From 3c66edf9eb663a9bdb354d7ec5d1640da6adf2c2 Mon Sep 17 00:00:00 2001
From: Cesar Taconeli <taconeli@ufpr.br>
Date: Mon, 9 May 2016 17:40:07 -0300
Subject: [PATCH] Adiciona slides e vinhetas da primeira parte do curso
---
inst/slides/images/graf1.pdf | Bin 0 -> 5384 bytes
inst/slides/images/graf2.pdf | Bin 0 -> 5655 bytes
inst/slides/images/processos14.pdf | Bin 0 -> 9618 bytes
vignettes/Ovelhas.Rmd | 240 ++++++++++++++++++++
vignettes/Sinistros.Rmd | 352 +++++++++++++++++++++++++++++
5 files changed, 592 insertions(+)
create mode 100644 inst/slides/images/graf1.pdf
create mode 100644 inst/slides/images/graf2.pdf
create mode 100644 inst/slides/images/processos14.pdf
create mode 100644 vignettes/Ovelhas.Rmd
create mode 100644 vignettes/Sinistros.Rmd
diff --git a/inst/slides/images/graf1.pdf b/inst/slides/images/graf1.pdf
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diff --git a/vignettes/Ovelhas.Rmd b/vignettes/Ovelhas.Rmd
new file mode 100644
index 0000000..d8b6cdd
--- /dev/null
+++ b/vignettes/Ovelhas.Rmd
@@ -0,0 +1,240 @@
+---
+title: "Análise de Contagens - Quase-Verossimilhança"
+author: >
+ Walmes M. Zeviani,
+ Eduardo E. Ribeiro Jr &
+ Cesar A. Taconeli
+vignette: >
+ %\VignetteIndexEntry{Análise de Contagens - Quase-Verossimilhança}
+ %\VignetteEngine{knitr::rmarkdown}
+ %\VignetteEncoding{UTF-8}
+---
+
+```{r setup, include=FALSE}
+source("_setup.R")
+```
+
+Dados referentes a um experimento delineado em blocos, com o objetivo de
+investigar o efeito de uma intervenção, por parte do cuidador, no
+comportamento de ovelhas.
+
+Para isso, foram considradas ovelhas de duas
+linhagens distintas (pouco ou muito reativas), submetidas a dois tipos
+diferentes de intervenção (observação ou observação + intervenção).
+
+A variável resposta aqui considerada é o número de mudanças na postura
+corporal do animal ao longo do período de observação.
+
+
+```{r, echo = FALSE, include=FALSE}
+##### Carregamento e tratamento inicial dos dados
+dados <- read.csv2('Dadoscomp.csv',sep=',')
+dados$tratamento <- factor(dados$tratamento)
+levels(dados$tratamento) <- c('Observ', 'Observ + Interv')
+dados$linhagem <- factor(dados$linhagem)
+levels(dados$linhagem) <- c('Pouco reativo', 'Muito reativo')
+dados2 <- dados[1:38,c(1:5,30:53)]
+dados3 <- dados[1:38,30:53] ### Somente as mudanças de postura durante a intervenção.
+r1 <- rowSums(dados3[,1:3])-1
+table(r1)
+r2 <- rowSums(dados3[,4:6])-1
+table(r2)
+r4 <- rowSums(dados3[,12:16])-1
+table(r4)
+d2 <- rowSums(dados[1:38,57:59])-1
+table(d2)
+
+datapost1 <- data.frame(r1, dados2[ ,c('tratamento', 'linhagem')])
+names(datapost1)[1] <- 'Nposturas'
+datapost2 <- data.frame(r2, dados2[ ,c('tratamento', 'linhagem')])
+names(datapost2)[1] <- 'Nposturas'
+datapost4 <- data.frame(r4, dados2[ ,c('tratamento', 'linhagem')])
+names(datapost4)[1] <- 'Nposturas'
+
+##### Pacotes requeridos
+require('lmtest')
+require('boot')
+require('car')
+require('RColorBrewer')
+require('sandwich')
+require('hnp')
+```
+
+
+### Verificação do conteúdo e a estrutura dos dados.
