Request for factorial ANOVA with generated means and sds about example-models

[bob-carpenter]

Is there a pointer to the JAGS model you're trying to translate? Or a definition of the prior and likelihood?

[wdonald1985]

Here is the model. When using RSTAN, I can get a linear model with factors to run properly. What I cant get, however, is estimates for all means through using the coefficients to generate quantities. Additionally, this model generates standard deviations for each group. I think the problem is in k-1 coding systems for categorical variables.

modelstring = "
model {
for ( i in 1:Ntotal ) {
y[i] ~ dt( mu[i] , 1/(ySigma[x1[i],x2[i]])^2 , nu )
mu[i] <- a0 + a1[x1[i]] + a2[x2[i]] + a1a2[x1[i],x2[i]]
}
# nu ~ dgamma(5.83,0.0483) # mode 100, sd 50
nu ~ dexp(1/30.0)
#
for ( j1 in 1:Nx1Lvl ) { for ( j2 in 1:Nx2Lvl ) {
sigma[j1,j2] ~ dgamma( sigmaSh , sigmaRa )
# Prevent from dropping too close to zero:
ySigma[j1,j2] <- max( sigma[j1,j2] , medianCellSD/1000 )
} }
sigmaSh <- 1 + sigmaMode * sigmaRa
sigmaRa <- ( sigmaMode + sqrt( sigmaMode^2 + 4_sigmaSD^2 ) ) /(2_sigmaSD^2)
sigmaMode ~ dgamma(sGammaShRa[1],sGammaShRa[2])
sigmaSD ~ dgamma(sGammaShRa[1],sGammaShRa[2])
#
a0 ~ dnorm( yMean , 1/(ySD*5)^2 )
#
for ( j1 in 1:Nx1Lvl ) { a1[j1] ~ dnorm( 0.0 , 1/a1SD^2 ) }
a1SD ~ dgamma(aGammaShRa[1],aGammaShRa[2])
#
for ( j2 in 1:Nx2Lvl ) { a2[j2] ~ dnorm( 0.0 , 1/a2SD^2 ) }
a2SD ~ dgamma(aGammaShRa[1],aGammaShRa[2])
#
for ( j1 in 1:Nx1Lvl ) { for ( j2 in 1:Nx2Lvl ) {
a1a2[j1,j2] ~ dnorm( 0.0 , 1/a1a2SD^2 )
} }
a1a2SD ~ dgamma(aGammaShRa[1],aGammaShRa[2]) # or try a folded t (Cauchy)
# Convert a0,a1[],a2[],a1a2[,] to sum-to-zero b0,b1[],b2[],b1b2[,] :
for ( j1 in 1:Nx1Lvl ) { for ( j2 in 1:Nx2Lvl ) {
m[j1,j2] <- a0 + a1[j1] + a2[j2] + a1a2[j1,j2] # cell means
} }
b0 <- mean( m[1:Nx1Lvl,1:Nx2Lvl] )
for ( j1 in 1:Nx1Lvl ) { b1[j1] <- mean( m[j1,1:Nx2Lvl] ) - b0 }
for ( j2 in 1:Nx2Lvl ) { b2[j2] <- mean( m[1:Nx1Lvl,j2] ) - b0 }
for ( j1 in 1:Nx1Lvl ) { for ( j2 in 1:Nx2Lvl ) {
b1b2[j1,j2] <- m[j1,j2] - ( b0 + b1[j1] + b2[j2] )
} }
} (Kruschke, 2015)

[andrewgelman]

Hi, you should include the Stan model, not the Bugs model!
A

On Apr 9, 2016, at 6:19 PM, wdonald1985 [email protected] wrote:

Here is the model. When using RSTAN, I can get a linear model with factors to run properly. What I cant get, however, is estimates for all means through using the coefficients to generate quantities. Additionally, this model generates standard deviations for each group. I think the problem is in k-1 coding systems for categorical variables.

modelstring = "
model {
for ( i in 1:Ntotal ) {
y[i] ~ dt( mu[i] , 1/(ySigma[x1[i],x2[i]])^2 , nu )
mu[i] <- a0 + a1[x1[i]] + a2[x2[i]] + a1a2[x1[i],x2[i]]
}

nu ~ dgamma(5.83,0.0483) # mode 100, sd 50

nu ~ dexp(1/30.0)

for ( j1 in 1:Nx1Lvl ) { for ( j2 in 1:Nx2Lvl ) {
sigma[j1,j2] ~ dgamma( sigmaSh , sigmaRa )

