R/asocialGradient_fn.R

In whoppitt/NBDA: A Package For Implementing Network-Based Diffusion Analysis

#Editted for constrained model


asocialGradient_fn <- function(parVect, nbdadata,retainInt=NULL){

#We need to know whether to remove the interaction variables. This depends on whether an offset is included for any of the s parameters in any of the diffusions.
#This will be passed on by the model fitting function, but if the function is called independently we need to calculate this here
  if(is.null(retainInt)){
    if(is.list(nbdadata)){
      retainInt<-FALSE
      for (i in 1:length(nbdadata)){
        nbdadataTemp2<-nbdadata[[i]];
        if(sum(nbdadataTemp2@offsetCorrection[,1])>0) retainInt<-TRUE
      }
    }else{
      retainInt<-sum(nbdadata@offsetCorrection[,1])>0
    }
  }

  if(is.list(nbdadata)){

    totalGradient <- rep(0, length(parVect));

    for(i in 1:length(nbdadata)){
      subdata <- nbdadata[[i]];
      totalGradient <- totalGradient + asocialGradient_fn(parVect= parVect, nbdadata=subdata,retainInt = retainInt);
    }

    return(totalGradient);

  }else{



  #calculate the number of each type of parameter
  noSParam <- dim(nbdadata@stMetric)[2] #s parameters
  noILVasoc<- dim(nbdadata@asocILVdata)[2] #ILV effects on asocial learning
  noILVmulti<- dim(nbdadata@multiILVdata)[2] #ILV multiplicative model effects

  if(nbdadata@asoc_ilv[1]=="ILVabsent") noILVasoc<-0
  if(nbdadata@int_ilv[1]=="ILVabsent") noILVint<-0
  if(nbdadata@multi_ilv[1]=="ILVabsent") noILVmulti<-0

  includeInOADA<-nbdadata@event.id %in% nbdadata@event.id[nbdadata@status==1]
  #Exclude the lines of data corresponding to the final period to endtime, if necedssary
  datalength <- sum(includeInOADA)

  #Extract vector giving which naive individuals were present in the diffusion for each acqusition event
  presentInDiffusion<-nbdadata@ presentInDiffusion[includeInOADA]

  #Extend par to include 0 s parameters
  parVect<-c(rep(0,noSParam),parVect)

  #Allow for the fact that the user might provide offsets to the s parameters which might need to be accounted for
  if(retainInt){
    noILVint<- dim(nbdadata@intILVdata)[2] #ILV effects on interation (social learning)
    if(nbdadata@int_ilv[1]=="ILVabsent") noILVint<-0
    if(length(parVect)!=noSParam+noILVasoc+noILVint+noILVmulti){
      cat("Error: parVect wrong length. \nNote a non-zero offset is provided for the s parameters. \nparVect must include values for the interaction effects\n")
      return(NA)
    }
  }else{
    noILVint<-0
    if(length(parVect)!=noSParam+noILVasoc+noILVint+noILVmulti){
      cat("Error: parVect wrong length. \nNote a zero offset is provided for the s parameters. \nparVect must not include values for the interaction effects\n")
      return(NA)
    }
  }

  #assign different paramreter values to the right vectors
  sParam <- parVect[1:noSParam]
  asocialCoef <- parVect[(noSParam+1):(noSParam+ noILVasoc)]
  multiCoef<-parVect[(noSParam+noILVasoc+noILVint+1):(noSParam+ noILVasoc+noILVint+noILVmulti)]

  if(nbdadata@asoc_ilv[1]=="ILVabsent") asocialCoef<-NULL
  if(nbdadata@int_ilv[1]=="ILVabsent") intCoef<-NULL
  if(nbdadata@multi_ilv[1]=="ILVabsent") multiCoef<-NULL



  # create a matrix of the coefficients to multiply by the observed data values, only if there are asocial variables
  if(nbdadata@asoc_ilv[1]=="ILVabsent"){
    asocialLP<-rep(0,datalength)
  }else{
    asocialCoef.mat <- matrix(data=rep(asocialCoef, datalength), nrow=datalength, byrow=T)
    asocial.sub <- nbdadata@asocILVdata[includeInOADA,]
    asocialLP <- apply(asocialCoef.mat*asocial.sub, MARGIN=1, FUN=sum)
  }
  asocialLP<-asocialLP+nbdadata@offsetCorrection[includeInOADA,2]