+
+```{r}
+str(datapost4)
+summary(datapost4)
+```
+
+
+
+### Análise descritiva
+
+```{r}
+tab <- data.frame(with(datapost4, table(tratamento, Nposturas)))
+
+myColours <- brewer.pal(2,"Blues")
+
+my.settings <- list(
+ superpose.polygon=list(col=myColours[2:5], border="transparent"),
+ strip.background=list(col=myColours[6]),
+ strip.border=list(col="black")
+)
+
+bwplot(Nposturas ~ linhagem | tratamento,
+ data=datapost4,
+ main="Mudanças de postura vs tratamento e linhagem",
+ xlab="Linhagem", ylab="Frequência")
+
+### Variância e média amostrais por tratamento e linhagem.
+
+mdp <- aggregate(Nposturas ~ tratamento:linhagem, datapost4, function(x) c(mean = mean(x), var = var(x)))
+mdp
+
+```
+
+
+### Regressão poisson com estimação por máxima verossimilhança.
+
+```{r}
+ajusteps <- glm(Nposturas ~ tratamento + linhagem, data=datapost4, family=poisson)
+summary(ajusteps)
+
+exp(coef(ajusteps)[2])
+### Estima-se que a frequência média de variação de postura no grupo com intervenção seja aproximadamente
+### a metade em relação ao grupo sem intervenção.
+
+##### Estimação do parâmetro de dispersão.
+X2 <- sum(resid(ajusteps,type='pearson')**2)
+phichap <- X2/ajusteps$df.residual
+phichap
+```
+
+### Diagnóstico do ajuste (gráficos).
+
+```{r}
+##### Diagnóstico do modelo - gráficos padrão do R.
+par(mfrow=c(2,2))
+plot(ajusteps, pch = 20, cex = 1.25)
+```
+
+```{r, echo = FALSE}
+envelope=function(modelo){
+ dados=na.omit(modelo$data)
+ nsim=100
+ n=modelo$df.null+1
+ r1=sort(rstandard(modelo,type='deviance'))
+ m1=matrix(0,nrow=n,ncol=nsim)
+ a2=simulate(modelo,nsim=nsim)
+
+ for (i in 1:nsim){
+ dados$y=a2[,i]
+ aj=update(modelo,y~.,data=dados)
+ m1[,i]=sort(rstandard(aj,type='deviance'))}
+
+ li=apply(m1,1,quantile,0.025)
+ m=apply(m1,1,quantile,0.5)
+ ls=apply(m1,1,quantile,0.975)
+
+ quantis=qnorm((1:n-0.5)/n)
+
+ plot(rep(quantis,2),c(li,ls),type='n',xlab='Percentil da N(0,1)',ylab='Resíduos')
+ title('Gráfico Normal de Probabilidades')
+ lines(quantis,li,type='l')
+ lines(quantis,m,type='l',lty=2)
+ lines(quantis,ls,type='l')
+ points(quantis,r1,pch=16,cex=0.75)
+}
+
+```
+
+```{r}
+##### Gráfico quantil-quantil com envelopes simulados.
+par(mfrow=c(1,1))
+envelope(ajusteps)
+```
+
+
+### Ajustando modelos por quase-verossimilhança.
+
+```{r}
+
+### Modelo quasi poisson (V(mu) = mu).
+ajuste12 <- glm(r4 ~ tratamento+linhagem, data=datapost4, family = 'quasipoisson')
+summary(ajuste12)
+
+### Forma alternativa de declarar o Modelo quase-poisson (V(mu) = mu).
+ajuste13 <- glm(r4 ~ tratamento+linhagem, data=datapost4, family = quasi(variance = 'mu', link='log'))
+summary(ajuste13)
+
+### Modelo de quase-verossimilhança (V(mu) = mu^2).
+ajuste14 <- glm(r4 ~ tratamento+linhagem, data=datapost4, family = quasi(variance = 'mu^2', link='log'))
+summary(ajuste14)
+
+### Gráficos de diagnóstico para o modelo de quase-verossimilhança.
+par(mfrow = c(2,2))
+plot(ajuste14, pch = 20, cex = 1.25)
+
+### Gráficos quantil-quantil para os resíduos dos modelos Poisson e de Quase-Verossimilhança.
