dpgrow: Bayesian semiparametric growth curve models.

Description

Employs a Dirichlet Process (DP) prior on the set of by-subject random effect parameters under repeated waves of measurements to allow the number of random effect parameters specified per subject, q, to be equal to the number of measurement waves, T. Random effects are grouped by subject and all q parameters receive the DP prior. The resulting joint marginal distribution over the data is a DP mixture.

Usage

dpgrow(y, subject, trt, time, n.random, n.fix_degree,
    formula, random.only, data, n.iter, n.burn, n.thin,
    shape.dp, rate.dp, plot.out, option)

Arguments

A univariate continuous response, specified as an N x 1 matrix or vector, where N captures the number of subject-time cases (repeated subject measures). Data may reflect unequal number of measures per subject. Missing o

subject

The objects on which repeated measures are conducted that serves as the random effects grouping factor. Input as an N x 1 matrix or vector of subject-measure cases in either integer or character formt; e.g. (1,1,1,2,2,3,3,3,...

trt

An integer or character matrix/vector of length N (number of cases) indicating treatment group assignments for each case. May also be input as length P vector, where P is the number of unique subjects, i

time

A univariate vector of length N, capturing the time points associated to each by-subject measure. Mav leave blank if only one time point (no repeated measures).

n.random

The desired number of subject random effect terms, q. Under option = "dp" may be set equal to the number of measurement waves, T. The y, trt, time vectors will together be used to create bo

n.fix_degree

The desired polynomial order in time to use for generating time-based fix effects. The fixed effects matrix will be constructed as,

(time, ...,
  time^(n.fix_degree), trt_1,time*trt_1, ...
  ,time^(n.fix_degree)*trt_l, trt_L,...,
  time^(n

formula

Nuisance fixed and random effects may be entered in formula with the following format, y ~ x_1 + x_2*x_3 | z_1*z_2 as an object of class formula. The bar, |, separates fixed and random effec

random.only

A Boolean variable indicating whether the input formula contains random (for fixed) effects in the case that only one set are entered. If excluded and formula is entered without a |, random.only defaults

data

a data.frame containing the variables with names as specified in formula, including the response, y.

n.iter

Total number of MCMC iterations.

n.burn

Number of MCMC iterations to discard. dpgrow will return (n.iter - n.burn) posterior samples.

n.thin

Gap between successive sampling iterations to save.

shape.dp

Shape parameter under a c ~ G(shape.dp, 1) prior on the concentration parameter of the DP (prior on the set of random effects parameters, b_1, ..., b_n ~ DP(c,G_0) where n is the total number of subjects.

rate.dp

Rate parameter under a c ~ G(shape.dp, rate.dp) prior on the concentration parameter of the DP.

plot.out

A boolean variable indicating whether user wants to return plots with output results. Defaults to TRUE.

option

Modeling option, of which there are two: 1. dp places a DP prior on the set of subject random effects; 2. lgm places the usual independent Gaussian priors on the set of random effects.

Value

S3 dpgrow object, for which many methods are available to return and view results. Generic functions applied to an object, res of class dpgrow, includes:
summary(res)returns call, the function call made to dpgrow and summary.results, which contains a list of objects that include 95% credible intervals for each set of sampled parameters, specified as (2.5%, mean, 97.5%, including fixed and random effects. Also contains model fit statistics, including DIC (and associated Dbar, Dhat, pD, pV), as well as the log pseudo marginal likelihood (LPML), a leave-one-out fit statistic. Note that for option = "dp", DIC is constructed as DIC3 (see Celeaux et. al. 2006), where the conditional likehihood evaluated at the posterior mode is replaced by the marginal predictive density. Lastly, the random and fixed effects design matrices, X, Z, are returned that include both the user input nuisance covariates appended to the time and treatment-based covariates constructed by dpgrow.
print(summary(res))prints contents of summary to console.
plot(res)returns results plots, including the set of subject random effects values and credible intervals, a sample of by-subject growth curves, mean growth curves split by each treatment and control, as well as selected trace plots for number of clusters and for precision parameters for the likehilood and random effects. Lastly, a trace plot for the deviance statistic is also included.
samples(res)contains (n.iter - n.burn) posterior sampling iterations for every model parameter, including fixed and random effects.
resid(res)contains the model residuals.

References

S. M. Paddock and T. D. Savitsky (2012) Bayesian Hierarchical Semiparametric Modeling of Longitudinal Post-treatment Outcomes from Open-enrollment Therapy Groups, submitted to: JRSS Series A (Statistics in Society). T. D. Savitsky and S. M. Paddock (2011) Visual Sufficient Statistics for Repeated Measures data with growcurves for R, submitted to: Journal of Statistical Software.

Examples

Run this code

## extract simulated dataset
library(growcurves)
data(datsim)
## attach(datsim)
## run dpgrow mixed effects model; returns object of class "dpgrow"
shape.dp	= 4
res		= dpgrow(y = datsim$y, subject = datsim$subject,
			trt = datsim$trt, time = datsim$time,
			n.random = datsim$n.random,
			n.fix_degree = 2, n.iter = 10000,
			n.burn = 2000, n.thin = 10,
			shape.dp = shape.dp, option = "dp")
plot.results	= plot(res) ## ggplot2 plot objects, including growth curves
summary.results = summary(res) ## parameter credible intervals,  fit statistics
samples.posterior = samples(res) ## posterior sampled values