results))
if(coef.table==FALSE & varimp==TRUE & model.ave==TRUE)
return(list(model.statistics=model.stats,
variable.importance.AICc=varimport.AICc,variable.importance.HP=varimport.HP,
subset.averaged.coefficients=subset.model.ave.results,
full.averaged.coefficients=full.model.ave.results))
if(coef.table==FALSE & varimp==FALSE & model.ave==TRUE)
return(list(model.statistics=model.stats,
subset.averaged.coefficients=subset.model.ave.results,
full.averaged.coefficients=full.model.ave.results))
if(coef.table==TRUE & varimp==TRUE & model.ave==FALSE)
return(list(model.statistics=model.stats,coefficients=coefficients,
variable.importance.AICc=varimport.AICc,variable.importance.HP=varimport.HP))
if(coef.table==TRUE & varimp==FALSE & model.ave==FALSE)
return(list(model.statistics=model.stats,coefficients=coefficients))
if(coef.table==FALSE & varimp==TRUE & model.ave==FALSE)
return(list(model.statistics=model.stats,
variable.importance.AICc=varimport.AICc,variable.importance.HP=varimport.HP))
if(coef.table==FALSE & varimp==FALSE & model.ave==FALSE)
return(list(model.statistics=model.stats))
}
beta.plot <-
function(shape1=.5,shape2=.5){
old.par<-par(no.readonly=TRUE)
on.exit(par(old.par))
par(mfrow=c(2,2))
n.plots<-length(shape1)*length(shape2)
k<-0
for(i in shape1){
for(j in shape2){
k<-k+1
curve(pbeta(x,shape1=i,shape2=j),0,1,
xlab='Z',ylab='Cumulative probability (quantile)',main='Cumulative Probability')
mtext(paste('(a=',i,', b=',j,')',sep=''),side=3,col='red')
curve(dbeta(x,shape1=i,shape2=j),0,1,
xlab='Z',ylab='Probability density',main='Probability Density')
mtext(paste('(a=',i,', b=',j,')',sep=''),side=3,col='red')
curve(qbeta(x,shape1=i,shape2=j),0,1,
xlab='Cumulative probability (quantile)',ylab='Z',main='Quantiles')
mtext(paste('(a=',i,', b=',j,')',sep=''),side=3,col='red')
y<-rbeta(1000,shape1=i,shape2=j)
hist(y,xlab='Z',ylab='Frequency',main='Random Observations')
mtext(paste('(a=',i,', b=',j,')',sep=''),side=3,col='red')
if(k<n.plots) readline('press return for next plot')
}
}
}
binom.plot <-
function(size=10,prob=.5){
old.par<-par(no.readonly=TRUE)
on.exit(par(old.par))
par(mfrow=c(2,2))
n.plots<-length(size)*length(prob)
k<-0
for(i in size){
n<-seq(0,i)
for(j in prob){
k<-k+1
barplot(pbinom(n,size=i,prob=j),names=as.character(n),
xlab='# Successes (k)',ylab='Cumulative probability (quantile)',
main='Cumulative Probability')
mtext(paste('(size=',i,', prob=',j,')',sep=''),side=3,col='red')
barplot(dbinom(n,size=i,prob=j),names=as.character(n),
xlab='# Successes (k)',ylab='Probability',main='Probability Mass')
mtext(paste('(size=',i,', prob=',j,')',sep=''),side=3,col='red')
barplot(qbinom(seq(0,1,.05),size=i,prob=j),names=seq(0,1,.05),
xlab='Cumulative probability (quantile)',ylab='# Successes (k)',
main='Quantiles')
mtext(paste('(size=',i,', prob=',j,')',sep=''),side=3,col='red')
y<-rbinom(1000,size=i,prob=j)
y.table<-as.data.frame(table(y))
y.levels<-as.data.frame(n)
names(y.levels)<-'y'
y.table<-merge(y.levels,y.table,all.x=TRUE)
y.table$Freq[is.na(y.table$Freq)]<-0
barplot(y.table$Freq,names=seq(0,i),xlab='# Successes (k)',ylab='Frequency',
main='Random Observations',col='gray')
mtext(paste('(size=',i,', prob=',j,')',sep=''),side=3,col='red')
if(k<n.plots) readline('press return for next plot')
}
}
}
box.plots <-
function(x,var='',by='',save.plot=FALSE,
col='blue',las=1,...){
oldpar<-par(no.readonly=TRUE)
if(!var==''){
y<-subset(x,select=eval(parse(text=var))) #select variables to summarize
y<-as.data.frame(y)
}
else{y<-as.data.frame(x)}
if(by==''){ #box-and-whisker w/o groups
par(mar=c(5,5,4,2)) #graphics settings
for(i in 1:ncol(y)){ #loop thru variables
boxplot(y[i],ylab=names(y[i]),col=col,las=las,
main=paste('Box-and-Whisker Plot of',names(y[i]),sep=' '),...)
