Nothing
R/ergmMEM_boot.R
In ergMargins: Process Analysis for Exponential Random Graph Models
Defines functions
ergm.MEM_boot
#' Function to compute marginal effect at means in ERGM
#' If var2 and inter are left NULL, the function returns the marginal effect at mean for var 1.
#' if var2 and inter are specified, function conducts tests of second differences to assess significance of an interaction
#'
#' @param model is an ergm object
#' @param var1 is the name of the main effect, character string
#' @param var2 is the name of the moderator, character string
#' @param inter is the name of the interaction, character string
#' @param at.2 is a vector specifying the levels of var2 at which to compute the marginal effects. If left NULL, it computes the MEM at all unique values of var2. Default is NULL.
#If the moderator is binary or specified at only 2 levels,
#the output object is a 2 dimensional list with one matrix of
#marginal effects and another of the second differences (ADC)
#If the moderator is continuous and specified at 3 or more levels,
#the output object contains a 3 dimensional list, where the Aggregate output is the
#average second difference and t tests based on the average second difference,
#the second differnece matrix is the matrix of second differneces between
#all adjacent levels of var 2, and the marginal matrix is the matrix of marginal effect at means
#standard errors are computed using the delta method.
ergm.MEM_boot<-function(model,
var1,
var2=NULL,
inter=NULL,
at.2=NULL,
at.controls=NULL,
control_vals=NULL,
return.dydx=FALSE){
##get edge probabilities
dyad.mat<-edge.prob2(model)[,-c(1)]
dyad.full.mat<-dyad.mat
p<-dyad.mat$probability
start.drops<-ncol(dyad.mat)-5
dyad.mat<-dyad.mat[,-c(start.drops:ncol(dyad.mat))]
theta<-btergm::coef(model)
if(any(names(theta)!=colnames(dyad.mat))){
colnames(dyad.mat)<-names(theta) #make sure names align
}
##assign fixed values for controls when specified
if(!is.null(at.controls)){
if(is.null(control_vals)){
stop("control_vals must be specified to use at.controls argument.")
}
if(length(at.controls)==1){
dyad.mat[,at.controls]<-control_vals
}else{
for(i in 1:length(at.controls)){
dyad.mat[,at.controls][,i]<-control_vals[i]
}
}
p<-as.matrix(dyad.mat)%*%theta
}
if(nrow(dyad.mat)>1e06){
message("There are over 1 million dyads in the ERGM sample space. Variance estimates for marginal effects may take a moment to compute.")
}
if(length(theta)>20){
message("There are more than 20 parameters in the model. Variance estimates for marginal effects may take a moment to compute.")
}
##identify unique values of at.2--not used if var2==NULL
if(is.null(at.2)){
at.2<-sort(unique(dyad.mat[,var2]))
}
if(length(at.2)>10){
warning("More than 10 values of at.2 exist for the moderating variable. It may take awhile to compute marginal effect at means. Consider specifying fewer values of at.2.")
}
theta_boot<-model@boot$t
#create marginal effects
dyad.means<-colMeans(dyad.mat,na.rm=TRUE)
p<-1/(1+exp(-dyad.means%*%theta))
##marginal effects with no interaction
if(is.null(var2)){
MEM.fun<-function(theta){
ME.ergm<-sapply(names(theta),function(x)
(p*(1-p)*theta[var1]))
mean(ME.ergm,na.rm = TRUE)}
MEM<-MEM.fun(theta)
MEM_boots<-apply(theta_boot,1,FUN=MEM.fun)
MEM.se<-sd(MEM_boots)
MEM.z<-MEM/MEM.se
P.MEM<-2*(stats::pnorm(-abs(MEM.z)))
MEM<-matrix(c(MEM,MEM.se,MEM.z,P.MEM),nrow=1,ncol=4)
colnames(MEM)<-c("MEM","Bootstrap SE","Z","P")