Prevent from dropping too close to zero:

ySigma[j1,j2] <- max( sigma[j1,j2] , medianCellSD/1000 )
} }
sigmaSh <- 1 + sigmaMode * sigmaRa
sigmaRa <- ( sigmaMode + sqrt( sigmaMode^2 + 4sigmaSD^2 ) ) /(2sigmaSD^2)
sigmaMode ~ dgamma(sGammaShRa[1],sGammaShRa[2])
sigmaSD ~ dgamma(sGammaShRa[1],sGammaShRa[2])

a0 ~ dnorm( yMean , 1/(ySD*5)^2 )

for ( j1 in 1:Nx1Lvl ) { a1[j1] ~ dnorm( 0.0 , 1/a1SD^2 ) }
a1SD ~ dgamma(aGammaShRa[1],aGammaShRa[2])

for ( j2 in 1:Nx2Lvl ) { a2[j2] ~ dnorm( 0.0 , 1/a2SD^2 ) }
a2SD ~ dgamma(aGammaShRa[1],aGammaShRa[2])

for ( j1 in 1:Nx1Lvl ) { for ( j2 in 1:Nx2Lvl ) {
a1a2[j1,j2] ~ dnorm( 0.0 , 1/a1a2SD^2 )
} }
a1a2SD ~ dgamma(aGammaShRa[1],aGammaShRa[2]) # or try a folded t (Cauchy)

Convert a0,a1[],a2[],a1a2[,] to sum-to-zero b0,b1[],b2[],b1b2[,] :

for ( j1 in 1:Nx1Lvl ) { for ( j2 in 1:Nx2Lvl ) {
m[j1,j2] <- a0 + a1[j1] + a2[j2] + a1a2[j1,j2] # cell means
} }
b0 <- mean( m[1:Nx1Lvl,1:Nx2Lvl] )
for ( j1 in 1:Nx1Lvl ) { b1[j1] <- mean( m[j1,1:Nx2Lvl] ) - b0 }
for ( j2 in 1:Nx2Lvl ) { b2[j2] <- mean( m[1:Nx1Lvl,j2] ) - b0 }
for ( j1 in 1:Nx1Lvl ) { for ( j2 in 1:Nx2Lvl ) {
b1b2[j1,j2] <- m[j1,j2] - ( b0 + b1[j1] + b2[j2] )

} }
} (Kruschke, 2015)

—
You are receiving this because you are subscribed to this thread.
Reply to this email directly or view it on GitHub #61 (comment)

[bob-carpenter]

Is that the right attached program? I don't see
any categorical variables.

Consistent indentation on code makes it much easier
to read. I may just be missing something.

• Bob

On Apr 9, 2016, at 6:19 PM, wdonald1985 [email protected] wrote:

Here is the model. When using RSTAN, I can get a linear model with factors to run properly. What I cant get, however, is estimates for all means through using the coefficients to generate quantities. Additionally, this model generates standard deviations for each group. I think the problem is in k-1 coding systems for categorical variables.

modelstring = "
model {
for ( i in 1:Ntotal ) {
y[i] ~ dt( mu[i] , 1/(ySigma[x1[i],x2[i]])^2 , nu )
mu[i] <- a0 + a1[x1[i]] + a2[x2[i]] + a1a2[x1[i],x2[i]]
}

nu ~ dgamma(5.83,0.0483) # mode 100, sd 50

nu ~ dexp(1/30.0)

for ( j1 in 1:Nx1Lvl ) { for ( j2 in 1:Nx2Lvl ) {
sigma[j1,j2] ~ dgamma( sigmaSh , sigmaRa )

