R/MEMS_pooled_ergm_nonparam.R

In netmediate: Micro-Macro Analysis for Social Networks

#
# This function estimates the MEMS using ERGM with parametric algorithm
#
#
# model is the ERGM object
#micro_process is the micro process of interest, provided as a character string
#macro_function is the function to be calculated on the network object. NOTE: currently only supports statistics calculated on network and igraph objects.
#object type is the type of object used in the function to calculate macro statistics. Currently only supports igraph and network objects. If left NULL, the object is assumed to be a network object.
#the interval provides the values over which to calculate the MEMS. It defaults to 0 and 1
#nsim is the number of Monte Carlo samples
# silent tells R whether to provide updates on the algorithm's progress
#full_output tells R whether to return simulated distribution in addition to summary statistic



MEMS_pooled_ergm_nonparam <- function(model,
                                   micro_process,
                                   macro_function,
                                   object_type=object_type,
                                   interval=interval,
                                   nsim=nsim,
                                   silent=silent,
                                   full_output=full_output,
                                   mediator=mediator,
                                   link_id=link_id,
                                   controls=controls,
                                   control_functions=control_functions) {

  message("Getting bootstrap parameter vector for network ")

  aMEMS_tracer<-1
  theta_list<-list()
  ergm_mat_list<-list()
  interval<-sort(interval) #order from lowest to highest

  for(i in 1:length(model)){


    ergm_mat_list[[i]]<-ergMargins::edge.prob2(model[[i]])
    if(nrow(ergm_mat_list[[i]])>=200000){warning("More than 200,000 observations in Model ",i,". Nonparametric estimation not recommended due to computational expensiveness. Try parametric estimation to reduce run times.")}
    theta_list[[i]]<-matrix(NA,nrow=nsim,ncol=length(coef(model[[i]])))
    colnames(theta_list[[i]])<-names(coef(model[[i]]))

    dyad_mat<-ergm_mat_list[[i]]
    start.drops<-ncol(dyad_mat)-5
    dyad_mat<-dyad_mat[,-c(2,start.drops:ncol(dyad_mat))]

    for(j in 1:nsim){

      bs_mat<-dyad_mat[sample(nrow(dyad_mat), replace=TRUE), ]
      bs_model<-glm(bs_mat$tie ~  1+., data = data.frame(bs_mat[,!colnames(bs_mat)%in%c("tie")]))
      theta_list[[i]][j,]<-coef(bs_model)

      if(silent==FALSE){

        message("Getting bootstrap parameters ", j, " of ", nsim, " complete for network ", i)

      }

    }


  }


  #create list of values to predict over
  mat_list<-list()
  for(j in 1:length(ergm_mat_list)){
    mat_list[[j]]<-ergm_mat_list[[j]]

    for(i in 1:length(interval)){
      mat_list[[j]][[i]]<-ergm_mat_list[[j]]
    }
  }

  #create lists of data for each link_id and control. These lists provide the data for AMME function
  if(!is.null(link_id)){

    link_list_data<-list()
    for(i in 1:nsim){
      link_list_data[[i]]<-matrix(NA,nrow=unique(length(link_id[[1]])),ncol=length(interval))
      rownames(link_list_data[[i]])<-unique(link_id[[1]])
    }

    if(length(controls)>0){
      controls_list<-as.list(controls)
      for(i in 1:length(controls)){
        sim_list<-list()
        for(j in 1:nsim){
          sim_list[[j]]<-matrix(NA,nrow=unique(length(link_id[[i+1]])),ncol=length(interval))
          rownames(sim_list[[j]])<-unique(link_id[[i+1]])
        }
        controls_list[[i]]<-sim_list
        names(controls_list)<-controls

      }
    }else{
      controls_list<-NULL
    }
  }

  message("Computing MEMS over ",interval[1],"-",interval[length(interval)]," interval")

  output_list<-list()
  for(i in 1:length(ergm_mat_list)){
    output_list[[i]]<-matrix(NA,nrow=nsim,ncol=length(interval))

  }

  for(entry in 1:length(output_list)){

    #simulate values for j parameters
    for(j in 1:nrow(theta_list[[entry]])){

      #create networks for k intervals

      net_list<-list()
      net_list[[entry]]<-model[[entry]]$network
      for(i in 1:length(interval)){

        pred_mat<-mat_list[[entry]][[i]]
        start.drops<-ncol(pred_mat)-5
        pred_mat<-pred_mat[,-c(1,start.drops:ncol(pred_mat))]
        cbcoef<-theta_list[[entry]][j,]
        cbcoef[micro_process]<-cbcoef[micro_process]*interval[i]

        #predict ties
        lp <- as.matrix(pred_mat) %*% cbcoef
        result <- c(1/(1 + exp(-lp)))
        pred_mat<-mat_list[[entry]][[i]]
        pred_mat$y <- rbinom(nrow(mat_list[[entry]][[i]]),1,result)      # create predicted ties

        #create network
        el<-pred_mat[,c("i","j","y")]
        el<-el[el$y==1,-c(3)]
        el<-as.matrix(el)

        #create network, assign vertex attributes, by creating empty network and adding new edges
        net_list[[entry]][[i]]<-model[[entry]]$network
        net_list[[entry]][[i]][,]<-0
        net_list[[entry]][[i]]<-network::add.edges(net_list[[entry]][[i]],tail=el[,1],head=el[,2])