rownames(MEM)<-var1
MEM<-signif(MEM,digits=5)
if(return.dydx==TRUE){
dydx<-sapply(names(theta),function(x)
(p*(1-p)*theta[var1]))
MEM<-list(MEM,dydx[var1],MEM_boots)
names(MEM)<-c("MEM","dydx","bootstraps")
}
return(MEM)
}else{
##marginal effects for interaction that does not vary with covariates
if(!is.na(pmatch("nodematch",inter))){
if(!is.na(pmatch("nodecov",var1)) | !is.na(pmatch("nodeicov",var1)) |
!is.na(pmatch("nodeocov",var1))){
##matched nodal characteristics are not a product term for node covariates, so compute marginal effects
#for var 1 and var 2, then use results to compute marignal effect for interaction
MEM.fun<-function(theta){
ME.ergm<-sapply(names(theta),function(x)
(p*(1-p)*theta[var1]))
mean(ME.ergm,na.rm = TRUE)}
MEM1<-MEM.fun(theta)
MEM1_boots<-apply(theta_boot,1,FUN=MEM.fun)
MEM1.se<-sd(MEM1_boots)
MEM1.z<-MEM1/MEM1.se
P.MEM1<-2*(stats::pnorm(-abs(MEM1.z)))
MEM.fun<-function(theta){
ME.ergm<-sapply(names(theta),function(x)
(p*(1-p)*theta[var2]))
mean(ME.ergm,na.rm = TRUE)}
MEM2<-MEM.fun(theta)
MEM2_boots<-apply(theta_boot,1,FUN=MEM.fun)
MEM2.se<-sd(MEM2_boots)
MEM2.z<-MEM2/MEM2.se
P.MEM2<-2*(stats::pnorm(-abs(MEM2.z)))
MEM<-matrix(c(MEM1,MEM1.se,MEM1.z,P.MEM1,
MEM2,MEM2.se,MEM2.z,P.MEM2),nrow=2,ncol=4,byrow=TRUE)
colnames(MEM)<-c("MEM","Bootstrap SE","Z","P")
rownames(MEM)<-c(var1,var2)
marginal.matrix<-MEM
##compute marginal effect
MEM.fun<-function(theta){
ME.ergm<-sapply(names(theta),function(x)
(p*(1-p)*theta[inter]))
mean(ME.ergm,na.rm = TRUE)}
MEM<-MEM.fun(theta)
MEM_boots<-apply(theta_boot,1,FUN=MEM.fun)
MEM.se<-sd(MEM_boots)
MEM.z<-MEM/MEM.se
P.MEM<-2*(stats::pnorm(-abs(MEM.z)))
MEM<-matrix(c(MEM,MEM.se,MEM.z,P.MEM),nrow=1,ncol=4)
colnames(MEM)<-c("MEM","Bootstrap SE","Z","P")
rownames(MEM)<-inter
# message("NOTE: Nodematch is an interaction, but it is not a product of the main effects (e.g., inter!=var1*var2). Returning the simple MEM for the interaction. Consider respecifying ERGM using nodefactor for main effects or absdiff instead of nodematch to measure homophily.")
marginal.matrix<-signif(marginal.matrix,digits=5)
MEM<-signif(MEM,digits=5)
MEM<-list(MEM,marginal.matrix)
names(MEM)<-c("Marginal effect for nodematch","Marginal effects for nodal covariates")
return(MEM)
}
}
#for undirected networks, binarize factor variables
if(!is.na(pmatch("nodefactor",var1))){
dyad.mat[,var1][which(dyad.mat[,var1]>=2)]<-1
}
if(!is.na(pmatch("nodefactor",var2))){
at.2<-c(0,1)
}
if(var1==var2){
self.int<-TRUE
var2<-paste(var1,".mod")
dyad.mat[,var2]<-dyad.mat[,var1]
}else{
self.int<-FALSE
}
##marginal effects for interactions
marginal.matrix<-matrix(0,nrow=length(at.2),ncol=5)
colnames(marginal.matrix)<-c("MEM","Bootstrap SE","Z","P","N")
rownames(marginal.matrix)<-paste(var2,"==",at.2)
dydx.list<-list()
for(i in 1:nrow(marginal.matrix)){
dyad.submeans<-dyad.means
dyad.submeans[var2]<-at.2[i]
#marginal effects for absolute differences
if(!is.na(pmatch("absdiff",inter))){
dyad.submeans[inter]<-abs(dyad.submeans[var1]-dyad.submeans[var2])
if(i ==1){message(paste("Note that marginal effects for absolute differences are computed holding",var1,"at its mean. The mean for",var1,"is", mean(dyad.mat[,var1])))}
if(self.int==TRUE){
dyad.submeans<-dyad.submeans[!colnames(dyad.submeans)%in%var2]
}
p<-1/(1+exp(-(dyad.submeans%*%theta)))
at.diffs<-abs(at.2[i]-mean(dyad.mat[,var1]))
MEM.fun<-function(theta){
