index.Rmd

--- 
lang: "PT-br"
title: "Introdução ao GAMLSS"
author: "Gustavo Thomas e Cristian Villegas"
date: "`r Sys.Date()`"
site: bookdown::bookdown_site
documentclass: book
bibliography: [book.bib, packages.bib]
# url: your book url like https://bookdown.org/yihui/bookdown
# cover-image: path to the social sharing image like images/cover.jpg
description: |
  This is a minimal example of using the bookdown package to write a book.
  The HTML output format for this example is bookdown::gitbook,
  set in the _output.yml file.
link-citations: yes
github-repo: rstudio/bookdown-demo
---


```{r, echo=FALSE}
knitr::opts_chunk$set(message = FALSE,
                      warning = TRUE,
                      cache = TRUE)
```


# Introdução



```{r}
library(knitr)
library(gamlss)
library(xtable)
PPP <- par(mfrow=c(2,2))
plot(R~Fl, data=rent, col=gray(0.7), pch=15, cex=0.5) 
plot(R~A, data=rent, col=gray(0.7), pch=15, cex=0.5) 
plot(R~H, data=rent, col=gray(0.7), pch=15, cex=0.5) 
plot(R~loc, data=rent, col=gray(0.7), pch=15, cex=0.5) 
```

```{r}
par(PPP)
# ----eval=FALSE----------------------------------------------------------
## R ~ Fl+A+H+loc
## ----cache=TRUE----------------------------------------------------------
r1 <-  gamlss(R ~ Fl+A+H+loc, family=NO,  data=rent, trace=FALSE)
l1 <- lm(R ~ Fl+A+H+loc,data=rent)
coef(r1)
coef(l1)
```


```{r, tidy=TRUE, tidy.opts=list(width=60)}
fitted(r1, "sigma")[1]
summary(r1)

Rsq(r1)

## ----LM_residual_plot,echo=TRUE,fig.show='hide', fig.asp=1---------------
plot(r1)

## ----cache=TRUE----------------------------------------------------------
### using gamlss
r2 <-  gamlss(R ~ Fl+A+H+loc, family=GA,  data=rent)
coef(r2)
coef(r2, "sigma")  ### extract log(sigma)
deviance(r2)

### using glm 
l2 <- glm(R ~ Fl+A+H+loc, family=Gamma(link="log"),  data=rent)
coef(l2)
summary(l2)$dispersion  ### extract phi
deviance(l2)

## ------------------------------------------------------------------------
summary(r2)

## ------------------------------------------------------------------------
r22 <-  gamlss(R ~ Fl+A+H+loc, family=IG,  data=rent, trace=FALSE)
GAIC(r1, r2, r22, k=0) # GD

## ----GLM_residual_plot,echo=TRUE,fig.show='hide', fig.asp=1--------------
plot(r2)

## ----cache=TRUE----------------------------------------------------------
r3 <-  gamlss(R ~ pb(Fl)+pb(A)+H+loc, family=GA,  data=rent, 
              trace=FALSE)
AIC(r2,r3)

## ------------------------------------------------------------------------
summary(r3)

## ----cache=TRUE----------------------------------------------------------
drop1(r3) 

## ----GAM_termplot, echo=TRUE,fig.show='hide', fig.asp=1,cache=TRUE-------
term.plot(r3, pages=1, ask=FALSE)

## ----GAM_wormplot, echo=TRUE,fig.show='hide', fig.asp=1,cache=TRUE-------
wp(r3, ylim.all=.6)

## ----cache=TRUE----------------------------------------------------------
r4 <-  gamlss(R ~ pb(Fl)+pb(A)+H+loc, sigma.fo=~pb(Fl)+pb(A)+H+loc, 
              family=GA, data=rent, trace=FALSE)
r5 <-  gamlss(R ~ pb(Fl)+pb(A)+H+loc, sigma.fo=~pb(Fl)+pb(A)+H+loc, 
              family=IG, data=rent, trace=FALSE)
AIC(r3, r4, r5)

## ----MADAM_termplot, echo=TRUE,fig.show='hide', fig.asp=1,cache=TRUE-----
term.plot(r4, pages=1, what="sigma", ask=FALSE)

## ----cache=TRUE----------------------------------------------------------
drop1(r4, what="sigma")

## ----MADAM_wormplot, echo=TRUE,fig.show='hide', fig.asp=1,cache=TRUE-----
wp(r4, ylim.all=.6)

## ----cache=TRUE----------------------------------------------------------
r6 <-  gamlss(R ~ pb(Fl)+pb(A)+H+loc, sigma.fo=~pb(Fl)+pb(A)+H+loc,
              nu.fo=~1, family=BCCGo,  data=rent, trace=FALSE)

r7 <-  gamlss(R ~ pb(Fl)+pb(A)+H+loc,sigma.fo=~pb(Fl)+pb(A)+H+loc,
              nu.fo=~pb(Fl)+pb(A)+H+loc, family=BCCGo,  data=rent, 
              trace=FALSE)

AIC(r4, r6, r7)
## ----WP_BCCG1_CH1, echo=TRUE, fig.show='hide', fig.asp=1-----------------
wp(r6, ylim.all=.6) ;  title("r6: BCCG(mu, sigma)")
wp(r7, ylim.all=.6) ;  title("r7:  BCCG(mu, sigma, nu)")
```

##  exercises   Chapter 1

```{r, eval=FALSE}
## data(airquality)
## plot(airquality[,-c(5,6)])

## # Fit the standard linear model
## air.lm <- lm(Ozone~Temp+Wind+Solar.R,data=airquality)
## summary(air.lm)

## op<-par(mfrow=c(1,3))
## termplot(air.lm,partial.resid=TRUE,se=T)
## par(op)

## op<-par(mfrow=c(1,2))
## plot(air.lm,which=1:2)
## par(op)

## library(gamlss)
## da <- na.omit(airquality)  # clear the data of NA's
## mno<-gamlss(Ozone~Temp+Wind+Solar.R, data=da)  # fit the model
## summary(mno)

## term.plot(mno, pages=1, partial=T)  # plot the fitted terms

## plot(mno)
## wp(mno)

## # fit different distributions
## mga <- gamlss(Ozone~Temp+Wind+Solar.R, data=da, family=GA)
## mig <- gamlss(Ozone~Temp+Wind+Solar.R, data=da, family=IG)
## mbccg <- gamlss(Ozone~Temp+Wind+Solar.R, data=da, family=BCCGo)
## GAIC(mno, mga, mig, mbccg)

## # fit smoothers
## mga1=gamlss(Ozone~pb(Temp)+pb(Wind)+pb(Solar.R),data=da,
##             family=GA)
## term.plot(mga1, pages=1)
## plot(mga1)
## wp(mga1)
```

## gamlss.demo()

```{r, eval=FALSE}
#install.packages("gamlss.demo", dep=TRUE)
#Based on rpanel
library(gamlss.demo)

#Examples
#t family distribution
demo.TF()

#Skew Normal Type 1 distribution
demo.SN1()

#Box-Cox Power Exponential distribution
demo.BCPE()

#Demos for smoothing techniques
demo.BSplines()
demo.PSplines()
demo.interpolateSmo()
demo.histSmo()

#Interface for demonstrating the gamlss.family distributions
demoDist()

#Demo for local polynomial smoothing
demoLpolyS()

#The demo for gamlss distributions and smoothing
gamlss.demo()

```