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#' Performs social network based diffusion analysis in a Bayesian context
#' @param formatteddata formatted data
#' @param its number of iterations
#' @param pilot_tuner1 tuning parameter for the social effect
#' @param pilot_tuner2 tuning parameter for the asocial effect
#' @param start1 start value for the social parameter
#' @param start2 start value for the asocial parameter
#' @export
smcmc = function(formatteddata,its,pilot_tuner1,pilot_tuner2,pilot_tuner3,start1,start2,start3){
TimeD = formatteddata[[1]][,7] # time interval of solving
censored = formatteddata[[1]][,6] # 1/0 binary variable indicating censored status after expt end
Aij = formatteddata[[1]][,8]# interaction covariate based on network
NaiveD = formatteddata[[2]] # naive status at each time point for each unique individual
spatcov = formatteddata[[1]][,10]# spatial/environmental covariate
s0= start1 # strength of social transmission
baseline_rate = lambda0 = start2# baseline rate of acquisition in absence of social transimission
environmental = beta0 = start3 # spatial covariate
acceptcounter = 0 #(not used)
Jumbo<-array(0,c(its,3)) # storage of updated parameters (except interactions) at each iteration
newparam<-array(0.5,3) # allocation of storage during update process
CurrentParam<-array(0.5,3)# allocation of storage during update process
newparam[1]=CurrentParam[1]<-s0 # used
newparam[2]=CurrentParam[2]<-lambda0 # used
newparam[3]=CurrentParam[3]<-beta0 # used
#----------------------------------
# FUNCTIONS
#----------------------------------
# updating the s parameter (allowed to take only positive values)
updates<-function(CurrentParam,newparam){
GU3<-runif(1,CurrentParam[1]-pilot_tuner1,CurrentParam[1]+ pilot_tuner1)
proposal = c(GU3,CurrentParam[2:3])
num<-CpS(proposal)[[1]]
den<-CpS(CurrentParam)[[1]]
acc<-exp(num-den)
acceptr<-min(1,acc)
r<-runif(1)
newparam[1]<-ifelse((r<=acceptr),GU3,CurrentParam[1])
return(newparam[1])
}
# updating the lambda (baseline rate of acquisition) parameter (allowed to take only positive values)
updatelambda<-function(CurrentParam,newparam){
GU3<-runif(1,CurrentParam[2]-pilot_tuner2,CurrentParam[2]+ pilot_tuner2)
proposal = c(CurrentParam[1],GU3,CurrentParam[3])
num<-CpS(proposal)[[1]]
den<-CpS(CurrentParam)[[1]]
acc<-exp(num-den)
acceptt<-min(1,acc)
r<-runif(1)
newparam[2]<-ifelse((r<=acceptt),GU3,CurrentParam[2])
acceptcounter<-ifelse((r<=acceptt),1,0)
list(newparam[2],acceptcounter)
}
updatecovariate<-function(CurrentParam,newparam){
GU3<-runif(1,CurrentParam[3]-5,CurrentParam[3]+ 5)
proposal = c(CurrentParam[1:2],GU3)
num<-CpS(proposal)[[1]]
den<-CpS(CurrentParam)[[1]]
acc<-exp(num-den)
acceptr<-min(1,acc)
r<-runif(1)
newparam[3]<-ifelse((r<=acceptr),GU3,CurrentParam[3])
return(newparam[3])
}
CpS = function(parameterproposal){
baseline = exp(parameterproposal[2])
social_rate = exp(parameterproposal[1])
spatialC = exp(parameterproposal[3])
hazard = baseline*exp(spatialC) + (social_rate)*Aij # hazard function
uncensored = 1-censored
log_likelihood_u = sum(log(hazard*exp(-hazard*TimeD))*uncensored) + sum(-hazard*TimeD*NaiveD)
log_likelihood_c = sum(-hazard*censored)
log_likelihood = log_likelihood_u + log_likelihood_c
lambdaprior<- log(dunif(parameterproposal[2],-10,10)) # s prior
sprior<- log(dunif(parameterproposal[1],-10,10))# lambda prior
sCprior<- log(dunif(parameterproposal[3],-10,10))# lambda prior
pzoid<-log_likelihood + lambdaprior + sprior + sCprior
pzoid
}
for(t in 1:its){
CurrentParam[1]=Jumbo[t,1]=updates(CurrentParam,newparam)[[1]] # s
CurrentParam[2]=Jumbo[t,2]=updatelambda(CurrentParam,newparam)[[1]] # lambda
CurrentParam[3]=Jumbo[t,3]=updatecovariate(CurrentParam,newparam)[[1]] # beta
}
burnin = its/10
par(mfrow=c(2,2))
plot(Jumbo[burnin:its,1],type="l",col="blue",ylab="social effect",main="Trace plot for social effect, s' ",lwd=2)
plot(Jumbo[burnin:its,2],type="l",col="red",ylab="asocial effect",main="Trace plot for asocial effect, lambda0' ",lwd=2)
plot(Jumbo[burnin:its,3],type="l",col="lightgoldenrod",ylab="spatial effect",
main="Trace plot for spatial effect, beta0' ",lwd=2)
params = c(mean(Jumbo[burnin:its,1]),mean(Jumbo[burnin:its,2]),mean(Jumbo[burnin:its,3]))
creds = c(sd(Jumbo[burnin:its,1]),sd(Jumbo[burnin:its,2]),sd(Jumbo[burnin:its,3]))
mcmcresults = list(Jumbo,params,creds)
mcmcresults
}
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