+par(mfrow=c(1,2))
+qqnorm(resid(ajusteps,type='deviance'), pch = 20, main = 'Poisson', las = 1)
+qqline(resid(ajusteps,type='deviance'))
+qqnorm(resid(ajuste14,type='deviance'), pch = 20, main = 'QL', las = 1)
+qqline(resid(ajuste14,type='deviance'))
+```
+
+
+### Usando estimação robusta e bootstrap.
+
+```{r}
+
+estrb <- coeftest(ajusteps, vcov=sandwich) ### Estimador sanduíche
+estrb
+
+### Usando bootstrap (R=999 simulações)
+ajusteboot <- Boot(ajusteps)
+plot(ajusteboot, index = 2) ### Distribuição bootstrap para o efeito de intervenção.
+summary(ajusteboot)
+
+
+```
+
+
+### Apanhado geral dos resultados.
+
+```{r}
+
+erroz <- rbind(summary(ajusteps)$coefficients[2,2:3], summary(ajuste13)$coefficients[2,2:3],
+ summary(ajuste14)$coefficients[2,2:3], estrb[2,2:3], c(summary(ajusteboot)[2,4],
+ mean(ajusteboot$t[,2]/summary(ajusteboot)[2,4])))
+
+ics <- rbind(confint.default(ajusteps)[2,],confint.default(ajuste13)[2,], confint.default(ajuste14)[2,],
+estrb[2,1] + c(-1.96,1.96) * estrb[2,2], mean(ajusteboot$t[,2])+c(-1.96,1.96)*summary(ajusteboot)[2,4])
+
+quadres <- cbind(erroz, ics)
+
+rownames(quadres) <- c('Poisson', 'Quasi(mu)', 'Quasi(mu^2)', 'Robusto (sanduiche)', 'Bootstrap')
+
+### Quadro resumo para as estimativas produzidas pelos quatro modelos.
+kable(quadres, format = "markdown", caption = "Comparativo dos modelos ajustados")
+
+### Vamos avaliar o efeito das observações com maiores resíduos nos achados do modelo
+dadosexclud <- datapost4[-c(8,18,28),]
+ajusteexclud <- glm(Nposturas ~ tratamento+linhagem, data=dadosexclud, family = quasi(variance = 'mu', link='log'))
+
+### Estimativas produzidas pelo modelo quasipoisson com e sem as três observações.
+
+c1 <- compareCoefs(ajuste13, ajusteexclud, print = FALSE)
+colnames(c1) <- c('Est. com outliers','E.P. com outliers','Est. sem outliers','E.P. sem outliers')
+kable(c1)
+
+### Efeito da intervenção desconsiderando as três observações.
+exp(coef(ajusteexclud)[2])
+
+### O efeito de intervenção aumenta, e torna-se mais significativo, mediante exclusão dos outliers.
+
+````
+
+
diff --git a/vignettes/Sinistros.Rmd b/vignettes/Sinistros.Rmd
new file mode 100644
index 0000000..c6ec870
--- /dev/null
+++ b/vignettes/Sinistros.Rmd
@@ -0,0 +1,352 @@
+---
+title: "Análise de Contagens - Poisson e Binomial Negativa"
+author: >
+ Walmes M. Zeviani,
+ Eduardo E. Ribeiro Jr &
+ Cesar A. Taconeli
+vignette: >
+ %\VignetteIndexEntry{Análise de Contagens - Poisson e Binomial Negativa}
+ %\VignetteEngine{knitr::rmarkdown}
+ %\VignetteEncoding{UTF-8}
+---
+
+```{r setup, include=FALSE}
+source("_setup.R")
+```
+
+
+Dados referentes ao número de sinistros registrados por 16483 clientes de
+uma seguradora de automóveis ao longo de um ano, contemplando as
+seguintes variáveis:
+
+* **Sinistros**: Número de sinistros registrados;
+* **Exposicao**: Período de cobertura do cliente durante o ano sob análise;
+* **Tipo**: Tipo de veículo (hatch, monobloco, picape, sedan, wagon e suv);
+* **Idade**: Idade do cliente (em anos);
+* **Sexo**: M para masculino e F para feminino;
+* **Civil**: Estado civil (Solteiro, Casado, Divorciado e Viuvo);
+* **Valor**: Valor do veículo segurado (em reais).
