Data standardization in Bayesian Model Averaging?

Dear all Bugs user,
Recently I am looking into the relationship between Shark's fin length (fl) and regions, group, sex by using BMA. See my two Winbugs files below, 18 different models were built up. One used the original data, one used standardized data. The one used original data has the totally different results from the one with standardized data has. Which one is more proper? I found many examples standardized their data, but I have no clue why? Really appreciate any one to help me solve this puzzle.

#### Original data

model

{

for(i in 1:M) {

fl[i] ~ dnorm(mu[i],tau)

mu[i] <- a1 + Ind.group*a2*group[i] + Ind.sex*a3*sex[i] + Ind.region*a4*region[i] + Ind.groupbysex*a5*group[i]*sex[i] + Ind.groupbyregion*a6*group[i]*region[i] + Ind.sexbyregion*a7*sex[i]*region[i]

}

tau~dgamma(1,1)

tau.constant<- 1.0E-6

tau.group <- 1.0E-6+(Ind.group*1.0E-5)

tau.sex<-1.0E-6+(Ind.sex*1.0E-5)

tau.region<- 1.0E-6+(Ind.region*1.0E-5)

tau.group.sex <-1.0E-6+(Ind.groupbysex*1.0E-5)

tau.group.region<- 1.0E-6+(Ind.groupbyregion*1.0E-5)

tau.sex.region <-1.0E-6+(Ind.sexbyregion*1.0E-5)

a1 ~ dnorm(0, tau.constant)

a2~ dnorm(0, tau.group)

a3~ dnorm(0, tau.sex)

a4 ~ dnorm(0, tau.region)

a5~ dnorm(0, tau.group.sex)

a6~ dnorm(0, tau.group.region)

a7~ dnorm(0, tau.sex.region)

Model ~ dcat(p[])

for (i in 1:18)

{

p[i]<- 1/18

Ind.Model[i]<-equals(Model,i)

}

Ind.group<-equals(Model,2)+equals(Model,5)+equals(Model,6)+equals(Model,8)+equals(Model,9)+equals(Model,10)+step(Model-11.5)

Ind.sex<-equals(Model,3)+equals(Model,5)+equals(Model,7)+equals(Model,8)+equals(Model,9)+step(Model-10.5)

Ind.region<-equals(Model,4)+equals(Model,6)+equals(Model,7)+equals(Model,8)+step(Model-9.5)

Ind.groupbysex<-equals(Model,9)+equals(Model,12)+equals(Model,15)+equals(Model,16)+equals(Model,18)

Ind.groupbyregion<-equals(Model,10)+equals(Model,13)+equals(Model,15)+equals(Model,17)+equals(Model,18)

Ind.sexbyregion<-equals(Model,11)+equals(Model,14)+step(Model-15.5)

}

Data click on one of the arrows to open the data

Initial values

list(tau=1, Model=1)

#`Results

node mean sd MC error 2.5% median 97.5% start sample

Ind.Model[1] 0.0 0.0 7.001E-13 0.0 0.0 0.0 5001 20400

Ind.Model[2] 0.0 0.0 7.001E-13 0.0 0.0 0.0 5001 20400

Ind.Model[3] 0.0 0.0 7.001E-13 0.0 0.0 0.0 5001 20400

Ind.Model[4] 0.0 0.0 7.001E-13 0.0 0.0 0.0 5001 20400

Ind.Model[5] 0.0 0.0 7.001E-13 0.0 0.0 0.0 5001 20400

Ind.Model[6] 0.0 0.0 7.001E-13 0.0 0.0 0.0 5001 20400

Ind.Model[7] 0.0 0.0 7.001E-13 0.0 0.0 0.0 5001 20400

Ind.Model[8] 0.004559 0.06736 0.002203 0.0 0.0 0.0 5001 20400

Ind.Model[9] 0.0 0.0 7.001E-13 0.0 0.0 0.0 5001 20400

Ind.Model[10] 0.0 0.0 7.001E-13 0.0 0.0 0.0 5001 20400

Ind.Model[11] 0.0 0.0 7.001E-13 0.0 0.0 0.0 5001 20400

Ind.Model[12] 0.0 0.0 7.001E-13 0.0 0.0 0.0 5001 20400

Ind.Model[13] 0.8742 0.3316 0.01016 0.0 1.0 1.0 5001 20400

Ind.Model[14] 0.003039 0.05505 0.001531 0.0 0.0 0.0 5001 20400

Ind.Model[15] 0.05559 0.2291 0.006856 0.0 0.0 1.0 5001 20400

Ind.Model[16] 1.961E-4 0.014 1.541E-4 0.0 0.0 0.0 5001 20400

Ind.Model[17] 0.0602 0.2378 0.007913 0.0 0.0 1.0 5001 20400

Ind.Model[18] 0.002206 0.04691 6.672E-4 0.0 0.0 0.0 5001 20400

###Standardized data

model

{

mean.group<-mean(group[1:1153])

mean.sex<- mean(sex[1:1153])

mean.region<- mean(region[1:1153])

mean.groupsex<-mean(groupsex[1:1153])

mean.groupregion<-mean(groupregion[1:1153])

mean.sexregion<-mean(sexregion[1:1153])

sd.group<-sd(group[1:1153])

sd.sex<-sd(sex[1:1153])

sd.region<- sd(region[1:1153])

sd.groupsex<-sd(groupsex[1:1153])

sd.groupregion<-sd(groupregion[1:1153])

sd.sexregion<-sd(sexregion[1:1153])

for(i in 1:M) {

groupregion[i]<-group[i]*region[i]

groupsex[i]<-group[i]*sex[i]

sexregion[i]<-sex[i]*region[i]