if(save.plot==TRUE){
dev.print(jpeg,file=paste('box.',names(y[i]),'.jpg',sep=''),width=600,height=800)
} #end save
if(!i==ncol(y)) {readline("Press return for next plot ")}
} #end loop thru variables
} #end bw w/o groups
else{ #box-and-whisker w/ groups
n<-by.names(x,by) #create by variable
y<-cbind(n,y) #bind with selected variables
par(mar=c(5,5,4,2)) #graphics settings
for(i in 3:ncol(y)){ #loop thru variables
boxplot(y[[i]]~y[[2]],col=col,las=las,
ylab=names(y[i]),main=paste('Box-and-Whisker Plot of',names(y[i]),sep=' '),...)
if(save.plot==TRUE){
dev.print(jpeg,file=paste('box.',names(y[i]),'.jpg',sep=''),width=600,height=800)
} #end save
if(!i==ncol(y)) {readline("Press return for next plot ")}
} #end loop thru variables
} #end bw w/groups
par(oldpar)
}
by.names <-
function(infile,by=names(infile)){
x <- unique(infile[,by, drop=FALSE])
z <- as.character(x[,1])
if(1 < length(by))
for(i in 2:length(by)) {
z <- paste(z,as.character(x[,i]), sep='.')
}
z <- data.frame(z)
names(z) <- '..key'
t <- paste(by,collapse='.')
z <- cbind(z,x,..id = 1:dim(z)[1])
infile <- cbind(1:dim(infile)[1],infile); names(infile)[1] <- '..seq'
z <- merge(infile[,c(by,'..seq')],z,by=by)
z <- z[sort(z$..seq,index.return=TRUE)$ix,]
row.names(z) <- z$..seq
z <- z[,c('..id','..key')]
names(z) <- c('id',t)
return(z)
}
calibrate.bins <-
function(bin.mid,N.avail,N.use,plot=TRUE,...){
#------------------------------------------------------------------------------------------------#
# This function calculates the coefficient of concordance of a set of predictions
# based on presense and psuedo-absense data in binned (tabular) form
# for the purpose of model calibration; i.e., determining the accuracy of the
# predicted probability of presence when applied to the entire study area.
#
# Kevin McGarigal July 17, 2017
#
# Arguments: bin.mid : vector of bin mid-point predicted values (must be in the range 0,1)
# N.avail : vector of available count in each bin
# N.use : vector of use count in each bin
# plot : logical should a plot be made
# ... : optional other arguments passed to plot
#------------------------------------------------------------------------------------------------#
#check on library dependencies
require(epiR)
#error condition check
stopifnot(all(bin.mid>=0 & bin.mid<=1))
#create objects
bin.number<-seq(1,length(bin.mid))
#warning condition check
if(any(avail==0 & use!=0))
warning(paste("Values were observed for bins where there were no available; ",
"i.e., use count > 0 and available count = 0. This can't happen",
"with a census, but it can with a sample. Ideally, all bins should",
"have available counts > 0. You may want to conduct a census or",
"increase your available sample or reduce the number of bins",
"until the available counts are all > 0."))
#remove bins where there are no use or available counts
bin.number2<-bin.number[!(N.avail==0 & N.use==0)]
bin.mid2<-bin.mid[!(N.avail==0 & N.use==0)]
N.avail2<-N.avail[!(N.avail==0 & N.use==0)]
N.use2<-N.use[!(N.avail==0 & N.use==0)]
P.use2<-N.use2/sum(N.use2)
#compute expected utilization (proportion) and counts by bin
denom<-sum(bin.mid2*N.avail2)
P.exp2<-(bin.mid2*N.avail2)/denom
N.exp2<-P.exp2*sum(N.use2)
#compute coefficient of concordance
#cc<-epi.ccc(N.exp,N.obs,ci="z-transform",conf.level=0.95)$rho.c
cc<-round(epi.ccc(P.exp2,P.use2,ci="z-transform",conf.level=0.95)$rho.c,2)
#create result object
result<-list(bin.counts=data.frame(bin=bin.number2,bin.mid=bin.mid2,
N.avail=N.avail2,P.exp=P.exp2,N.exp=N.exp2,N.use=N.use2,
P.use=P.use2),concordance=cc)
#plot observed vs expected proportions
if(plot){
plot(P.exp2,P.use2,xlab='Expected proportion',ylab='Observed proportion',...)
