#
#  Cap. 1 - Pinheiro e Bates
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#  Exemplo Rail - Se??o 1.1
#
 require(nlme)
 Rail
 names(Rail)
 class(Rail$Rail)
 class(Rail$travel)
 plot(Rail$travel, Rail$Rail, xlab="tempo", ylab="trilho")
 boxplot(Rail$travel~Rail$Rail)
# Ignorando os Trilhos
 summary(Rail$Rail)
 summary(Rail$travel)
 sd(Rail$travel)
 fm1rail.lm<-lm(travel~1,data=Rail)
 summary(fm1rail.lm)
 boxplot(fm1rail.lm$residuals~Rail$Rail)
 plot(fm1rail.lm)
#  Fixed Effect Model with Rail
#   Anova convencional
 summary(aov(travel~Rail, data=Rail))
 plot(aov(travel~Rail, data=Rail))
# 
#   X é o efeito de cada trilho 
 summary(lm(travel~Rail -1,data=Rail))
 plot(lm(travel~Rail -1,data=Rail))
#
#   X é com intercepto (efeito do trilho 1)  
 Rail$Rail1<-factor(Rail$Rail, ordered=F)
 summary(lm(travel~Rail1,data=Rail))
 plot(lm(travel~Rail1,data=Rail))
#
#   X é com componentes ortogonais
#     os componentes n?o tem interpreta??o pois os n?veis n?o s?o ordenados
 summary(lm(travel~Rail,data=Rail))
 plot(lm(travel~Rail -1,data=Rail))
# 
#  Random Effect Model
  fm1Rail.lme<-lme(travel ~ 1, data=Rail, random= ~1|Rail)
  summary(fm1Rail.lme)
  plot(fm1Rail.lme)
  intervals(fm1Rail.lme)
#
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