G[i]<-(group[i]-mean.group)/sd.group

S[i]<-(group[i]-mean.sex)/sd.sex

R[i]<-(region[i]-mean.region)/sd.region

GS[i]<-(groupsex[i]-mean.groupsex)/sd.groupsex

GR[i]<-(groupregion[i]-mean.groupregion)/sd.groupregion

SR[i]<-(sexregion[i]-mean.sexregion)/sd.sexregion

}

for(i in 1:M) {

fl[i] ~ dnorm(mu[i],tau)

mu[i] <- a1 + Ind.group*a2*G[i] + Ind.sex*a3*S[i] + Ind.region*a4*R[i] + Ind.groupbysex*a5*GS[i] + Ind.groupbyregion*a6*GR[i] + Ind.sexbyregion*a7*SR[i]

}

tau~dgamma(1,1)

tau.constant<- 1.0E-6

tau.group <- 1.0E-6+(Ind.group*1.0E-5)

tau.sex<-1.0E-6+(Ind.sex*1.0E-5)

tau.region<- 1.0E-6+(Ind.region*1.0E-5)

tau.group.sex <-1.0E-6+(Ind.groupbysex*1.0E-5)

tau.group.region<- 1.0E-6+(Ind.groupbyregion*1.0E-5)

tau.sex.region <-1.0E-6+(Ind.sexbyregion*1.0E-5)

a1 ~ dnorm(0, tau.constant)

a2~ dnorm(0, tau.group)

a3~ dnorm(0, tau.sex)

a4 ~ dnorm(0, tau.region)

a5~ dnorm(0, tau.group.sex)

a6~ dnorm(0, tau.group.region)

a7~ dnorm(0, tau.sex.region)

Model ~ dcat(p[])

for (i in 1:18)

{

p[i]<- 1/18

Ind.Model[i]<-equals(Model,i)

}

Ind.group<-equals(Model,2)+equals(Model,5)+equals(Model,6)+equals(Model,8)+equals(Model,9)+equals(Model,10)+step(Model-11.5)

Ind.sex<-equals(Model,3)+equals(Model,5)+equals(Model,7)+equals(Model,8)+equals(Model,9)+step(Model-10.5)

Ind.region<-equals(Model,4)+equals(Model,6)+equals(Model,7)+equals(Model,8)+step(Model-9.5)

Ind.groupbysex<-equals(Model,9)+equals(Model,12)+equals(Model,15)+equals(Model,16)+equals(Model,18)

Ind.groupbyregion<-equals(Model,10)+equals(Model,13)+equals(Model,15)+equals(Model,17)+equals(Model,18)

Ind.sexbyregion<-equals(Model,11)+equals(Model,14)+step(Model-15.5)

}

Data click on one of the arrows to open the data

Initial values

list(tau=1, Model=1)

#`Results

node mean sd MC error 2.5% median 97.5% start sample

Ind.Model[1] 0.0 0.0 5.164E-14 0.0 0.0 0.0 15001 750000

Ind.Model[2] 0.0 0.0 5.164E-14 0.0 0.0 0.0 15001 750000

Ind.Model[3] 0.0 0.0 5.164E-14 0.0 0.0 0.0 15001 750000

Ind.Model[4] 0.0 0.0 5.164E-14 0.0 0.0 0.0 15001 750000

Ind.Model[5] 0.0 0.0 5.164E-14 0.0 0.0 0.0 15001 750000

Ind.Model[6] 0.0 0.0 5.164E-14 0.0 0.0 0.0 15001 750000

Ind.Model[7] 0.0 0.0 5.164E-14 0.0 0.0 0.0 15001 750000

Ind.Model[8] 0.0 0.0 5.164E-14 0.0 0.0 0.0 15001 750000

Ind.Model[9] 0.0 0.0 5.164E-14 0.0 0.0 0.0 15001 750000

Ind.Model[10] 0.0 0.0 5.164E-14 0.0 0.0 0.0 15001 750000

Ind.Model[11] 0.0 0.0 5.164E-14 0.0 0.0 0.0 15001 750000

Ind.Model[12] 0.0 0.0 5.164E-14 0.0 0.0 0.0 15001 750000

Ind.Model[13] 0.0 0.0 5.164E-14 0.0 0.0 0.0 15001 750000

Ind.Model[14] 0.0 0.0 5.164E-14 0.0 0.0 0.0 15001 750000

Ind.Model[15] 0.0 0.0 5.164E-14 0.0 0.0 0.0 15001 750000

Ind.Model[16] 0.007037 0.08359 0.001292 0.0 0.0 0.0 15001 750000

Ind.Model[17] 0.0 0.0 5.164E-14 0.0 0.0 0.0 15001 750000

Ind.Model[18] 0.993 0.08359 0.001292 1.0 1.0 1.0 15001 750000

___________________________

Guojing YANG
Research Fellow
Wildlife & Landscape Sciences Theme
School for Environmental Research
Charles Darwin University
Darwin NT 0909
Ph: (08) 8946 6646
Fax: (08) 8946 7720

http://www.cdu.edu.au/ser/GuojingYangProfile.htm

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