Nothing
Log.lqr = function(formula,data = NULL,
subset = NULL,
p=0.5,a=0,b=1,
dist = "normal",
nu=NULL,
gamma=NULL,
precision = 10^-6,
epsilon = 0.001,
CI=0.95,
silent = FALSE){
pred = function(predlog,a,b)
{
return((b*exp(predlog)+a)/(1+exp(predlog)))
}
cat('\n')
call <- match.call()
cat("Call:\n")
print(call)
cat('\n')
if(is.null(subset)){subset = ""}
xy = get_xy(formula0 = formula,
data0 = data,
subset0 = subset)
x = xy$x
y.original = xy$y
y = log((y.original - a + epsilon)/(b - y.original + epsilon))
par(mfrow=c(1,1))
if(length(p)==1)
{
## Verify error at parameters specification
if(!is.null(dist) && dist != "normal" && dist != "t" && dist != "laplace" && dist != "slash" && dist != "cont") stop("The dist values are normal, t, laplace, slash or cont.")
#No data
#if( (length(x) == 0) | (length(y) == 0)) stop("All parameters must be provided.")
#Validating if exists NA's
if(sum(y[is.na(y)==TRUE]) > 0) stop("There are some NA's values in y")
if(sum(x[is.na(x)==TRUE]) > 0) stop("There are some NA's values in x")
#Validating dims data set
if(ncol(as.matrix(y)) > 1) stop("y must have just one column")
if( length(y) != nrow(as.matrix(x)) ) stop("x variable does not have the same number of lines than y")
#Validating supports
if(p >= 1 | p <= 0) stop("p must be a real number in (0,1)")
if(!is.null(gamma) && (gamma >= 1 | gamma <= 0) && dist == "cont") stop("nu must be a real number in (0,1)")
if(!is.null(nu) && (nu >= 1 | nu <= 0) && dist == "cont") stop("nu must be a real number in (0,1)")
if(!is.null(nu) && (nu >= 100 | nu < 2) && dist == "t") stop("nu must be a positive real number at least 2.")
if(!is.null(nu) && nu <= 0 && dist == "slash") stop("nu must be a positive real number.")
if(precision <= 0) stop("precision must be a positive value (suggested to be small)")
#if(MaxIter <= 0 |MaxIter%%1!=0) stop("MaxIter must be a positive integer value")
if(CI >= 1 | CI <= 0) stop("CI must be a real number in (0,1)")
#Running the algorithm
#out <- suppressWarnings(EM(y,x,p,dist,nu,gamma,precision,envelope))
if(!silent){
cat('\n')
call <- match.call()
cat("Call:\n")
print(call)
cat('\n')
}
if(is.null(nu)) {nu=""}
if(is.null(gamma)) {gamma=""}
out <- EM(y,x,p,dist,nu,gamma,precision,envelope = FALSE)
if(!silent){
cat("Distribution:",dist,'\n')
cat("Quantile:",p,'\n')
#cat("Iterations =",out$iter)
cat('\n')
cat('Estimates:\n')
cat('\n')
print(out$table)
cat('---\n')
cat('Signif. codes: 0 "***" 0.001 "**" 0.01 "*" 0.05 "." 0.1 " " 1\n')
cat('\n')
cat('sigma =',out$theta[ncol(as.matrix(x))+1],'\n')
if(dist == "normal" || dist == "laplace"){
cat('\n')
}
if(dist == "t" || dist == "slash"){
cat('nu =',out$nu,'\n')
cat('\n')
}
if(dist == "cont"){
cat('nu =',out$nu,'\n')
cat('gamma =',out$gamma,'\n')
cat('\n')
}
cat('Model selection criteria:\n')
cat('\n')
critFin <- c(out$loglik, out$AIC, out$BIC, out$HQ)
critFin <- round(t(as.matrix(critFin)),digits=3)
dimnames(critFin) <- list(c("Value"),c("Loglik", "AIC", "BIC","HQ"))
print(critFin)
cat('\n')
}
if(dist == "normal" || dist == "laplace"){
obj.out = list(iter = out$iter,criteria = out$criterio,
beta = out$theta[1:ncol(as.matrix(x))],
sigma= out$theta[ncol(as.matrix(x))+1],
SE=out$SE,table = out$table,loglik=out$loglik,
AIC=out$AIC,BIC=out$BIC,HQ=out$HQ,
fitted.values = out$fitted.values,residuals=out$residuals)
}
if(dist == "t" || dist == "slash"){
obj.out = list(iter = out$iter,criteria = out$criterio,
beta = out$theta[1:ncol(as.matrix(x))],
sigma= out$theta[ncol(as.matrix(x))+1],nu = out$nu,
SE=out$SE,table = out$table,loglik=out$loglik,
AIC=out$AIC,BIC=out$BIC,HQ=out$HQ,
fitted.values = out$fitted.values,residuals=out$residuals)
}
if(dist == "cont"){
obj.out = list(iter = out$iter,criteria = out$criterio,
beta = out$theta[1:ncol(as.matrix(x))],
sigma= out$theta[ncol(as.matrix(x))+1],nu = out$nu,
gamma = out$gamma,
SE=out$SE,table = out$table,loglik=out$loglik,
AIC=out$AIC,BIC=out$BIC,HQ=out$HQ,
fitted.values = out$fitted.values,residuals=out$residuals)
}
obj.out$fitted.values = pred(predlog = obj.out$fitted.values,a,b)
obj.out$residuals = y.original - obj.out$fitted.values
}
else
{
p = sort(p)
obj.out = vector("list", length(p))
## Verify error at parameters specification
if(all(p > 0 & p < 1) == FALSE) stop("p vector must contain real values in (0,1)")
if(!is.null(dist) && dist != "normal" && dist != "t" && dist != "laplace" && dist != "slash" && dist != "cont") stop("The dist values are normal, t, laplace, slash or cont.")
