####################
# Bowling (Katie Schomaker) problem:  2 logistic regressions for improvement
#   game1->2 and game 2->3
# Solution to 2011 PubH 7440 Midterm 1, 2/22/11
####################


model{   
	  for(j in 1:W) {
          for (i in 1:3) {useless[i,j] <- Y[i,j]}   #  trick to avoid deleting Y from the data list
          Z1[j] ~ dbern( p1[j] )
          Z2[j] ~ dbern( p2[j] )

#   centered logit models;   E(PP[1]) = .95, E(PP[2]) = .81
        logit(p1[j]) <- beta0[1] + beta1[1]*(week[j]-mean(week[]))    #  pD = 2.0, DIC = 20.2
        logit(p2[j]) <- beta0[2] + beta1[2]*(week[j]-mean(week[]))    #  pD = 2.1, DIC = 22.7

	    }  # end of j loop

	  for (i in 1:2){
          PP[i] <- 1-step(beta1[i])
          beta0[i] ~ dflat()
 	    beta1[i] ~ dflat()
          }   
	
	}  #  end of WinBUGS code

## data:
list(week = c(1,2,3,4,5,6,7,8,9,10,11,12,13,14), W =14, 
            Z1 = c(1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0),
            Z2 = c(0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0),
		Y = structure(.Data =  c(85, 78, 64, 94, 87,110,122,100,110,123,105,112,103,140,
             136,142, 87,129,113, 65,110,103, 92,133,118, 94,132,125,
              92,127,136,149,119,148,120,159,127,121,117,153,118,108), .Dim = c(3,14)))
        
## inits:
list(beta0 = c(-5,-5), beta1 = c(-5,-5))
list(beta0 = c(0,0), beta1 = c(0,0))
list(beta0 = c(5,5), beta1 = c(5,5))