ME.ergm<-sapply(names(theta),function(x)
(p*(1-p)*(theta[var1]+(theta[inter]*at.diffs))))
mean(ME.ergm,na.rm = TRUE)}
dydx.list[[i]]<-sapply(names(theta),function(x)
(p*(1-p)*(theta[var1]+(theta[inter]*at.diffs))))
}else{
#marginal effects for product terms
dyad.submeans[inter]<-dyad.submeans[var1]*dyad.submeans[var2]
if(self.int==TRUE){
dyad.submeans<-dyad.submeans[!colnames(dyad.submeans)%in%var2]
}
p<-1/(1+exp(-(dyad.submeans%*%theta)))
MEM.fun<-function(theta){
ME.ergm<-sapply(names(theta),function(x)
(p*(1-p)*(theta[var1]+(theta[inter]*at.2[i]))))
mean(ME.ergm,na.rm = TRUE)}
dydx.list[[i]]<-sapply(names(theta),function(x)
(p*(1-p)*(theta[var1]+(theta[inter]*at.2[i]))))
}
MEM<-MEM.fun(theta)
marginal.matrix[i,1]<-MEM
MEM_boots<-apply(theta_boot,1,FUN=MEM.fun)
if(i==1){
MEM_boots1<-matrix(MEM_boots)
}else{
MEM_boots1<-cbind(MEM_boots1,matrix(MEM_boots))}
}
MEM.se<-apply(MEM_boots1,2,sd)
marginal.matrix[,2]<-MEM.se
marginal.matrix[,3]<-marginal.matrix[,1]/MEM.se
marginal.matrix[,4]<-2*(stats::pnorm(-abs(marginal.matrix[,3])))
marginal.matrix[,5]<-length(p)
if(length(at.2)==1){
MEM<-t(as.matrix(marginal.matrix[,-c(5)]))
rownames(MEM)<-rownames(marginal.matrix)
if(return.dydx==TRUE){
MEM<-list(MEM,dydx.list,MEM_boots1)
names(MEM)<-c("Average Marginal effects","Marginal effects","bootstrap")
}
return(MEM)
}
second.diffs.mat<-as.matrix(diff(marginal.matrix)[,1:4])
if(length(at.2)==2){
second.diffs.mat<-t(second.diffs.mat)
}
for(j in 1:nrow(second.diffs.mat)){
k<-j+1
diff.se<-sd(MEM_boots1[k,]-MEM_boots1[,j])
df<-marginal.matrix[j,5]-length(theta)
z.ADC<-(second.diffs.mat[j,1])/diff.se
P.ADC<-2*stats::pnorm(-abs(z.ADC))
second.diffs.mat[j,2]<-diff.se
second.diffs.mat[j,3]<-z.ADC
second.diffs.mat[j,4]<-P.ADC
}
colnames(second.diffs.mat)<-c("Second. diff.","bootSE","Wald Z","P")
rownames(second.diffs.mat)<-paste(at.2[-c(length(at.2))],"to",at.2[-c(1)])
marginal.matrix<-signif(marginal.matrix,digits=5)
second.diffs.mat<-signif(second.diffs.mat,digits=5)
if(length(at.2)==2){
if(return.dydx==FALSE){
ADC<-list(second.diffs.mat,marginal.matrix[,-c(ncol(marginal.matrix))])
names(ADC)<-c("Second differences","Average Marginal effects")}else{
ADC<-list(second.diffs.mat,marginal.matrix[,-c(ncol(marginal.matrix))],dydx.list,MEM_boots1)
names(ADC)<-c("Second differences","Average Marginal effects","Marginal effects","bootstraps")
}
return(ADC)
}else{
#use absolute t value in case of extreme negatives or positives
summary.output<-matrix(c(mean(second.diffs.mat[,1]),mean(abs(second.diffs.mat[,3])),NA),nrow=1,ncol=3)
colnames(summary.output)<-c("Mean Second diff.","Mean |Z|", "P")
summary.output[1,3]<-2*stats::pnorm(abs(summary.output[1,2]),lower.tail = FALSE)
summary.output<-signif(summary.output,digits=5)
if(return.dydx==FALSE){
ADC<-list(summary.output,second.diffs.mat,marginal.matrix[,-c(ncol(marginal.matrix))])
names(ADC)<-c("Aggregate output","Second differences","Average Marginal effects")}else{
ADC<-list(summary.output,second.diffs.mat,marginal.matrix[,-c(ncol(marginal.matrix))],dydx.list,MEM_boots)
names(ADC)<-c("Aggregate output","Second differences","Average Marginal effects","Marginal effects","bootstraps")
}
return(ADC)
}
}
}
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Defines functions ergm.MEM_boot
#' Function to compute marginal effect at means in ERGM
#' If var2 and inter are left NULL, the function returns the marginal effect at mean for var 1.
