Nothing
R/ergmAME_count.R
In ergMargins: Process Analysis for Exponential Random Graph Models
Defines functions
ergm.AME_count
#' Function to compute average marginal effects in ERGM
#' If var2 and inter are left NULL, the function returns the average marginal effect 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 AME 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 average marginal effects
#standard errors are computed using the delta method.
ergm.AME_count<-function(model,
var1,
var2=NULL,
inter=NULL,
at.2=NULL,
at.controls=NULL,
control_vals=NULL,
return.dydx=FALSE,
return.at.2=FALSE){
reference<-model$reference
if(grepl("Binomial", as.character(reference)[2],fixed = TRUE)){
ref<-"binomial"
}
if("Poisson"%in%as.character(reference)){
ref<-"poisson"
}
if("Geometric"%in%as.character(reference)){
ref<-"geometric"
}
if("Uniform"%in%as.character(reference)){
ref<-"uniform"
}
max_y<-max(as.sociomatrix(model$network,model$network$gal$ergm$response[1]))
#get sufficient statistics
suff_stats<-ergmCntPrep(formula=model$formula,
nw=model$network,
response=model$network$gal$ergm$response[1],
reference=ref,
max.count = max_y)
out<-lapply(suff_stats$cs,as.data.frame)
for(i in 1:length(out)){
out[[i]]$m<-nrow(out[[i]])
}
dyad.mat<-dplyr::bind_rows(out)
#get predicted probs then do m x p to get predicted counts
theta<-btergm::coef(model)
m<-dyad.mat$m
dyad.mat<-dyad.mat[,-ncol(dyad.mat)]
lp<-as.matrix(dyad.mat)%*%theta
p<-m*(1/(1+exp(-lp)))
vc<-stats::vcov(model)
##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]
}
}
#get predicted counts
lp<-as.matrix(dyad.mat)%*%theta
p<-m*(1/(1+exp(-lp)))
}
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 average marginal effects. Consider specifying fewer values of at.2.")
}
##marginal effects with no interaction
if(is.null(var2)){
AME.fun<-function(theta){
ME.ergm<-sapply(names(theta),function(x)
p*theta[var1])
mean(ME.ergm,na.rm = TRUE)}
AME<-AME.fun(theta)
Jac<-numDeriv::jacobian(AME.fun,theta)
variance.ame<-Jac%*%vc%*%t(Jac)
AME.se<-sqrt(variance.ame)
AME.z<-AME/AME.se
P.AME<-2*(stats::pnorm(-abs(AME.z)))
AME<-matrix(c(AME,AME.se,AME.z,P.AME),nrow=1,ncol=4)
colnames(AME)<-c("AME","Delta SE","Z","P")
rownames(AME)<-var1
AME<-signif(AME,digits=5)
if(return.dydx==TRUE){
dydx<-sapply(names(theta),function(x)
p*theta[var1])
AME<-list(AME,dydx[,var1],Jac)
names(AME)<-c("AME","dydx","Jac")
}
return(AME)
}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
AME.fun<-function(theta){
ME.ergm<-sapply(names(theta),function(x)
p*theta[var1])
mean(ME.ergm,na.rm = TRUE)}
AME1<-AME.fun(theta)
Jac<-numDeriv::jacobian(AME.fun,theta)
variance.ame1<-Jac%*%vc%*%t(Jac)
AME1.se<-sqrt(variance.ame1)
AME1.z<-AME1/AME1.se
P.AME1<-2*(stats::pnorm(-abs(AME1.z)))
AME.fun<-function(theta){
ME.ergm<-sapply(names(theta),function(x)
p*theta[var2])
mean(ME.ergm,na.rm = TRUE)}
AME2<-AME.fun(theta)
Jac<-numDeriv::jacobian(AME.fun,theta)
variance.ame2<-Jac%*%vc%*%t(Jac)
AME2.se<-sqrt(variance.ame2)
AME2.z<-AME2/AME2.se
P.AME2<-2*(stats::pnorm(-abs(AME2.z)))
AME<-matrix(c(AME1,AME1.se,AME1.z,P.AME1,
AME2,AME2.se,AME2.z,P.AME2),nrow=2,ncol=4,byrow=TRUE)
colnames(AME)<-c("AME","Delta SE","Z","P")
rownames(AME)<-c(var1,var2)
marginal.matrix<-AME
##compute marginal effect
AME.fun<-function(theta){
ME.ergm<-sapply(names(theta),function(x)
p*theta[inter])
mean(ME.ergm,na.rm = TRUE)}
AME<-AME.fun(theta)
Jac<-numDeriv::jacobian(AME.fun,theta)
variance.inter<-Jac%*%vc%*%t(Jac)
AME.se<-sqrt(variance.inter)
AME.z<-AME/AME.se
P.AME<-2*(stats::pnorm(-abs(AME.z)))
AME<-matrix(c(AME,AME.se,AME.z,P.AME),nrow=1,ncol=4)
colnames(AME)<-c("AME","Delta SE","Z","P")
rownames(AME)<-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 AME 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)
AME<-signif(AME,digits=5)
AME<-list(AME,marginal.matrix)