+
+
+
+```{r, echo = FALSE, include=FALSE}
+
+require(lattice)
+require(hnp)
+require(MASS)
+require(effects)
+
+# setwd("C:/Users/CCE/Dropbox/Backup Parana/Parana/Curso - dados discretos")
+dados <- read.csv2('Baseauto2.csv', header=TRUE, sep=',')
+
+options(scipen = 3) ### Era zero.
+
+##### Preparando os dados.
+names(dados) <- c('Bonus','Tipo','Estado','Idade','Sexo','Civil','Valor','Exposicao','Sinistros')
+dados <- dados[,c('Tipo','Idade','Sexo','Civil','Valor','Exposicao','Sinistros')]
+levels(dados$Tipo) <- c('outros','outros','outros','outros','hatch','outros','mono','picape','picape','picape','sedan','wagon','suv')
+dados <- dados[-which(dados$Tipo=='outros'),]
+dados$Tipo <- factor(dados$Tipo)
+dados <- dados[which(dados$Valor != 0),]
+dados$Civil <- relevel(dados$Civil, ref = 'Solteiro')
+dados$lexpo <- log(dados$Exposicao)
+dados$Valor <- dados$Valor/1000
+
+```
+
+### Verificação do conteúdo e a estrutura dos dados.
+
+```{r}
+head(dados, 10) ### Dez primeiras linhas da base.
+str(dados)
+```
+
+### Análise descritiva da distribuição do número de sinistros.
+
+```{r}
+table(dados$Sinistros) ### Distribuição do números de sinistros.
+taxageral <- sum(dados$Sinistros)/sum(dados$Exposicao); taxageral ### Taxa de sinistros na amostra.
+
+tab <- aggregate(cbind(Exposicao, Sinistros) ~ Sexo, data = dados, sum)
+taxa <- with(tab, Sinistros/Exposicao)
+tab <- cbind(tab, taxa); tab ### Distribuição do número de sinistros por sexo.
+
+dados$idadecat <- cut(dados$Idade, breaks=c(18,30,60, 92), include.lowest = T)
+tab <- aggregate(cbind(Exposicao, Sinistros) ~ idadecat, data = dados, sum)
+taxa <- with(tab, Sinistros/Exposicao)
+tab <- cbind(tab, taxa); tab ### Distribuição do número de sinistros por sexo.
+
+tabidsex <- aggregate(cbind(Exposicao, Sinistros) ~ Sexo + idadecat, data = dados, sum)
+Taxaidsex <- with(tabidsex, Sinistros/Exposicao)
+tabidsex <- cbind(tabidsex, Taxaidsex); tabidsex ### Distribuição do número de sinistros por idade e sexo.
+
+tab <- aggregate(cbind(Exposicao, Sinistros) ~ Tipo, data = dados, sum)
+taxa <- with(tab, Sinistros/Exposicao)
+tab <- cbind(tab, taxa); tab ### Distribuição do número de sinistros por tipo de veículo.
+
+tab <- aggregate(cbind(Exposicao, Sinistros) ~ Civil, data = dados, sum)
+taxa <- with(tab, Sinistros/Exposicao)
+tab <- cbind(tab, taxa); tab ### Distribuição do número de sinistros por estado civil.
+
+dados$valorcat <- cut(dados$Valor, breaks=quantile(dados$Valor), include.lowest = T)
+tab <- aggregate(cbind(Exposicao, Sinistros) ~ valorcat, data = dados, sum)
+taxa <- with(tab, Sinistros/Exposicao)
+tab <- cbind(tab, taxa); tab ### Distribuição do número de sinistros por valor do veículo.
+```
+
+## Regressão usando o modelo log-linear poisson.
+
+```{r}
+dados <- na.omit(dados)
+ajusteps <- glm(Sinistros ~ Tipo+Sexo+Idade+I(Idade**2)+Valor+Civil+offset(log(Exposicao)), data = dados, family=poisson)
+summary(ajusteps)
+
+##### Estimação do parâmetro de dispersão.
+
+exp(coef(ajusteps))
+
+X2 <- sum(resid(ajusteps,type='pearson')**2)
+phichap <- X2/ajusteps$df.residual
+phichap ### Indicador de superdispersão.
+```
+
+### Diagnóstico do ajuste (gráficos).
