fh_hetop {HETOP}

Fit Fay-Herriot Heteroskedastic Ordered Probit (FH-HETOP) Model using JAGS

Description

Fits the FH-HETOP model described by Lockwood, Castellano and Shear (2018) using the jags function in R2jags.

Usage

fh_hetop(ngk, fixedcuts, p, m, gridL, gridU, Xm=NULL, Xs=NULL,
seed=12345, modelfileonly = FALSE, modloc=NULL, ...)

Arguments

ngk

Numeric matrix of dimension G x K in which column k of row g indicates the number of units from group g falling into category k.

fixedcuts

A vector of length 2 providing the first two cutpoints, to identify the location and scale of the group parameters. Note that this suffices for any K >= 3.

p

Vector of length 2 giving degrees of freedom for cubic spline basis to parameterize Efron priors for group means and group standard deviations; see References.

m

Vector of length 2 giving number of grid points to parameterize Efron priors for group means and group standard deviations; see References.

gridL

Vector of length 2 of lower bounds for grids to parameterize Efron priors for group means and group standard deviations; see References.

gridU

Vector of length 2 of upper bounds for grids to parameterize Efron priors for group means and group standard deviations; see References.

Xm

Optional matrix of covariates for the group means.

Xs

Optional matrix of covariates for the log group standard deviations.

seed

Passed to set.seed.

modelfileonly

If TRUE, function returns location of JAGS model file only, without running JAGS. Default is FALSE.

modloc

Optional character vector of length 1 providing the full path to the name of file where the JAGS model code will be written. Defaults to NULL, in which case the code will be written to a temporary file.

...

Additional arguments to jags.

Details

The function is basically a wrapper for jags, building model code depending on the specification of the Efron priors and any covariates for the group means and group standard deviations. Details on the FH-HETOP model are provided by Lockwood, Castellano and Shear (2018).

Covariates to predict the group means and group log standard deviations are optional. However, Xm and Xs must both be either NULL, or specified; the current version of this function cannot use covariates to predict one set of parameters but not use any covariates to predict the other set. While covariates in general must be present or absent simultaneously for the two sets of parameters, it is not necessary that the same covariates be used to predict the two sets of parameters. All covariates must be centered so that they sum to zero across groups.

Value

A object of class rjags, with additional information specific to the FH-HETOP model. The additional information is stored as a list called fh_hetop_extras with the following components:

Finfo

A list containing information used to estimate the population distribution of the residuals from the FH-HETOP model. Note that the posterior samples of the parameters defining the residual distribution can be found in the BUGSoutput element of the returned object.

Dinfo

A list containing information about the data used to the fit the model, including the counts, covariates and fixed cutpoints.

waicinfo

A list containing information about the WAIC for the estimated model; see help file for waic_hetop.

est_star_samps

A list with posterior samples of parameters with respect to the 'star' scale which defines the location and scale of the group means and standard deviations that corresponds to a marginal population mean of zero and marginal population standard deviation of 1. Additional details in help file for mle_hetop

est_star_mug

A dataframe containing various estimates of the group means on the 'star' scale, including posterior means, Constrained Bayes and Triple-Goal estimates. Additional details in help file for triple_goal.

est_star_sigmag

A dataframe containing various estimates of the group standard deviations on the 'star' scale, including posterior means, Constrained Bayes and Triple-Goal estimates. Additional details in help file for triple_goal.

Author(s)

J.R. Lockwood [e-mail]

References

Efron B. (2016). “Empirical Bayes deconvolution estimates,” Biometrika 103(1):1–20.

Lockwood J.R., Castellano K.E. and Shear B.R. (2018). “Flexible Bayesian models for inferences from coarsened, group-level achievement data,” Journal of Educational and Behavioral Statistics. 43(6):663–692.

See Also

jags

Examples

set.seed(1001)

## define mean-centered covariates
G  <- 12
z1 <- sample(c(0,1), size=G, replace=TRUE)
z2 <- 0.5*z1 + rnorm(G)
Z  <- cbind(z1 - mean(z1), z2 = z2 - mean(z2))

## define true parameters dependent on covariates
beta_m    <- c(0.3,  0.8)
beta_s    <- c(0.1, -0.1)
mug       <- Z[,1]*beta_m[1] + Z[,2]*beta_m[2] + rnorm(G, sd=0.3)
sigmag    <- exp(0.3 + Z[,1]*beta_s[1] + Z[,2]*beta_s[2] + 0.2*rt(G, df=7))
cutpoints <- c(-1.0, 0.0, 1.2)

## generate data
ng   <- rep(200,G)
ngk  <- gendata_hetop(G, K = 4, ng, mug, sigmag, cutpoints)
print(ngk)

## fit FH-HETOP model including covariates
## NOTE: using an extremely small number of iterations for testing,
##       so that convergence is not expected
m <- fh_hetop(ngk, fixedcuts = c(-1.0, 0.0), p = c(10,10),
              m = c(100, 100), gridL = c(-5.0, log(0.10)),
              gridU = c(5.0, log(5.0)), Xm = Z, Xs = Z,
              n.iter = 100, n.burnin = 50)

print(m)
print(names(m$fh_hetop_extras))

s <- m$BUGSoutput$summary
print(data.frame(truth = c(beta_m, beta_s), s[grep("beta", rownames(s)),]))

print(cor(mug,    s[grep("mu",    rownames(s)),"mean"]))
print(cor(sigmag, s[grep("sigma", rownames(s)),"mean"]))

## manual calculation of WAIC (see help file for waic_hetop)
tmp <- waic_hetop(ngk, m$BUGSoutput$sims.matrix)
identical(tmp, m$fh_hetop_extras$waicinfo)