names(AME)<-c("Marginal effect for nodematch","Marginal effects for nodal covariates")
return(AME)
}
}
#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("AME","Delta SE","Z","P","N")
rownames(marginal.matrix)<-paste(var2,"==",at.2)
dydx.list<-list()
for(i in 1:nrow(marginal.matrix)){
dyad.submat<-dyad.mat
dyad.submat[,var2]<-at.2[i]
if(class(model)%in%"mtergm"){
if(ergm::is.curved(model@ergm)){
theta<-ergm::ergm.eta(theta,model@ergm$etamap)
}
}else{
if(ergm::is.curved(model)){
theta<-ergm::ergm.eta(theta,model$etamap)
}
}
#marginal effects for absolute differences
if(!is.na(pmatch("absdiff",inter))){
dyad.submat[,inter]<-abs(dyad.submat[,var1]-dyad.submat[,var2])
if(i ==1){message(paste("Note that marginal effects for absolute differences are computed holding",var1,"at its mean. The mean for",var1,"is", mean(dyad.mat[,var1])))}
if(self.int==TRUE){
dyad.submat<-dyad.submat[,!colnames(dyad.submat)%in%var2]
}
p<-m*(1/(1+exp(-(apply(dyad.submat,1,function(x) t(x)%*%theta)))))
if(class(model)%in%"mlergm"){
theta<-model$theta
vc<-solve(vc) #invert the fisher matrix
}else{
theta<-btergm::coef(model)
}
at.diffs<-abs(at.2[i]-mean(dyad.mat[,var1]))
AME.fun<-function(theta){
ME.ergm<-sapply(names(theta),function(x)
(p*(theta[var1]+(theta[inter]*at.diffs))))
mean(ME.ergm,na.rm = TRUE)}
dydx.list[[i]]<-sapply(names(theta),function(x)
(p*(theta[var1]+(theta[inter]*at.diffs))))
}else{
#marginal effects for product terms
dyad.submat[,inter]<-dyad.submat[,var1]*dyad.submat[,var2]
if(self.int==TRUE){
dyad.submat<-dyad.submat[,!colnames(dyad.submat)%in%var2]
}
p<-m*(1/(1+exp(-(apply(dyad.submat,1,function(x) t(x)%*%theta)))))
if(class(model)%in%"mlergm"){
theta<-model$theta
vc<-solve(vc) #invert the fisher matrix
}else{
theta<-btergm::coef(model)
}
AME.fun<-function(theta){
ME.ergm<-sapply(names(theta),function(x)
(p*(theta[var1]+(theta[inter]*at.2[i]))))
mean(ME.ergm,na.rm = TRUE)}
dydx.list[[i]]<-sapply(names(theta),function(x)
(p*(theta[var1]+(theta[inter]*at.2[i]))))
}
AME<-AME.fun(theta)
Jac<-numDeriv::jacobian(AME.fun,theta)
marginal.matrix[i,1]<-AME
if(i==1){
Jac1<-matrix(Jac)
}else{
Jac1<-cbind(Jac1,matrix(Jac))}
}
variance.ame<-t(Jac1)%*%vc%*%Jac1
AME.se<-sqrt(diag(variance.ame))
marginal.matrix[,2]<-AME.se
marginal.matrix[,3]<-marginal.matrix[,1]/AME.se
marginal.matrix[,4]<-2*(stats::pnorm(-abs(marginal.matrix[,3])))
marginal.matrix[,5]<-length(p)
if(length(at.2)==1){
AME<-t(as.matrix(marginal.matrix[,-c(5)]))
rownames(AME)<-rownames(marginal.matrix)
if(return.dydx==TRUE){
AME<-list(AME,dydx.list,Jac1)
names(AME)<-c("Average Marginal effects","Marginal effects","Jac")
}
if(return.at.2==TRUE){
AME<-list(main.results=AME,
at.2=at.2)
}
return(AME)
}
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<-sqrt((marginal.matrix[j,2]^2)+(marginal.matrix[k,2]^2)-2*variance.ame[j,k])
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.","SE","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,Jac1)
names(ADC)<-c("Second differences","Average Marginal effects","Marginal effects","Jac")
}
if(return.at.2==TRUE){
ADC<-list(ADC,at.2)
names(ADC)<-c("main.results","at.2")
}
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,Jac1)
names(ADC)<-c("Aggregate output","Second differences","Average Marginal effects","Marginal effects","Jac")
}
if(return.at.2==TRUE){
ADC<-list(ADC,at.2)
names(ADC)<-c("main.results","at.2")
}
return(ADC)
}
}
}
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Defines functions ergm.AME_count
#' Function to compute average marginal effects in ERGM
#' If var2 and inter are left NULL, the function returns the average marginal effect 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 AME 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 average marginal effects
#standard errors are computed using the delta method.
