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#' Analysis: Page
#'
#' This function performs exponential page regression analysis.
#' @param trat Numeric vector with dependent variable.
#' @param resp Numeric vector with independent variable.
#' @param initial Starting estimates
#' @param sample.curve Provide the number of observations to simulate curvature (default is 1000)
#' @param error Error bar (It can be SE - \emph{default}, SD or FALSE)
#' @param ylab Variable response name (Accepts the \emph{expression}() function)
#' @param xlab treatments name (Accepts the \emph{expression}() function)
#' @param theme ggplot2 theme (\emph{default} is theme_bw())
#' @param legend.position legend position (\emph{default} is "top")
#' @param r2 coefficient of determination of the mean or all values (\emph{default} is all)
#' @param scale Sets x scale (\emph{default} is none, can be "log")
#' @param point defines whether you want to plot all points ("all") or only the mean ("mean")
#' @param width.bar Bar width
#' @param textsize Font size
#' @param pointsize shape size
#' @param linesize line size
#' @param linetype line type
#' @param pointshape format point (default is 21)
#' @param colorline Color lines
#' @param fillshape Fill shape
#' @param comment Add text after equation
#' @param xname.formula Name of x in the equation
#' @param yname.formula Name of y in the equation
#' @param round round equation
#' @param fontfamily Font family
#' @return The function returns a list containing the coefficients and their respective values of p; statistical parameters such as AIC, BIC, pseudo-R2, RMSE (root mean square error); largest and smallest estimated value and the graph using ggplot2 with the equation automatically.
#' @details
#' The exponential model is defined by:
#' \deqn{y = e^{-k \cdot x^n}}
#' @author Gabriel Danilo Shimizu
#' @author Leandro Simoes Azeredo Goncalves
#' @references Seber, G. A. F. and Wild, C. J (1989) Nonlinear Regression, New York: Wiley & Sons (p. 330).
#' @export
#'
#' @examples
#' library(AgroReg)
#' data("granada")
#' attach(granada)
#' PAGE(time,100-WL)
PAGE=function(trat,
resp,
initial=NA,
sample.curve=1000,
ylab="Dependent",
xlab="Independent",
theme=theme_classic(),
legend.position="top",
error="SE",
r2="all",
point="all",
width.bar=NA,
scale="none",
textsize = 12,
pointsize = 4.5,
linesize = 0.8,
linetype=1,
pointshape = 21,
fillshape = "gray",
colorline = "black",
round=NA,
yname.formula="y",
xname.formula="x",
comment=NA,
fontfamily="sans"){
if(is.na(width.bar)==TRUE){width.bar=0.01*mean(trat)}
requireNamespace("ggplot2")
ymean=tapply(resp,trat,mean)
if(error=="SE"){ysd=tapply(resp,trat,sd)/sqrt(tapply(resp,trat,length))}
if(error=="SD"){ysd=tapply(resp,trat,sd)}
if(error=="FALSE"){ysd=0}
desvio=ysd
xmean=tapply(trat,trat,mean)
if(is.na(initial[1])==TRUE){
mod=lm(log(resp)~trat)
k=coef(mod)[1]
n=coef(mod)[2]
initial=list(k=k,n=n)}
model=nls(resp~exp(k*trat^n),start = initial)
coef=summary(model)
if(is.na(round)==TRUE){
b=coef$coefficients[,1][1]
d=coef$coefficients[,1][2]}
if(is.na(round)==FALSE){
b=round(coef$coefficients[,1][1],round)
d=round(coef$coefficients[,1][2],round)}
if(r2=="all"){r2=1-deviance(model)/deviance(lm(resp~1))}
if(r2=="mean"){
model1=nls(ymean~exp(k*xmean^n),start = initial)
r2=1-deviance(model1)/deviance(lm(ymean~1))}
r2=floor(r2*100)/100
equation=sprintf("~~~%s==e^{%0.3e*%s^%0.3e} ~~~~~ italic(R^2) == %0.2f",
yname.formula,
b,
xname.formula,
d,
r2)
if(is.na(comment)==FALSE){equation=paste(equation,"~\"",comment,"\"")}
xp=seq(min(trat),max(trat),length.out = sample.curve)
preditos=data.frame(x=xp,
y=predict(model,newdata = data.frame(trat=xp)))
predesp=predict(model)
predobs=resp
rmse=sqrt(mean((predesp-predobs)^2))
x=preditos$x
y=preditos$y
s=equation
data=data.frame(xmean,ymean)
data1=data.frame(trat=xmean,resp=ymean)
if(point=="mean"){
graph=ggplot(data,aes(x=xmean,y=ymean))
if(error!="FALSE"){graph=graph+geom_errorbar(aes(ymin=ymean-ysd,ymax=ymean+ysd),
width=width.bar,
size=linesize)}
graph=graph+
geom_point(aes(color="black"),size=pointsize,shape=pointshape,fill=fillshape)}
if(point=="all"){
graph=ggplot(data.frame(trat,resp),aes(x=trat,y=resp))
graph=graph+
geom_point(aes(color="black"),size=pointsize,shape=pointshape,fill=fillshape)}
graph=graph+theme+geom_line(data=preditos,aes(x=x,
y=y,color="black"),size=linesize,lty=linetype)+
scale_color_manual(name="",values=colorline,label=parse(text = equation))+
theme(axis.text = element_text(size=textsize,color="black",family = fontfamily),
axis.title = element_text(size=textsize,color="black",family = fontfamily),
legend.position = legend.position,
legend.text = element_text(size=textsize,family = fontfamily),
legend.direction = "vertical",
legend.text.align = 0,
legend.justification = 0)+
ylab(ylab)+xlab(xlab)
if(scale=="log"){graph=graph+scale_x_log10()}
temp1=seq(min(trat),max(trat),length.out=sample.curve)
result=predict(model,newdata = data.frame(trat=temp1),type="response")
maximo=temp1[which.max(result)]
respmax=result[which.max(result)]
minimo=temp1[which.min(result)]
respmin=result[which.min(result)]
aic=AIC(model)
bic=BIC(model)
graphs=data.frame("Parameter"=c("X Maximum",
"Y Maximum",
"X Minimum",
"Y Minimum",
"AIC",
"BIC",
"r-squared",
"RMSE"),
"values"=c(maximo,
respmax,
minimo,
respmin,
aic,
bic,
r2,
rmse))
graficos=list("Coefficients"=coef,
"values"=graphs,
"plot"=graph)
graficos
}
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