      }

      ##now need to calculate statistics on each network in list
      #then need to calculate difference statistics and MEMS or aMEMS
      #then need to store output

      if(object_type[1]%in%c("network")){

        for(i in 1:length(interval)){
          b<-macro_function(net_list[[entry]][[i]])
          if(!is.null(link_id)){
            node_start<- which(is.na(link_list_data[[j]][,i]))[1]
            node_index<-node_start+(length(b)-1)
            link_list_data[[j]][node_start:node_index,i]<-b
          } ##store vector of output when calling AMME

          if(length(b)>1){
            b<-mean(b,na.rm=TRUE)
            aMEMS_tracer<-1} ##handle node and multiple obs characteristics for MEMS output
          output_list[[entry]][j,i]<-b
        }

      }else{
        #for igraph functions
        for(i in 1:length(interval)){
          net_list[[entry]][[i]]<-intergraph::asIgraph(net_list[[entry]][[i]])
          b<-macro_function(net_list[[entry]][[i]])
          if(!is.null(link_id)){
            node_start<- which(is.na(link_list_data[[j]][,i]))[1]
            node_index<-node_start+(length(b)-1)
            link_list_data[[j]][node_start:node_index,i]<-b
          } #store vector of output when calling AMME
          if(length(b)>1){
            b<-mean(b,na.rm=TRUE)
            aMEMS_tracer<-1} ##handle node and multiple obs characteristics
          output_list[[entry]][j,i]<-b
          if(length(controls)>0){
            net_list[[entry]][[i]]<-intergraph::asNetwork(net_list[[entry]][[i]]) # convert back to network for control operations
          }

        }

      }

      ##get controls

      if(length(controls)>0){

        for(control in 1:length(controls_list)){
          if(object_type[control+1]%in%c("network")){

            for(i in 1:length(interval)){
              b<-control_functions[[control]](net_list[[entry]][[i]])
              node_start<- which(is.na(controls_list[[control]][[j]][,i]))[1]
              node_index<-node_start+(length(b)-1)
              controls_list[[control]][[j]][node_start:node_index,i]<-b
            }

          }else{
            #for igraph functions
            for(i in 1:length(interval)){
              net_list[[i]]<-intergraph::asIgraph(net_list[[entry]][[i]])
              b<-control_functions[[control]](net_list[[entry]][[i]])
              node_start<- which(is.na(controls_list[[control]][[j]][,i]))[1]
              node_index<-node_start+(length(b)-1)
              controls_list[[control]][[j]][node_start:node_index,i]<-b
              net_list[[entry]][[i]]<-intergraph::asNetwork(net_list[[entry]][[i]]) #convert back to network object for further loops

            }

          }

        }
      } #closes if controls statement



      if(silent==FALSE){
        print(paste("Simulation ",j," out of", nsim," complete for network ", entry))
      }
    }
    node_start<-node_start+network::network.size(model[[entry]]$network)


  }

  if(aMEMS_tracer==1 & is.null(link_id)){
    message("More than one macro statistic is being calculated. Reporting the aMEMS.")
  }

  for(i in 1:length(output_list)){

    if(i == 1){
      output_data<-output_list[[i]]
    }else{
      output_data<-rbind(output_data,output_list[[i]])
    }

  }

  diff_data<-matrix(NA,nrow=nrow(output_data),ncol=ncol(output_data)-1)

  for(i in 1:ncol(diff_data)){
    k<-i+1

    diff_data[,i]<-output_data[,k]-output_data[,i]
  }

  summary_dat<-matrix(NA,nrow=2,ncol=5)
  rownames(summary_dat)<-c("MEMS","Prop. Change in M")
  colnames(summary_dat)<-c("Estimate","Std. Dev.","lower 95% CI","Upper 95% CI","BS p-val")

  summary_dat[1,1]<-mean(diff_data,na.rm=TRUE)
  summary_dat[1,2]<-sd(diff_data,na.rm=TRUE)

  if(summary_dat[1,1]<0){
    summary_dat[1,5]<-length(diff_data[which(diff_data>0)])/(length(model)*nsim*ncol(diff_data))
  }else{
    summary_dat[1,5]<-length(diff_data[which(diff_data<0)])/(length(model)*nsim*ncol(diff_data))

  }
  summary_dat[1,3]<-quantile(diff_data,.025,na.rm=TRUE)
  summary_dat[1,4]<-quantile(diff_data,.975,na.rm=TRUE)



  prop_change<-matrix(NA,nrow=nrow(output_data),ncol=ncol(output_data)-1)

  for(i in 1:ncol(prop_change)){
    k<-i+1

    prop_change[,i]<-(diff_data[,i]/output_data[,k])
  }

  prop_change<-prop_change[!is.infinite(prop_change)]

  summary_dat[2,1]<-mean(prop_change,na.rm=TRUE)

  message("Note that a single aMEMS is returned for all networks. To obtain distinct MEMS estimates for each network, call the MEMS function specifying a single model, rather than a list of models.")
  if(full_output==FALSE){
    return(summary_dat)
  }else{
    out_dat<-list(summary_dat=summary_dat,
                  output_data=output_data,
                  mems_samples=diff_data)
    if(is.null(link_id)){

      return(out_dat) #return data no controls

    }else{

      #return data for AMME call
      out_dat<-list(out_dat_main=link_list_data,
                    out_dat_controls=controls_list)

      return(out_dat)


    }
  }

}