ergm.AME_count<-function(model,
var1,
var2=NULL,
inter=NULL,
at.2=NULL,
at.controls=NULL,
control_vals=NULL,
return.dydx=FALSE,
return.at.2=FALSE){
reference<-model$reference
if(grepl("Binomial", as.character(reference)[2],fixed = TRUE)){
ref<-"binomial"
}
if("Poisson"%in%as.character(reference)){
ref<-"poisson"
}
if("Geometric"%in%as.character(reference)){
ref<-"geometric"
}
if("Uniform"%in%as.character(reference)){
ref<-"uniform"
}
max_y<-max(as.sociomatrix(model$network,model$network$gal$ergm$response[1]))
#get sufficient statistics
suff_stats<-ergmCntPrep(formula=model$formula,
nw=model$network,
response=model$network$gal$ergm$response[1],
reference=ref,
max.count = max_y)
out<-lapply(suff_stats$cs,as.data.frame)
for(i in 1:length(out)){
out[[i]]$m<-nrow(out[[i]])
}
dyad.mat<-dplyr::bind_rows(out)
#get predicted probs then do m x p to get predicted counts
theta<-btergm::coef(model)
m<-dyad.mat$m
dyad.mat<-dyad.mat[,-ncol(dyad.mat)]
lp<-as.matrix(dyad.mat)%*%theta
p<-m*(1/(1+exp(-lp)))
vc<-stats::vcov(model)
##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]
}
}
#get predicted counts
lp<-as.matrix(dyad.mat)%*%theta
p<-m*(1/(1+exp(-lp)))
}
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 average marginal effects. Consider specifying fewer values of at.2.")
}
##marginal effects with no interaction
if(is.null(var2)){
AME.fun<-function(theta){
ME.ergm<-sapply(names(theta),function(x)
p*theta[var1])
mean(ME.ergm,na.rm = TRUE)}
AME<-AME.fun(theta)
Jac<-numDeriv::jacobian(AME.fun,theta)
variance.ame<-Jac%*%vc%*%t(Jac)
AME.se<-sqrt(variance.ame)
AME.z<-AME/AME.se
P.AME<-2*(stats::pnorm(-abs(AME.z)))
AME<-matrix(c(AME,AME.se,AME.z,P.AME),nrow=1,ncol=4)
colnames(AME)<-c("AME","Delta SE","Z","P")
rownames(AME)<-var1
AME<-signif(AME,digits=5)
if(return.dydx==TRUE){
dydx<-sapply(names(theta),function(x)
p*theta[var1])
AME<-list(AME,dydx[,var1],Jac)
names(AME)<-c("AME","dydx","Jac")
}
return(AME)
}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
AME.fun<-function(theta){
ME.ergm<-sapply(names(theta),function(x)
p*theta[var1])
mean(ME.ergm,na.rm = TRUE)}
AME1<-AME.fun(theta)
Jac<-numDeriv::jacobian(AME.fun,theta)
variance.ame1<-Jac%*%vc%*%t(Jac)
AME1.se<-sqrt(variance.ame1)
AME1.z<-AME1/AME1.se
P.AME1<-2*(stats::pnorm(-abs(AME1.z)))
AME.fun<-function(theta){
ME.ergm<-sapply(names(theta),function(x)
p*theta[var2])
mean(ME.ergm,na.rm = TRUE)}
AME2<-AME.fun(theta)
Jac<-numDeriv::jacobian(AME.fun,theta)
variance.ame2<-Jac%*%vc%*%t(Jac)
AME2.se<-sqrt(variance.ame2)
AME2.z<-AME2/AME2.se
P.AME2<-2*(stats::pnorm(-abs(AME2.z)))
AME<-matrix(c(AME1,AME1.se,AME1.z,P.AME1,
AME2,AME2.se,AME2.z,P.AME2),nrow=2,ncol=4,byrow=TRUE)
colnames(AME)<-c("AME","Delta SE","Z","P")
rownames(AME)<-c(var1,var2)
marginal.matrix<-AME
##compute marginal effect
AME.fun<-function(theta){
ME.ergm<-sapply(names(theta),function(x)
p*theta[inter])
mean(ME.ergm,na.rm = TRUE)}
AME<-AME.fun(theta)
Jac<-numDeriv::jacobian(AME.fun,theta)
variance.inter<-Jac%*%vc%*%t(Jac)
AME.se<-sqrt(variance.inter)
AME.z<-AME/AME.se
P.AME<-2*(stats::pnorm(-abs(AME.z)))
AME<-matrix(c(AME,AME.se,AME.z,P.AME),nrow=1,ncol=4)
colnames(AME)<-c("AME","Delta SE","Z","P")
rownames(AME)<-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 AME 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)
AME<-signif(AME,digits=5)