## Verify error at parameters specification
#No data
if( (length(x) == 0) | (length(y) == 0)) stop("All parameters must be provided.")
#Validating if exists NA's
if(sum(y[is.na(y)==TRUE]) > 0) stop("There are some NA's values in y")
if(sum(y[is.na(x)==TRUE]) > 0) stop("There are some NA's values in x")
#Validating dims data set
if(ncol(as.matrix(y)) > 1) stop("y must have just one column")
if( length(y) != nrow(as.matrix(x)) ) stop("x variable does not have the same number of lines than y")
#Validating supports
if(!is.null(gamma) && (gamma >= 1 | gamma <= 0) && dist == "cont") stop("nu must be a real number in (0,1)")
if(!is.null(nu) && (nu >= 1 | nu <= 0) && dist == "cont") stop("nu must be a real number in (0,1)")
if(!is.null(nu) && (nu >= 100 | nu < 2) && dist == "t") stop("nu must be a positive real number at least 2.")
if(!is.null(nu) && nu <= 0 && dist == "slash") stop("nu must be a positive real number.")
if(precision <= 0) stop("precision must be a positive value (suggested to be small)")
#if(MaxIter <= 0 |MaxIter%%1!=0) stop("MaxIter must be a positive integer value")
if(CI >= 1 | CI <= 0) stop("CI must be a real number in (0,1)")
#if(is.logical(envelope) == FALSE) stop("show.convergence must be TRUE or FALSE.")
if(silent == FALSE){
cat('\n')
call <- match.call()
cat("Call:\n")
print(call)
cat('\n')
}
if(is.null(nu)) {nu=""}
if(is.null(gamma)) {gamma=""}
for(k in 1:length(p))
{
#Running the algorithm
out <- EM(y,x,p[k],dist,nu,gamma,precision,envelope = FALSE)
if(silent == FALSE){
cat('\n')
cat('\n')
cat('-------------\n')
#cat("Distribution:",dist,'\n')
cat("Quantile:",p[k],'\n')
#cat("Iterations =",out$iter)
cat('\n')
cat('sigma =',round(out$theta[ncol(as.matrix(x))+1],5),'\n')
if(dist == "normal" || dist == "laplace"){
cat('\n')
}
if(dist == "t" || dist == "slash"){
cat('nu =',out$nu,'\n')
cat('\n')
}
if(dist == "cont"){
cat('nu =',out$nu,'\n')
cat('gamma =',out$gamma,'\n')
cat('\n')
}
cat('Model selection criteria:\n')
cat('\n')
critFin <- c(out$loglik, out$AIC, out$BIC, out$HQ)
critFin <- round(t(as.matrix(critFin)),digits=3)
dimnames(critFin) <- list(c("Value"),c("Loglik", "AIC", "BIC","HQ"))
print(critFin)
cat('\n')
}
if(dist == "normal" || dist == "laplace"){
obj.outk = list(iter = out$iter,criteria = out$criterio,
beta = out$theta[1:ncol(as.matrix(x))],
sigma= out$theta[ncol(as.matrix(x))+1],
SE=out$SE,table = out$table,loglik=out$loglik,
AIC=out$AIC,BIC=out$BIC,HQ=out$HQ,
fitted.values = out$fitted.values,residuals=out$residuals)
}
if(dist == "t" || dist == "slash"){
obj.outk = list(iter = out$iter,criteria = out$criterio,
beta = out$theta[1:ncol(as.matrix(x))],
sigma= out$theta[ncol(as.matrix(x))+1],nu = out$nu,
SE=out$SE,table = out$table,loglik=out$loglik,
AIC=out$AIC,BIC=out$BIC,HQ=out$HQ,
fitted.values = out$fitted.values,residuals=out$residuals)
}
if(dist == "cont"){
obj.outk = list(iter = out$iter,criteria = out$criterio,
beta = out$theta[1:ncol(as.matrix(x))],
sigma= out$theta[ncol(as.matrix(x))+1],nu = out$nu,
gamma = out$gamma,
SE=out$SE,table = out$table,loglik=out$loglik,
AIC=out$AIC,BIC=out$BIC,HQ=out$HQ,