#' if var2 and inter are specified, function conducts tests of second differences to assess significance of an interaction
#'
#' @param model is an ergm object
#' @param var1 is the name of the main effect, character string
#' @param var2 is the name of the moderator, character string
#' @param inter is the name of the interaction, character string
#' @param at.2 is a vector specifying the levels of var2 at which to compute the marginal effects. If left NULL, it computes the MEM at all unique values of var2. Default is NULL.
#If the moderator is binary or specified at only 2 levels,
#the output object is a 2 dimensional list with one matrix of
#marginal effects and another of the second differences (ADC)
#If the moderator is continuous and specified at 3 or more levels,
#the output object contains a 3 dimensional list, where the Aggregate output is the
#average second difference and t tests based on the average second difference,
#the second differnece matrix is the matrix of second differneces between
#all adjacent levels of var 2, and the marginal matrix is the matrix of marginal effect at means
#standard errors are computed using the delta method.
ergm.MEM_boot<-function(model,
var1,
var2=NULL,
inter=NULL,
at.2=NULL,
at.controls=NULL,
control_vals=NULL,
return.dydx=FALSE){
##get edge probabilities
dyad.mat<-edge.prob2(model)[,-c(1)]
dyad.full.mat<-dyad.mat
p<-dyad.mat$probability
start.drops<-ncol(dyad.mat)-5
dyad.mat<-dyad.mat[,-c(start.drops:ncol(dyad.mat))]
theta<-btergm::coef(model)
if(any(names(theta)!=colnames(dyad.mat))){
colnames(dyad.mat)<-names(theta) #make sure names align
}
##assign fixed values for controls when specified
if(!is.null(at.controls)){
if(is.null(control_vals)){
stop("control_vals must be specified to use at.controls argument.")
}
if(length(at.controls)==1){
dyad.mat[,at.controls]<-control_vals
}else{
for(i in 1:length(at.controls)){
dyad.mat[,at.controls][,i]<-control_vals[i]
}
}
p<-as.matrix(dyad.mat)%*%theta
}
if(nrow(dyad.mat)>1e06){
message("There are over 1 million dyads in the ERGM sample space. Variance estimates for marginal effects may take a moment to compute.")
}
if(length(theta)>20){
message("There are more than 20 parameters in the model. Variance estimates for marginal effects may take a moment to compute.")
}
##identify unique values of at.2--not used if var2==NULL
if(is.null(at.2)){
at.2<-sort(unique(dyad.mat[,var2]))
}
if(length(at.2)>10){
warning("More than 10 values of at.2 exist for the moderating variable. It may take awhile to compute marginal effect at means. Consider specifying fewer values of at.2.")
}
theta_boot<-model@boot$t
#create marginal effects
dyad.means<-colMeans(dyad.mat,na.rm=TRUE)
p<-1/(1+exp(-dyad.means%*%theta))
##marginal effects with no interaction
if(is.null(var2)){
MEM.fun<-function(theta){
ME.ergm<-sapply(names(theta),function(x)
(p*(1-p)*theta[var1]))
mean(ME.ergm,na.rm = TRUE)}
MEM<-MEM.fun(theta)
MEM_boots<-apply(theta_boot,1,FUN=MEM.fun)
MEM.se<-sd(MEM_boots)
MEM.z<-MEM/MEM.se
P.MEM<-2*(stats::pnorm(-abs(MEM.z)))
MEM<-matrix(c(MEM,MEM.se,MEM.z,P.MEM),nrow=1,ncol=4)
colnames(MEM)<-c("MEM","Bootstrap SE","Z","P")
rownames(MEM)<-var1
MEM<-signif(MEM,digits=5)
if(return.dydx==TRUE){
dydx<-sapply(names(theta),function(x)