AME<-list(AME,marginal.matrix)
names(AME)<-c("Marginal effect for nodematch","Marginal effects for nodal covariates")
return(AME)
}
}
#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("AME","Delta SE","Z","P","N")
rownames(marginal.matrix)<-paste(var2,"==",at.2)
dydx.list<-list()
for(i in 1:nrow(marginal.matrix)){
dyad.submat<-dyad.mat
dyad.submat[,var2]<-at.2[i]
if(class(model)%in%"mtergm"){
if(ergm::is.curved(model@ergm)){
theta<-ergm::ergm.eta(theta,model@ergm$etamap)
}
}else{
if(ergm::is.curved(model)){
theta<-ergm::ergm.eta(theta,model$etamap)
}
}
#marginal effects for absolute differences
if(!is.na(pmatch("absdiff",inter))){
dyad.submat[,inter]<-abs(dyad.submat[,var1]-dyad.submat[,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.submat<-dyad.submat[,!colnames(dyad.submat)%in%var2]
}
p<-m*(1/(1+exp(-(apply(dyad.submat,1,function(x) t(x)%*%theta)))))
if(class(model)%in%"mlergm"){
theta<-model$theta
vc<-solve(vc) #invert the fisher matrix
}else{
theta<-btergm::coef(model)
}
at.diffs<-abs(at.2[i]-mean(dyad.mat[,var1]))
AME.fun<-function(theta){
ME.ergm<-sapply(names(theta),function(x)
(p*(theta[var1]+(theta[inter]*at.diffs))))
mean(ME.ergm,na.rm = TRUE)}
dydx.list[[i]]<-sapply(names(theta),function(x)
(p*(theta[var1]+(theta[inter]*at.diffs))))
}else{
#marginal effects for product terms
dyad.submat[,inter]<-dyad.submat[,var1]*dyad.submat[,var2]
if(self.int==TRUE){
dyad.submat<-dyad.submat[,!colnames(dyad.submat)%in%var2]
}
p<-m*(1/(1+exp(-(apply(dyad.submat,1,function(x) t(x)%*%theta)))))
if(class(model)%in%"mlergm"){
theta<-model$theta
vc<-solve(vc) #invert the fisher matrix
}else{
theta<-btergm::coef(model)
}
AME.fun<-function(theta){
ME.ergm<-sapply(names(theta),function(x)
(p*(theta[var1]+(theta[inter]*at.2[i]))))
mean(ME.ergm,na.rm = TRUE)}
dydx.list[[i]]<-sapply(names(theta),function(x)
(p*(theta[var1]+(theta[inter]*at.2[i]))))
}
AME<-AME.fun(theta)
Jac<-numDeriv::jacobian(AME.fun,theta)
marginal.matrix[i,1]<-AME
if(i==1){
Jac1<-matrix(Jac)
}else{
Jac1<-cbind(Jac1,matrix(Jac))}
}
variance.ame<-t(Jac1)%*%vc%*%Jac1
AME.se<-sqrt(diag(variance.ame))
marginal.matrix[,2]<-AME.se
marginal.matrix[,3]<-marginal.matrix[,1]/AME.se
marginal.matrix[,4]<-2*(stats::pnorm(-abs(marginal.matrix[,3])))
marginal.matrix[,5]<-length(p)
if(length(at.2)==1){
AME<-t(as.matrix(marginal.matrix[,-c(5)]))
rownames(AME)<-rownames(marginal.matrix)
if(return.dydx==TRUE){
AME<-list(AME,dydx.list,Jac1)
names(AME)<-c("Average Marginal effects","Marginal effects","Jac")
}
if(return.at.2==TRUE){
AME<-list(main.results=AME,
at.2=at.2)
}
return(AME)
}
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<-sqrt((marginal.matrix[j,2]^2)+(marginal.matrix[k,2]^2)-2*variance.ame[j,k])
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.","SE","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,Jac1)
names(ADC)<-c("Second differences","Average Marginal effects","Marginal effects","Jac")
}
if(return.at.2==TRUE){
ADC<-list(ADC,at.2)
names(ADC)<-c("main.results","at.2")
}
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,Jac1)
names(ADC)<-c("Aggregate output","Second differences","Average Marginal effects","Marginal effects","Jac")
}
if(return.at.2==TRUE){
ADC<-list(ADC,at.2)
names(ADC)<-c("main.results","at.2")
}
return(ADC)
}
}
}
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