abline(0,1,lty=2,lwd=2)
mtext(text=paste('Coefficient of Concordance = ',cc[1],sep=''),side=3,cex=1.5)
}
return(result)
}
chisq.plot <-
function(df=1,ncp=0,xlim=c(0,3)){
old.par<-par(no.readonly=TRUE)
on.exit(par(old.par))
par(mfrow=c(2,2))
n.plots<-length(df)
k<-0
for(i in df){
k<-k+1
curve(pchisq(x,df=i,ncp=ncp),xlim[1],xlim[2],
xlab='Z',ylab='Cumulative probability (quantile)',main='Cumulative Probability')
mtext(paste('(df=',i,')',sep=''),side=3,col='red')
curve(dchisq(x,df=i,ncp=ncp),xlim[1],xlim[2],
xlab='Z',ylab='Probability density',main='Probability Density')
mtext(paste('(df=',i,')',sep=''),side=3,col='red')
curve(qchisq(x,df=i,ncp=ncp),0,1,
xlab='Cumulative probability (quantile)',ylab='Z',main='Quantiles')
mtext(paste('(df=',i,')',sep=''),side=3,col='red')
y<-rchisq(1000,df=i,ncp=ncp)
hist(y,xlab='Z',ylab='Frequency',main='Random Observations')
mtext(paste('(df=',i,')',sep=''),side=3,col='red')
if(k<n.plots) readline('press return for next plot')
}
}
ci.lines <-
function(model,interval=95,type='expected',...){
xm<-mean(model$model[,2])
n<-length(model$model[,2])
ssx<-sum(model$model[,2]^2)-sum(model$model[,2])^2/n
prob<-1-((1-(interval/100))/2)
s.t<-qt(prob,(n-2))
xv<-seq(min(model$model[,2]),max(model$model[,2]),(max(model$model[,2])-min(model$model[,2]))/100)
yv<-coef(model)[1]+coef(model)[2]*xv
if(type=='expected') se<-sqrt(summary(model)$sigma^2*(1/n+((xv-xm)^2/ssx)))
else if(type=='predicted') se<-sqrt(summary(model)$sigma^2*(1+(1/n)+((xv-xm)^2/ssx)))
else stop('Invalid interval specified, must be expected or prediction')
ci<-s.t*se
uyv<-yv+ci
lyv<-yv-ci
lines(xv,uyv,...)
lines(xv,lyv,...)
}
class.monte <-
function(y,grouping,prop=.5,type='qda',perm=1000,prior,...){
y<-as.data.frame(y)
if(!missing(grouping)){
grp<-as.factor(grouping)
}
else{
grp<-as.factor(y[,1]) #groups assumed to be in first column
y<-y[,-1]
}
G<-length(levels(grp))
z<-matrix(NA,perm,G+2) #create blank matrix
for(i in 1:perm){
out<-tryCatch(
{
ran.split(y,grp,prop=prop)
if(type=='qda'){
if(missing(prior)) y.da<-qda(training.data,grouping=training.grp)
else y.da<-qda(training.data,grouping=training.grp,prior=prior)
} else if(type=='lda'){
if(missing(prior)) y.da<-lda(training.data,grouping=training.grp)
else y.da<-lda(training.data,grouping=training.grp,prior=prior)
}
},
error=function(e) e
)
if(inherits(out, 'simpleError')){
next
}
#create confusion matrix and compute correct classification rates
y.pred<-predict(y.da,newdata=validate.data)
y.table<-table(validate.grp,y.pred$class)
for(j in 1:G){
z[i,j]<-y.table[j,j]/sum(y.table[j,])
}
z[i,G+1]<-sum(diag(y.table))/sum(y.table)
if(missing(prior)){
z[i,G+2]<-cohen.kappa(y.table)
} else{
z[i,G+2]<-tau(y.table,prior=prior)
}
}
#summarize results across permutations
cat('Number of valid random training data sets')
print(sum(!is.na(z[,1])))
z2<-as.data.frame(apply(z,2,function(x){ #calculate stats
z2<-c(quantile(x,probs=c(0,.05,.5,.95,1),na.rm=TRUE),
mean(x,na.rm=TRUE))
names(z2)<-c('minimum','5th percentile','median','95th percentile','maximum','mean')
z2<-round(z2,3) #round elements to 3 decimal places
}))
if(missing(prior)){
colnames(z2)<-c(levels(grp),'Total','Kappa')
}
else{
colnames(z2)<-c(levels(grp),'Total','Tau')