(p*(1-p)*theta[var1]))
MEM<-list(MEM,dydx[var1],MEM_boots)
names(MEM)<-c("MEM","dydx","bootstraps")
}
return(MEM)
}else{
##marginal effects for interaction that does not vary with covariates
if(!is.na(pmatch("nodematch",inter))){
if(!is.na(pmatch("nodecov",var1)) | !is.na(pmatch("nodeicov",var1)) |
!is.na(pmatch("nodeocov",var1))){
##matched nodal characteristics are not a product term for node covariates, so compute marginal effects
#for var 1 and var 2, then use results to compute marignal effect for interaction
MEM.fun<-function(theta){
ME.ergm<-sapply(names(theta),function(x)
(p*(1-p)*theta[var1]))
mean(ME.ergm,na.rm = TRUE)}
MEM1<-MEM.fun(theta)
MEM1_boots<-apply(theta_boot,1,FUN=MEM.fun)
MEM1.se<-sd(MEM1_boots)
MEM1.z<-MEM1/MEM1.se
P.MEM1<-2*(stats::pnorm(-abs(MEM1.z)))
MEM.fun<-function(theta){
ME.ergm<-sapply(names(theta),function(x)
(p*(1-p)*theta[var2]))
mean(ME.ergm,na.rm = TRUE)}
MEM2<-MEM.fun(theta)
MEM2_boots<-apply(theta_boot,1,FUN=MEM.fun)
MEM2.se<-sd(MEM2_boots)
MEM2.z<-MEM2/MEM2.se
P.MEM2<-2*(stats::pnorm(-abs(MEM2.z)))
MEM<-matrix(c(MEM1,MEM1.se,MEM1.z,P.MEM1,
MEM2,MEM2.se,MEM2.z,P.MEM2),nrow=2,ncol=4,byrow=TRUE)
colnames(MEM)<-c("MEM","Bootstrap SE","Z","P")
rownames(MEM)<-c(var1,var2)
marginal.matrix<-MEM
##compute marginal effect
MEM.fun<-function(theta){
ME.ergm<-sapply(names(theta),function(x)
(p*(1-p)*theta[inter]))
mean(ME.ergm,na.rm = TRUE)}
MEM<-MEM.fun(theta)
MEM_boots<-apply(theta_boot,1,FUN=MEM.fun)
MEM.se<-sd(MEM_boots)
MEM.z<-MEM/MEM.se
P.MEM<-2*(stats::pnorm(-abs(MEM.z)))
MEM<-matrix(c(MEM,MEM.se,MEM.z,P.MEM),nrow=1,ncol=4)
colnames(MEM)<-c("MEM","Bootstrap SE","Z","P")
rownames(MEM)<-inter
# message("NOTE: Nodematch is an interaction, but it is not a product of the main effects (e.g., inter!=var1*var2). Returning the simple MEM for the interaction. Consider respecifying ERGM using nodefactor for main effects or absdiff instead of nodematch to measure homophily.")
marginal.matrix<-signif(marginal.matrix,digits=5)
MEM<-signif(MEM,digits=5)
MEM<-list(MEM,marginal.matrix)
names(MEM)<-c("Marginal effect for nodematch","Marginal effects for nodal covariates")
return(MEM)
}
}
#for undirected networks, binarize factor variables
if(!is.na(pmatch("nodefactor",var1))){
dyad.mat[,var1][which(dyad.mat[,var1]>=2)]<-1
}
if(!is.na(pmatch("nodefactor",var2))){
at.2<-c(0,1)
}
if(var1==var2){
self.int<-TRUE
var2<-paste(var1,".mod")
dyad.mat[,var2]<-dyad.mat[,var1]
}else{
self.int<-FALSE
}
##marginal effects for interactions
marginal.matrix<-matrix(0,nrow=length(at.2),ncol=5)
colnames(marginal.matrix)<-c("MEM","Bootstrap SE","Z","P","N")
rownames(marginal.matrix)<-paste(var2,"==",at.2)
dydx.list<-list()
for(i in 1:nrow(marginal.matrix)){
dyad.submeans<-dyad.means
dyad.submeans[var2]<-at.2[i]
#marginal effects for absolute differences
if(!is.na(pmatch("absdiff",inter))){
dyad.submeans[inter]<-abs(dyad.submeans[var1]-dyad.submeans[var2])
if(i ==1){message(paste("Note that marginal effects for absolute differences are computed holding",var1,"at its mean. The mean for",var1,"is", mean(dyad.mat[,var1])))}
if(self.int==TRUE){
dyad.submeans<-dyad.submeans[!colnames(dyad.submeans)%in%var2]
}
p<-1/(1+exp(-(dyad.submeans%*%theta)))
at.diffs<-abs(at.2[i]-mean(dyad.mat[,var1]))