fitted.values = out$fitted.values,residuals=out$residuals)
}
obj.outk$fitted.values = pred(predlog = obj.outk$fitted.values,a,b)
obj.outk$residuals = y.original - obj.outk$fitted.values
obj.out[[k]] = obj.outk
}
# table.est = table.ast = matrix(NA,nrow = ncol(x),ncol = length(p))
# print(table.est)
# print(table.est)
#
# for(k in 1:length(p))
# {
# print(obj.out[[k]]$table)
# print(obj.out[[k]]$table[,1])
# table.est[,k] = obj.out[[k]]$table[,1]
# table.ast[,k] = obj.out[[k]]$table[,5]
# }
#
# colnames(table.est) = p
# colnames(table.ast) = p
# rownames(table.est) = colnames(x)
# rownames(table.ast) = colnames(x)
#
# cat('Estimates values:\n')
# cat('\n')
# print(table.est)
# cat('Estimates significance:\n')
# cat('\n')
# print(table.ast)
# cat('---\n')
# cat('Signif. codes: 0 "***" 0.001 "**" 0.01 "*" 0.05 "." 0.1 " " 1\n')
# cat('\n')
#
par(mfrow=c(1,1))
d=length(obj.out[[1]]$beta)
betas = eps = matrix(NA,length(p),d+1)
for (i in 1:length(p))
{
j = p[i]
betas[i,] = c(obj.out[[i]]$beta,obj.out[[i]]$sigma)
eps[i,] = obj.out[[i]]$SE[1:(d+1)]
}
LIMSUP = t(betas + qnorm(1-((1-(CI))/2))*eps)
LIMINF = t(betas - qnorm(1-((1-(CI))/2))*eps)
labels = list()
#for(i in 1:d){labels[[i]] = bquote(beta[.(i)])}
for(i in 1:d){labels[[i]] = colnames(x)[i]}
labels[[d+1]] = bquote(sigma)
par(mar=c(4, 4.5, 1, 0.5))
op <- par(mfrow=c(ifelse((d+1)%%2==0,(d+1)%/%2,((d+1)%/%2)+1),2),oma=c(0,0,2,0))
for(i in 1:(d+1)){
if(length(p)<4)
{
ymin = min(betas[,i],LIMSUP[i,],LIMINF[i,])
ymax = max(betas[,i],LIMSUP[i,],LIMINF[i,])
plot(p,betas[,i],ylim=c(ymin-2*mean(eps[,i]),ymax+2*mean(eps[,i])),xaxt='n', type='n',xlab='quantiles',ylab=labels[[i]])
axis(side=1, at=p)
polygon(c(p,rev(p)),c(LIMSUP[i,],rev(LIMINF[i,])), col = "gray50", border = NA)
lines(p,betas[,i])
lines(p,LIMSUP[i,])
lines(p,LIMINF[i,])
abline(h=0,lty=2)
}
else
{
smoothingSpline = smooth.spline(p, betas[,i], spar=0.1)
smoothingSplineU = smooth.spline(p, betas[,i]+(qnorm(1-((1-(CI))/2)))*eps[,i], spar=0.1)
smoothingSplineL = smooth.spline(p, betas[,i]-(qnorm(1-((1-(CI))/2)))*eps[,i], spar=0.1)
plot(p, betas[,i], type='n',xaxt='n',xlab='quantiles',lwd=2,ylim=c(min(smoothingSplineL$y)-2*mean(eps[,i]),max(smoothingSplineU$y)+2*mean(eps[,i])),ylab=labels[[i]])
axis(side=1, at=p)
#create filled polygon in between the lines
polygon(c(smoothingSplineL$x,rev(smoothingSplineU$x)),c(smoothingSplineU$y,rev(smoothingSplineL$y)), col = "gray50", border = NA)
#plot lines for high and low range
lines(p, betas[,i], type='l',lwd=1)
lines(smoothingSplineU,lwd=1)
lines(smoothingSplineL,lwd=1)
abline(h=0,lty=2)
}
}
par(mfrow=c(1,1))
title("Point estimative and 95% CI for model parameters", outer=TRUE)
}
class(obj.out) = "qr"
#message("The interpretation of the regression coefficients is analogous to the interpretation of the coefficients of a logistic regression for binary outcomes. For references, please check Galarza, C.M., Zhang P. and Lachos, V.H. (2020). Logistic Quantile Regression for Bounded Outcomes Using a Family of Heavy-Tailed Distributions. Sankhya B.")
invisible(obj.out)
}
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