Prevent from dropping too close to zero:

ySigma[j1,j2] <- max( sigma[j1,j2] , medianCellSD/1000 )
} }
sigmaSh <- 1 + sigmaMode * sigmaRa
sigmaRa <- ( sigmaMode + sqrt( sigmaMode^2 + 4sigmaSD^2 ) ) /(2sigmaSD^2)
sigmaMode ~ dgamma(sGammaShRa[1],sGammaShRa[2])
sigmaSD ~ dgamma(sGammaShRa[1],sGammaShRa[2])

a0 ~ dnorm( yMean , 1/(ySD*5)^2 )

for ( j1 in 1:Nx1Lvl ) { a1[j1] ~ dnorm( 0.0 , 1/a1SD^2 ) }
a1SD ~ dgamma(aGammaShRa[1],aGammaShRa[2])

for ( j2 in 1:Nx2Lvl ) { a2[j2] ~ dnorm( 0.0 , 1/a2SD^2 ) }
a2SD ~ dgamma(aGammaShRa[1],aGammaShRa[2])

for ( j1 in 1:Nx1Lvl ) { for ( j2 in 1:Nx2Lvl ) {
a1a2[j1,j2] ~ dnorm( 0.0 , 1/a1a2SD^2 )
} }
a1a2SD ~ dgamma(aGammaShRa[1],aGammaShRa[2]) # or try a folded t (Cauchy)

Convert a0,a1[],a2[],a1a2[,] to sum-to-zero b0,b1[],b2[],b1b2[,] :

for ( j1 in 1:Nx1Lvl ) { for ( j2 in 1:Nx2Lvl ) {
m[j1,j2] <- a0 + a1[j1] + a2[j2] + a1a2[j1,j2] # cell means
} }
b0 <- mean( m[1:Nx1Lvl,1:Nx2Lvl] )
for ( j1 in 1:Nx1Lvl ) { b1[j1] <- mean( m[j1,1:Nx2Lvl] ) - b0 }
for ( j2 in 1:Nx2Lvl ) { b2[j2] <- mean( m[1:Nx1Lvl,j2] ) - b0 }
for ( j1 in 1:Nx1Lvl ) { for ( j2 in 1:Nx2Lvl ) {
b1b2[j1,j2] <- m[j1,j2] - ( b0 + b1[j1] + b2[j2] )

} }
} (Kruschke, 2015)

—
You are receiving this because you commented.
Reply to this email directly or view it on GitHub

[wdonald1985]

Through trial and many errors my RSTAN model is not looking very good. I'll post it after I clean it up a bit. Thanks!

[bob-carpenter]

Was there a JAGS model you're trying to translate? The one you sent
didn't have any categorical variables I could find.

• Bob

P.S. I'd strongly recommend version control to recover clean old versions
of things. Where possible, I'd also recommend starting with the simplest
thing that works and building out rather than trying to build a complicated
model all at once.

On Apr 10, 2016, at 1:38 PM, wdonald1985 [email protected] wrote:

Through trial and many errors my RSTAN model is not looking very good. I'll post it after I clean it up a bit. Thanks!

—
You are receiving this because you commented.
Reply to this email directly or view it on GitHub

[wdonald1985]

Hello:
Apologies on taking so long to provide the script to my model. Since you are both very well know statisticians, I wanted to ensure my code was up to par. This is a 3 * 2 interaction with categorical predictors. Since I am only getting one estimate for sigma, I think my model is assuming homogeneous variances. I want a model that does not make this assumption, thereby providing 6 estimates for sigma. Additionally, I would like a way to get the lower level estimates, for example, estimates for VS and GEAR without having to build another model.

myData <- mtcars
X <- model.matrix(~ vs * gear, data = myData)
K <- 6 // number of columns in matrix
N <- length(mtcars$mpg)
standat= list(X = X,K =K, N =N, y =y)
stanmodelcode = '
data {
int<lower=0> N;
vector[N] y;
int<lower=0> K;
matrix [N, K]X ;
}
parameters {
real <lower =0> sigma;
vector [K] beta;
}
transformed parameters {
}
model {
y ~ normal(X * beta, sigma);
}
generated quantities {
real mu0_3;
real mu1_3;
real mu0_4;
real mu1_4;
real mu0_5;
real mu1_5;
mu0_3 <- beta[1];
mu1_3 <- beta[1] + beta[2];
mu0_4 <- beta[1] + beta[3];
mu1_4 <- beta[1] + beta[2] + beta[3] + beta[5];
mu0_5 <- beta[1] + beta [4];
mu1_5 <- beta[1] + beta[2] + beta[4] + beta[6];
}
'
fit = stan(model_code=stanmodelcode, data=standat, iter=1200, warmup=10, seed = 1,
chains=2, thin=2)