+
+```{r}
+##### Diagnóstico do modelo - gráficos.
+par(mfrow=c(2,2))
+plot(ajusteps)
+
+
+par(mfrow=c(1,1))
+envelope=function(modelo){
+ dados=na.omit(modelo$data)
+ nsim=100
+ n=modelo$df.null+1
+ r1=sort(rstandard(modelo,type='deviance'))
+ m1=matrix(0,nrow=n,ncol=nsim)
+ a2=simulate(modelo,nsim=nsim)
+
+ for (i in 1:nsim){
+ dados$y=a2[,i]
+ aj=update(modelo,y~.,data=dados)
+ m1[,i]=sort(rstandard(aj,type='deviance'))}
+
+ li=apply(m1,1,quantile,0.025)
+ m=apply(m1,1,quantile,0.5)
+ ls=apply(m1,1,quantile,0.975)
+
+ quantis=qnorm((1:n-0.5)/n)
+
+ plot(rep(quantis,2),c(li,ls),type='n',xlab='Percentil da N(0,1)',ylab='Resíduos')
+ title('Gráfico Normal de Probabilidades')
+ lines(quantis,li,type='l')
+ lines(quantis,m,type='l',lty=2)
+ lines(quantis,ls,type='l')
+ points(quantis,r1,pch=16,cex=0.75)
+}
+
+envelope(ajusteps)
+
+```
+
+
+### Re-ajuste do modelo associando um parâmetro ao termo offset (log-exposicao)
+
+```{r}
+ajusteps2 <- glm(Sinistros ~ Tipo + Sexo + Idade +I(Idade**2) + Valor + Civil+log(Exposicao), data = dados, family=poisson)
+summary(ajusteps2)
+anova(ajusteps, ajusteps2, test = 'Chisq')
+```
+
+
+### Regressão usando a distribuição binomial negativa.
+
+```{r}
+ajustenb2 <- glm.nb(Sinistros ~ Tipo+Sexo+Idade+I(Idade**2)+Valor+Civil+log(Exposicao),data= dados)
+summary(ajustenb2)
+
+### Verificando possibilidade de excluir estado civil e tipo de veículo do modelo.
+ajustenb3 <- update(ajustenb2, ~.-(Civil+Tipo))
+anova(ajustenb2, ajustenb3)
+
+## Estimação do parâmetro de dispersão
+X2 <- sum(resid(ajustenb3,type='pearson')**2)
+phichap <- X2/ajustenb3$df.residual
+phichap
+```
+
+
+### Diagnóstico do ajuste (gráficos).
+
+```{r}
+##### Diagnóstico do modelo - gráficos.
+par(mfrow=c(2,2))
+plot(ajustenb3)
+```
+
+
+```{r, echo = FALSE}
+dadosnb3 <- dados[,c('Sexo','Idade','Valor','Exposicao','Sinistros')]
+
+par(mfrow=c(1,1))
+envelope=function(modelo){
+ dados=na.omit(dadosnb3)
+ nsim=100
+ n=modelo$df.null+1
+ r1=sort(rstandard(modelo,type='deviance'))
+ m1=matrix(0,nrow=n,ncol=nsim)
+ a2=simulate(modelo,nsim=nsim)
+
+ for (i in 1:nsim){
+ dados$y=a2[,i]
+ aj=update(modelo,y~.,data=dados)
+ m1[,i]=sort(rstandard(aj,type='deviance'))}
+
+ li=apply(m1,1,quantile,0.025)
+ m=apply(m1,1,quantile,0.5)
+ ls=apply(m1,1,quantile,0.975)
+
+ quantis=qnorm((1:n-0.5)/n)
+
+ plot(rep(quantis,2),c(li,ls),type='n',xlab='Percentil da N(0,1)',ylab='Resíduos')
+ title('Gráfico Normal de Probabilidades')
+ lines(quantis,li,type='l')
+ lines(quantis,m,type='l',lty=2)
+ lines(quantis,ls,type='l')
+ points(quantis,r1,pch=16,cex=0.75)
+}
+```
+
+
+```{r}
+par(mfrow=c(1,1))
+envelope(ajustenb3)
+```
+
+
+
+### Explorando os efeitos das covariáveis. Estimativas pontuais e ICs (95%)
+
+```{r}
+intervalos <- confint(ajustenb3)
+estimat <- cbind(ajustenb3$coefficients, intervalos)
+colnames(estimat)[1] <- 'Estimativa pontual'
+