}
cat('Split-sample Cross-Validation Classification Summary\n')
cat('Correct Classification Rate:\n')
return(z2)
}
clus.composite <-
function(x,grp){
grp<-as.factor(grp)
groups<-levels(grp)
#compute mean by cluster
z<-aggregate(x,list(grp),mean)
z<-z[,-1]
return(z)
}
clus.stats <-
function(x,grp,digits=3){
covar<<-function(x,na.rm) sd(x,na.rm=TRUE)/mean(x,na.rm=TRUE)*100
x<-as.data.frame(x)
grp<-as.factor(grp)
groups<-levels(grp)
#compute number of obs. per cluster
cl.nobs<-as.numeric(table(grp))
#compute means by cluster
cl.mean<-aggregate(x,by=list(grp),mean)
cl.mean<-cl.mean[,-1]
cl.mean<-round(cl.mean,digits=digits)
cl.mean<-as.data.frame(t(cl.mean))
names(cl.mean)<-groups
#compute cv by cluster
cl.cv<-aggregate(x,by=list(grp),covar)
cl.cv<-cl.cv[,-1]
cl.cv<-round(cl.cv,digits=digits)
cl.cv<-as.data.frame(t(cl.cv))
names(cl.cv)<-groups
#compute kruskal-wallis rank sum test p-value
p.value<-rep(0,length(x))
for(i in 1:length(x)){
p<-kruskal.test(x[,i],grp)
p.value[i]<-p$p.value
}
p.value<-round(p.value,3)
x.mean<-cbind(cl.mean,p.value)
#create list object
z<-list(cl.nobs,cl.mean,cl.cv)
names(z)<-c('Cluster.nobs','Cluster.mean','Cluster.cv')
return(z)
}
cohen.kappa <-
function(y){
N<-sum(y)
ccr<-sum(diag(y))/sum(y)
p<-apply(y,1,sum)/N
q<-apply(y,2,sum)/N
num<-ccr-sum(p*q)
den<-1-sum(p*q)
kappa<-num/den
kappa[kappa<0]<-0
return(kappa)
}
col.summary <-
function(x,var=NULL,by=NULL,outfile=NULL,...){
options(warn=-1)
#statistical functions
nobs<-function(x) length(x)
cv<-function(x,na.rm) sd(x,na.rm=TRUE)/mean(x,na.rm=TRUE)*100
zeros<-function(x,na.rm) sum(x==0,na.rm=TRUE)
pct.zeros<-function(x,na.rm) sum(x==0,na.rm=TRUE)/length(x)*100
nobs.missing<-function(x,na.rm) sum(is.na(x))
pct.missing<-function(x,na.rm) sum(is.na(x))/length(x)*100
se<-function(x,na.rm) sd(x,na.rm=TRUE)/sqrt(length(x)-sum(is.na(x)))
se.ratio<-function(x,na.rm) se(x)/mean(x,na.rm=TRUE)*100
richness<-function(x,na.rm) nobs(x)-zeros(x)-nobs.missing(x)
#select subset of variables
if(!is.null(var)){
y<-subset(x,select=eval(parse(text=var)))
}
else{y<-x}
#summary table w/o groups
if(is.null(by)){
z<-data.frame(apply(y,2,function(x){ #calculate stats
z<-c(nobs(x),min(x,na.rm=TRUE),max(x,na.rm=TRUE),
mean(x,na.rm=TRUE),median(x,na.rm=TRUE),sum(x,na.rm=TRUE),
sd(x,na.rm=TRUE),cv(x),zeros(x),pct.zeros(x),nobs.missing(x),
pct.missing(x),se(x),se.ratio(x),richness(x))
names(z)<-c('nobs','min','max','mean',
'median','sum','sd','cv','zeros','pct.zeros',
'nobs.missing','pct.missing','se','se.ratio',
'richness') #create col names
z<-round(z,3) #round elements to 3 decimal places
}))
if(!is.null(outfile)){ #save results to output file
write.table(z,file=paste(outfile,'.csv',sep=''),quote=FALSE,sep=',')
}
}
#summary table by groups
else{
n<-by.names(x,by) #create by variable
m<-levels(n[,2]) #create object with group levels
z<-vector('list',length(m)) #create list object for output
names(z)<-m #assign names to list components
for(i in 1:length(m)){ #loop thru by groups
y1<-y[n[,2]==m[i],] #select records within group
zz<-data.frame(apply(y1,2,function(x){ #calculate stats
zz<-c(nobs(x),min(x,na.rm=TRUE),max(x,na.rm=TRUE),
mean(x,na.rm=TRUE),median(x,na.rm=TRUE),sum(x,na.rm=TRUE),
