#' @title T-test of two regression slopes or intercepts
#'
#' @description
#' This function performs a t-test to test whether two regression slopes or two regression intercepts are equal or not.
#' It can also be used to test whether a regression slope or intercept is equal to a given value.
#'
#' @details
#' The t-test can be performed on two \code{x} and \code{y} value vectors if also bringing a factor vector separating the x and y data in two subgroups.
#' It can also be performed on two independant \code{x} and \code{y} value vectors, that are \code{x}, \code{y}, \code{x2} and \code{y2}.
#' Finally, it can be performed on two lm outputs (no matter if the output comes from \code{lm()} or \code{summary(lm()))}.
#'
#' @param x the x-values to be used. Can contain the two groups of data if the parameter \code{factor} is provided. Otherwise, contain the x-values for the first group.
#' @param y the y-values to be used. As for \code{x}, it can contain the two groups of data if the parameter \code{factor} is provided. Otherwise, contain the y-values for the first group.
#' @param factor mandatory if providing \code{x} and \code{y} data to separate two groups.
#' @param x2 the x-values to be used for the second group.
#' @param y2 the y-values to be used for the second group.
#' @param object_1 the output of the linear model for the first group; can be an output of \code{"lm"} or of \code{"summary(lm)"}
#' @param object_2 the output of the linear model for the second group; can be an output of \code{"lm"} or of \code{"summary(lm)"}
#' @param delta An optional level value to compare a single slope with.
#' @param parameter the parameter of the regression line to be tested; by default the \code{"slope"}, otherwise can be the \code{"intercept"}
#'
#' @importFrom stats lm pt
#'
#' @return Returns an object containing the absolute difference between the two estimated parameters (\code{$Estimate}), the standard error of this difference (\code{$Std. Error}), the t-value of the t-test (\code{$t value}), the degrees of freedom of the test (\code{$df}) and the p-value of the bilateral t-test (\code{$p-value}).
#'
#' @examples
#'
#' ## To test a pre-established vs estimated parameter
#' x<-c(sort(runif(100,0,100)))
#' y<-c()
#' slope<-runif(1,-100,100)
#' intercept<-runif(1,-100,100)
#' for (i in 1:length(x)){
#' y[i]<-x[i]*slope+intercept+runif(1,-abs(slope)/100,abs(slope)/100)
#' }
#' parameter<-"slope"
#' reg.param.t.test(x,y,slope,parameter="intercept")
#' reg.param.t.test(y~x,slope,"slope")
#' reg.param.t.test(lm(y~x),slope,parameter) ## This tests if the function retrieves the original defined slope as equal to the slope of
#' reg.param.t.test(lm(y~x),intercept,"intercept") ## This tests if the function retrieves the original defined intercept as equal to the intercept of lm()
#' reg.param.t.test(lm(y~x),0,parameter)[c(1,2,3,5)]==summary(lm(y~x))$coefficients[2,]
#' reg.param.t.test(lm(y~x),0,"intercept")[c(1,2,3,5)]==summary(lm(y~x))$coefficients[1,]
#'
#' ## To compare two pre-established slopes
#' x1<-sort(runif(50,0,20))
#' x2<-sort(runif(50,0,20))
#' slope1<-runif(1,-100,100)
#' intercept<-runif(1,-100,100)
#' slope2<-runif(1,-100,100)
#' y1<-c()
#' y2<-c()
#' for (i in 1:length(x1)){
#' y1[i]<-x1[i]*slope1+intercept+runif(1,-abs(slope1)/100,abs(slope1)/100)
#' y2[i]<-x2[i]*slope2+intercept+runif(1,-abs(slope2)/100,abs(slope2)/100)
#' }
#' x12<-c(x1,x2)
#' y12<-c(y1,y2)
#' fac<-c(rep("1",50),rep("2",50))
#' parameter<-"slope"
#' object_1<-summary(lm(y12[fac==levels(factor(fac))[1]]~x12[fac==levels(factor(fac))[1]]))
#' object_2<-summary(lm(y12[fac==levels(factor(fac))[2]]~x12[fac==levels(factor(fac))[2]]))
#' plot(x1,y1,type="l",col="blue",ylim=c(min(min(y1),min(y2)),max(max(y1),max(y2))))
#' points(x2,y2,type="l",col="red")
#' reg.param.t.test(x12,y12,fac,parameter)
#' reg.param.t.test(y12~x12,fac,parameter)
#' reg.param.t.test(y1~x1,y2~x2,parameter)
#' reg.param.t.test(x1,y1,x2,y2,parameter)
#' reg.param.t.test(object_1,object_2,parameter)
#' summary(lm(y12~x12*fac))$coefficients[4,] ## Results do not perfectly fit but are roughly the same, don't know why now...