  # now calculate the multiplicative LP and add to the asocial LP
  if(nbdadata@multi_ilv[1]=="ILVabsent"){
    multiLP<-rep(0,datalength)
  }else{
    multiCoef.mat <- matrix(data=rep(multiCoef, datalength), nrow=datalength, byrow=T)
    multi.sub <- nbdadata@multiILVdata[includeInOADA,]
    multiLP <- apply(multiCoef.mat*multi.sub, MARGIN=1, FUN=sum)
  }
  multiLP<-multiLP+nbdadata@offsetCorrection[includeInOADA,4]
  asocialLP<-asocialLP+multiLP

  unscaled.st<-nbdadata@offsetCorrection[includeInOADA,1]


  #Allow for the fact that the user might provide offsets to the s parameters which might need to be accounted for
  if(retainInt){

    #assign different paramreter values to the right vectors
    intCoef<- parVect[(noSParam+noILVasoc+1):(noSParam+ noILVasoc+noILVint)]

    #interaction variables
    if(nbdadata@int_ilv[1]=="ILVabsent"){
      socialLP<-rep(0,datalength)
    }else{
      intCoef.mat <- matrix(data=rep(intCoef, datalength), nrow=datalength, byrow=T)
      int.sub <- nbdadata@intILVdata[includeInOADA,]
      socialLP <- apply(intCoef.mat*int.sub, MARGIN=1, FUN=sum)
    }
    # calculate
    socialLP<-socialLP+nbdadata@offsetCorrection[includeInOADA,3]+multiLP
  }else{socialLP<-rep(0,datalength)}


  #The totalRate is set to zero for naive individuals not in the diffusion for a given event
  totalRate <- (exp(asocialLP) + exp(socialLP)*unscaled.st)* presentInDiffusion


#### ASOCIAL PARAMETERS

  #### ASOCIAL PARAMETERS

  if(nbdadata@asoc_ilv[1]!="ILVabsent"){

    asocial_grad <- vector("numeric", length=length(nbdadata@asoc_ilv))
    for (i in 1:length(nbdadata@asoc_ilv)){

      # UNCONSTRAINED OR ADDITIVE - first derivative of the likelihood function for asocial variables
      asocial_grad[i] <- sum((nbdadata@asocILVdata[nbdadata@status==1,i]*(exp(asocialLP[nbdadata@status==1])))/totalRate[nbdadata@status==1] -tapply(nbdadata@asocILVdata[includeInOADA,i]*(exp(asocialLP))*presentInDiffusion, INDEX=nbdadata@event.id[includeInOADA], FUN=sum)/tapply(totalRate, INDEX=nbdadata@event.id[includeInOADA], FUN=sum))
      # NUM: variable for solver * solver asocial rate / solver total rate
      # DENOM: variable for all individiduals * asocial rate, summed over all acquisition events / total naive rate
    } # closes loop through asocialVar
  } else {asocial_grad <- NULL} # closes if !isn.null(asocialVar)

  if(nbdadata@multi_ilv[1]!="ILVabsent"){

    multi_grad <- vector("numeric", length=length(nbdadata@multi_ilv))
    for (i in 1:length(nbdadata@multi_ilv)){

      # UNCONSTRAINED OR ADDITIVE - first derivative of the likelihood function for asocial variables
      multi_grad[i] <- sum(nbdadata@multiILVdata[nbdadata@status==1,i] - tapply(nbdadata@multiILVdata[includeInOADA,i]*(totalRate), INDEX=nbdadata@event.id[includeInOADA], FUN=sum)/tapply(totalRate, INDEX=nbdadata@event.id[includeInOADA], FUN=sum))
      # NUM: variable for solver * solver asocial rate / solver total rate
      # DENOM: variable for all individiduals * asocial rate, summed over all acquisition events / total naive rate
    } # closes loop through asocialVar
  } else {multi_grad <- NULL} # closes if !isn.null(asocialVar)

  #### SOCIAL PARAMETERS

  if(nbdadata@int_ilv[1]!="ILVabsent"&retainInt){

    social_grad <- vector("numeric", length=length(nbdadata@int_ilv))
    for (i in 1:length(nbdadata@int_ilv)){


      social_grad[i] <- sum((nbdadata@intILVdata[nbdadata@status==1,i]*(unscaled.st[nbdadata@status==1]*exp(socialLP[nbdadata@status==1])))/totalRate[nbdadata@status==1] - tapply(nbdadata@intILVdata[includeInOADA,i]*unscaled.st*(exp(socialLP))*presentInDiffusion, INDEX=nbdadata@event.id[includeInOADA], FUN=sum)/tapply(totalRate, INDEX=nbdadata@event.id[includeInOADA], FUN=sum))
      # variable for solver * solver social rate / solver total rate
      # variable for all individiduals * social rate, summed over all acquisition events / total naive rate
    } # closes loop through social var
  } else {social_grad <- NULL} # closes if !is.null(nbdadata@asoc)


  gradient <- c(asocial_grad, social_grad, multi_grad)
  return(-gradient)
}
} # end function