sd(x,na.rm=TRUE),cv(x),zeros(x),pct.zeros(x),nobs.missing(x),
pct.missing(x),se(x),se.ratio(x),richness(x))
names(zz)<-c('nobs','min','max','mean',
'median','sum','sd','cv','zeros','pct.zeros',
'nobs.missing','pct.missing','se','se.ratio',
'richness') #create col names
zz<-round(zz,3) #round elements to 3 decimal places
}))
z[[i]]<-zz
if(!is.null(outfile)){ #save results to output file
write(m[i],file=paste(outfile,'.csv',sep=''),append=TRUE)
write.table(zz,file=paste(outfile,'.csv',sep=''),quote=FALSE,append=TRUE,sep=',')
}
} #end loop thru groups
} #end summary table w/ groups
return(z)
}
commission.mc <-
function(fit,test=FALSE,reps=1000,sensitivity=.95,plot=TRUE,...){
owarn <- options("warn")
on.exit(options(warn=owarn$warn))
options(warn=-1)
##################################################################################
#functions
##################################################################################
#function for computing false positive (commission) error rate on glm object
FP<-function(fit,sensitivity=.95){
temp<-as.data.frame(cbind(fit$y,fit$fitted.values))
names(temp)<-c('observed','fitted')
cutpoint<-quantile(temp$fitted[temp$observed==1],prob=1-sensitivity)
FP<-(nrow(temp[temp$fitted>=cutpoint & temp$observed==0,])/
nrow(temp[temp$observed==0,]))
z<-list('cutpoint'=cutpoint,'FP'=FP)
return(z)
}
##################################################################################
#compute observed FP and cutpoint
temp<-FP(fit,sensitivity)
FP.obs<-temp$FP
cutpoint<-temp$cutpoint
#null (random) distribution of FP
if(test==TRUE){
FP.null<-NULL
if(is.null(fit$na.action)==TRUE){
z2<-fit$data
}
else{
z2<-fit$data[-fit$na.action,]
}
nobs<-nrow(z2)
for(i in 1:reps){
z2[,c(as.character(fit$formula[[2]]))]<-z2[sample(1:nobs,replace=FALSE),
c(as.character(fit$formula[[2]]))]
e<-new.env()
e$fit<-fit
for(i in names(z2)) assign(i,z2[[i]],envir=e)
temp<-glm(fit$formula,family=fit$family,offset=fit$offset,weights=fit$prior.weights,data=e)
temp<-as.data.frame(cbind(temp$y,temp$fitted.values))
names(temp)<-c('observed','fitted')
cut.perm<-quantile(temp$fitted[temp$observed==1],prob=1-sensitivity)
FP.perm<-(nrow(temp[temp$fitted>=cut.perm & temp$observed==0,])/nrow(temp[temp$observed==0,]))
FP.null<-c(FP.null,FP.perm)
}
#compute p-value
p.value<-sum(FP.null<=FP.obs)
p.value<-(1+p.value)/(1+reps)
}
if(plot==TRUE){
xmin<-min(FP.obs,min(FP.null))
xmax<-max(FP.obs,max(FP.null))
hist(FP.null,col='blue',xaxs='i',yaxs='i',xlim=c(xmin,xmax),
xlab='False positive error rate',cex.lab=1.5,
main='Randomization test of false positive error rate',...)
abline(v=FP.obs,col='black',lty=2,lwd=2,...)
legend('topleft',inset=c(.1,.1),legend='Observed',lty=2,lwd=2,bty='n')
legend('topleft',inset=c(.1,.2),legend='Null',fill='blue',bty='n')
}
z<-as.data.frame(rbind('Cutpoint'=cutpoint,'Observed commission rate'=round(FP.obs,3),
'P-value'=format.pval(p.value,digits=3,eps=.001)))
names(z)=''
return(z)
}
concordance <-
function(use.data,avail.data,formula,method='glm',weights=NULL,
paired=FALSE,use.strata=NULL,avail.strata=NULL,v=10,bins=NULL,balanced=TRUE,
max.p=NULL,
obex.plot=TRUE,cc.plot=TRUE,...){
#add method for split-sample validation
#check on library dependencies