#'
#' @importFrom rlang is_formula
#' @export
<-(x,y,,x2,y2,object_1,object_2,delta,parameter){
((parameter)){parameter<-"slope"}
((delta)){delta<-}
((object_2)){object_2<-}
((object_1)){object_1<-}
((y2)==){
((y2=="slope"|y2=="intercept")){
parameter<-y2
y2<-
}
}
((y2)){y2<-}
((x2)==){
(((x2)&(x2)>1)&(y2)){
y2<-x2
x2<-
}
((x2=="slope"|x2=="intercept")){
parameter<-x2
x2<-
}
}
((x2)){x2<-}
(()==){
(()){
(()==1){
delta<-
<-
}
{
x2<-
<-
}
}
(()==1){
parameter<-
<-
}
}
(()){<-}
((y)==){
((y)){
((y)&(y)==1){
delta<-y
y<-
}
(((y)|(y))&(y)>1){
<-y
y<-
}
}
(rlang::is_formula(y)){
object_2<-((y))
y<-
}
((y)&(((y)$)&((y)$=="lm"|(y)$=="summary.lm"))){
object_2<-y
y<-
}
}
((x)==){
(rlang::is_formula(x)){
((object_2)){
x_lm<-(x)
x<-(x_lm[2], envir = ())
y<-(x_lm[1], envir = ())
}
{
object_1<-((x))
x<-
}
}
((x)&(((x)$)&((x)$=="lm"|(x)$=="summary.lm"))){
object_1<-x
x<-
}
}
dfsup<-0
((object_1)==&(object_2)&(delta)==){
object_2<-(=((delta,delta),(0,0)),=(0))
(object_2)$<-"summary.lm"
dfsup<--1
}
(((object_1)==|(object_2)==)&((x)==|(y)==|()==|(x2)==|(y2)==)==){
("You provided a lm output and a vector; please choose the method to use and provide either two lm outputs or x and y data together with a factorial vector distinguishing two groups")
}
((object_1)&(object_2)){
((x2)&(y2)){
((x)){
((y)){
('Only the vector "factor" is provided; please also provide "x" and "y" vectors or provide two lm outputs')
}
(()){
('Only the vector "y" is provided; please also provide "x" and "factor" vectors or provide two lm outputs')
}
{
('Only the vectors "y" and "factor" are provided; please also provide "x" vector or provide two lm outputs')
}
}
{
((y)==&(()&(delta))){
('Only the vectors "x" and "y" are provided; please also provide either "factor" vector, a "delta" level, or two lm outputs')
}
((y)==&(()==|(delta)==)){
('Only the vectors "x" and "factor" or "delta" are provided; please also provide "y" vector or provide two lm outputs')
}
((y)&(()&(delta))){
('Only the vector "x" is provided; please also provide "y" and "factor" vectors or delta level, or provide two lm outputs')
}
}
(()==&(delta)){
group_names<-(())
object_1<-((y[factor==group_names[1]]~x[factor==group_names[1]]))
object_2<-((y[factor==group_names[2]]~x[factor==group_names[2]]))
}
{
object_1<-((y~x))
object_2<-(=((delta,delta),(0,0)),=(0))
(object_2)$<-"summary.lm"
dfsup<--1
}
}
(((x)&(y)&(x2)&(y2))==){
object_1<-((y~x))
object_2<-((y2~x2))
}
}
{
((object_1)==&(delta)==){
("A single lm output is provided, please provide a comparison value (delta), or provide either two lm output or the original data (x and y data together with a factorial vector distinguishing two groups)")
}
((object_1)==){
((object_1)$=="lm"){
object_1<-(object_1)
}
}
((object_1)==){
((object_2)$=="lm"){
object_2<-(object_2)
}
}
}
(parameter=="slope"){
parameter<-2
}
(parameter=="intercept"){
parameter<-1
}
parameter_1<-object_1$[parameter,1]
parameter_2<-object_2$[parameter,1]
se_parameter_1<-object_1$[parameter,2]
se_parameter_2<-object_2$[parameter,2]
n_1<-(object_1$)
n_2<-(object_2$)
n<-n_1+n_2
num<-parameter_1-parameter_2
denom<-(se_parameter_1^2+se_parameter_2^2)
<-num/denom
<-n-4-dfsup
p<-2*(-(),)
results<-(num,denom,,,p)
(results)<-("Estimate","Std. Error","t value","df","p-value")
(results)
}
