m11.5 _ m11.6

Book<- read_excel("X:/StatisticsPlatform/Website/ELearning/Workshops/Bayesian Analysis/Data/Book1.xlsx")
d<-Book%>%dplyr::select(block,ADG,BW_start,Country)
d$bl<-d$block
table(d$Country, d$bl)
d$block<-NULL
d<-d[complete.cases(d), ]
d$Country<-as.factor(d$Country)
dim(d)
head(d)
fit<-glm(bl~ ADG + BW_start + Country, 
         data=d, 
         family="poisson",x=TRUE, y=TRUE)
summary(fit)

m11.5 <- ulam(
  alist(
    bl ~ dpois(lambda) ,
    log(lambda) <- a + b*ADG +c*BW_start + d[Country] ,
    a            ~ dnorm( 4     , 0.3 ),
    b            ~ dnorm( 0.01  , 0.005 ),
    c            ~ dnorm( 0.1   , 0.01 ),
    d[Country]   ~ dnorm( 0.5   , 0.05 )
  ) , data=d, chains=4, cores=4,log_lik=TRUE)
show(m11.5)
precis(m11.5 , 2 )
pairs(m11.5 )
traceplot(m11.5)
trankplot(m11.5 )

fit<-glm.nb(bl~ ADG + BW_start + Country, 
         data=d, model=TRUE,x=TRUE, y=TRUE)
summary(fit)

m11.6 <- ulam(
  alist(
    bl ~ dgampois(mu, exp(log_scale)),
    log(mu) <- a + b*ADG +c*BW_start + d[Country] ,
    a            ~ dnorm( 4     , 0.3   ),
    b            ~ dnorm( 0.01  , 0.005 ),
    c            ~ dnorm( 0.1   , 0.01  ),
    d[Country]   ~ dnorm( 0.5   , 0.05  ),
    log_scale    ~ dnorm( 3     , 0.5   )
  ) , data=d, chains=4, cores=4,log_lik=TRUE)
show(m11.6)
precis(m11.6 , 2 )
pairs(m11.6 )
traceplot(m11.6)
trankplot(m11.6 )

rethinking::compare( m11.5 , m11.6 , func=PSIS )
k <- PSIS( m11.6 , pointwise=TRUE )$k
xyplot(as.factor(bl)~ADG | Country, data=d, 
      xlab="log ADG" , 
      ylab="total blocks" ,
      col=rangi2 , lwd=2 ,
      ylim=c(0,75) , cex=1+normalize(k) )