MEM.fun<-function(theta){
ME.ergm<-sapply(names(theta),function(x)
(p*(1-p)*(theta[var1]+(theta[inter]*at.diffs))))
mean(ME.ergm,na.rm = TRUE)}
dydx.list[[i]]<-sapply(names(theta),function(x)
(p*(1-p)*(theta[var1]+(theta[inter]*at.diffs))))
}else{
#marginal effects for product terms
dyad.submeans[inter]<-dyad.submeans[var1]*dyad.submeans[var2]
if(self.int==TRUE){
dyad.submeans<-dyad.submeans[!colnames(dyad.submeans)%in%var2]
}
p<-1/(1+exp(-(dyad.submeans%*%theta)))
MEM.fun<-function(theta){
ME.ergm<-sapply(names(theta),function(x)
(p*(1-p)*(theta[var1]+(theta[inter]*at.2[i]))))
mean(ME.ergm,na.rm = TRUE)}
dydx.list[[i]]<-sapply(names(theta),function(x)
(p*(1-p)*(theta[var1]+(theta[inter]*at.2[i]))))
}
MEM<-MEM.fun(theta)
marginal.matrix[i,1]<-MEM
MEM_boots<-apply(theta_boot,1,FUN=MEM.fun)
if(i==1){
MEM_boots1<-matrix(MEM_boots)
}else{
MEM_boots1<-cbind(MEM_boots1,matrix(MEM_boots))}
}
MEM.se<-apply(MEM_boots1,2,sd)
marginal.matrix[,2]<-MEM.se
marginal.matrix[,3]<-marginal.matrix[,1]/MEM.se
marginal.matrix[,4]<-2*(stats::pnorm(-abs(marginal.matrix[,3])))
marginal.matrix[,5]<-length(p)
if(length(at.2)==1){
MEM<-t(as.matrix(marginal.matrix[,-c(5)]))
rownames(MEM)<-rownames(marginal.matrix)
if(return.dydx==TRUE){
MEM<-list(MEM,dydx.list,MEM_boots1)
names(MEM)<-c("Average Marginal effects","Marginal effects","bootstrap")
}
return(MEM)
}
second.diffs.mat<-as.matrix(diff(marginal.matrix)[,1:4])
if(length(at.2)==2){
second.diffs.mat<-t(second.diffs.mat)
}
for(j in 1:nrow(second.diffs.mat)){
k<-j+1
diff.se<-sd(MEM_boots1[k,]-MEM_boots1[,j])
df<-marginal.matrix[j,5]-length(theta)
z.ADC<-(second.diffs.mat[j,1])/diff.se
P.ADC<-2*stats::pnorm(-abs(z.ADC))
second.diffs.mat[j,2]<-diff.se
second.diffs.mat[j,3]<-z.ADC
second.diffs.mat[j,4]<-P.ADC
}
colnames(second.diffs.mat)<-c("Second. diff.","bootSE","Wald Z","P")
rownames(second.diffs.mat)<-paste(at.2[-c(length(at.2))],"to",at.2[-c(1)])
marginal.matrix<-signif(marginal.matrix,digits=5)
second.diffs.mat<-signif(second.diffs.mat,digits=5)
if(length(at.2)==2){
if(return.dydx==FALSE){
ADC<-list(second.diffs.mat,marginal.matrix[,-c(ncol(marginal.matrix))])
names(ADC)<-c("Second differences","Average Marginal effects")}else{
ADC<-list(second.diffs.mat,marginal.matrix[,-c(ncol(marginal.matrix))],dydx.list,MEM_boots1)
names(ADC)<-c("Second differences","Average Marginal effects","Marginal effects","bootstraps")
}
return(ADC)
}else{
#use absolute t value in case of extreme negatives or positives
summary.output<-matrix(c(mean(second.diffs.mat[,1]),mean(abs(second.diffs.mat[,3])),NA),nrow=1,ncol=3)
colnames(summary.output)<-c("Mean Second diff.","Mean |Z|", "P")
summary.output[1,3]<-2*stats::pnorm(abs(summary.output[1,2]),lower.tail = FALSE)
summary.output<-signif(summary.output,digits=5)
if(return.dydx==FALSE){
ADC<-list(summary.output,second.diffs.mat,marginal.matrix[,-c(ncol(marginal.matrix))])
names(ADC)<-c("Aggregate output","Second differences","Average Marginal effects")}else{
ADC<-list(summary.output,second.diffs.mat,marginal.matrix[,-c(ncol(marginal.matrix))],dydx.list,MEM_boots)
names(ADC)<-c("Aggregate output","Second differences","Average Marginal effects","Marginal effects","bootstraps")
}
return(ADC)
}
}
}
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