+### Quadro de estimativas
+round(estimat, 5)
+```
+
+
+### Gráficos de efeitos
+
+```{r}
+
+dados$lexpo <- log(dados$Exposicao)
+ajustenb3 <- glm.nb(Sinistros ~ Sexo+Idade+I(Idade**2)+Valor+lexpo,data= dados)
+
+efeitos <- allEffects(ajustenb3, given.values=c(lexpo=0))
+
+trellis.par.set(list(axis.text = list(cex = 1.2)))
+
+plot(efeitos[[2]], type='response',main=list(
+ label="Taxa de sinistros vs. Idade",
+ cex=1.5),
+ xlab=list(
+ label="Idade (anos)",
+ cex=1.5),
+ ylab=list(
+ label="Taxa de sinistros",
+ cex=1.5))
+
+plot(efeitos[[1]], type='response',main=list(
+ label="Taxa de sinistros vs. Sexo",
+ cex=1.5),
+ xlab=list(
+ label="Sexo",
+ cex=1.5),
+ ylab=list(
+ label="Taxa de sinistros",
+ cex=1.5))
+
+plot(efeitos[[4]], type='response',main=list(
+ label="Taxa de sinistros vs. Valor do automóvel",
+ cex=1.5),
+ xlab=list(
+ label="Valor (x1000 reais)",
+ cex=1.5),
+ ylab=list(
+ label="Taxa de sinistros",
+ cex=1.5))
+
+```
+
+
+
+
+```{r, echo = FALSE}
+
+## Frequências ajustadas pelas duas distribuições, com e sem covariaveis.
+
+### Poisson sem ajuste de covariáveis.
+n <- nrow(dados)
+mediasin <- mean(dados$Sinistros)
+freqps <- round(n*dpois(0:10,mediasin))
+
+
+### Poisson com covariaveis
+pred1 <- predict(ajusteps,type='response')
+intervalo <- 0:10
+matprob <- matrix(0, nrow=nrow(dados), ncol=length(intervalo))
+probpois <- function(interv, taxa)
+ dpois(intervalo,taxa)
+for(i in 1:nrow(dados))
+ matprob[i,] <- probpois(interv = intervalo, taxa = pred1[i])
+pbarra <- colMeans(matprob)
+freqpsaj <- round(n*pbarra)
+
+
+
+### Binomial negativa sem covariaveis.
+ajustenb <- glm.nb(Sinistros ~ 1,data=dados)
+
+media <- exp(coefficients(ajustenb))
+shape <- ajustenb$theta
+freqbn <- round(n*dnbinom(0:10, mu = media, size = shape)); freqbn
+
+
+### Binomial negativa com covariaveis
+pred2 <- predict(ajustenb3,type='response')
+
+intervalo <- 0:10
+matprob <- matrix(0,nrow=nrow(dados),ncol=length(intervalo))
+probnb <- function(interv, media, shape)
+ dnbinom(intervalo, mu = media, size = shape)
+for(i in 1:nrow(dados))
+ matprob[i,] <- probnb(interv = intervalo, media = pred2[i], shape = ajustenb3$theta)
+pbarra <- colMeans(matprob)
+frebnaj <- round(n*pbarra)
+ams <- c(table(dados$Sinistros), rep(0,5))
+matfreq <- rbind(ams, freqps, freqpsaj, freqbn, frebnaj)
+colnames(matfreq) <- 0:10
+rownames(matfreq) <- c('Amostra', 'Poisson não ajustada por covariáveis', 'Poisson ajustada por covariáveis',
+ 'BN não ajustada por covariáveis', 'BN ajustada por covariáveis')
+```
+
+
+### Frequências amostrais e frequências ajustadas pelas distribuições Poisson e Binomial Negativa (sem e com inclusão de covariáveis)
+
+```{r, results = 'markup'}
+kable(matfreq, format = "markdown", caption = "Frequências amostrais e freuências ajustadas para o número de sinistros")
+```
+
+
+
+
+
+
+
+
+
+
+
--
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