| Title: | Bayesian Semiparametric Models for Meta-Analysis |
| Version: | 0.1-2 |
| Date: | 2019-01-12 |
| Author: | Deborah Burr |
| Maintainer: | Deborah Burr <burr@stat.ufl.edu> |
| Description: | The main functions carry out Gibbs' sampler routines for nonparametric and semiparametric Bayesian models for random effects meta-analysis. |
| License: | GPL-2 |
| LazyLoad: | yes |
| NeedsCompilation: | no |
| Packaged: | 2019-01-13 16:46:16 UTC; DebDoss |
| Repository: | CRAN |
| Date/Publication: | 2019-01-13 20:20:03 UTC |
bspmma: Bayesian Semiparametric Models for Meta-Analysis
Description
Two functions carry out Gibbs' sampler routines to estimate the posterior distributions from either a non-parametric Bayesian model for random effects meta-analysis, or from a semi-parametric model. A group of three functions are used to compute Bayes factors to compare the two models. Three sample datasets are included. There are routines for graphing the posteriors and computing summary statistics.
Details
| Package: | bspmma |
| Version: | 0.1-2 |
| Date: | 2019-01-19 |
| License: | GPL-2 |
| LazyLoad: | yes |
| Built: | R 2.9.2; ; 2012-07-13 19:04:37 UTC; unix |
Index:
bf.c Compute Bayes Factors for Comparing Values of
the Dirichlet Precision Parameter in the
Conditional Dirichlet Model
bf.c.o Compute Bayes Factors for Conditional vs.
Ordinary Dirichlet Models
bf.o Compute Bayes Factors for Comparing Values of
the Dirichlet Precision Parameter in the
Ordinary Dirichlet Model
bf1 Generate Chains for Computation of Bayes
Factors
bf2 Compute Constants for Multi-Chain Algorithm to
Compute Bayes Factors
breast.17 Aspirin and Breast Cancer: 17 studies
bspmma-package bspmma: Bayesian Semiparametric Models for
Meta-Analysis
caprie.3grps CAPRIE Study: Three Risk Groups
ddtm.s Decontamination of the Digestive Tract
Mortality, Short Dataset
describe.post Brief summary statistics of the posterior for
convenient comparison of several models
dirichlet.c Mixture of Conditional Dirichlet Model
dirichlet.o Mixture of Ordinary Dirichlet Model
draw.bf Plot Function for Bayes Factors
draw.post Overlapping Plots of Posterior Distributions
for Several Models
print.dir.cond printing method for objects of class dir.cond
print.dir.ord printing method for objects of class dir.ord
The main functions are explained in Burr (2012), and are
illustrated on the datasets breast.17 and ddtm.s.
The function dirichlet.c carries out the Markov chain Monte Carlo
(MCMC) algorithm to simulate data from the posterior distribution under
the conditional Dirichlet model described in Burr and Doss (2005).
The computation of Bayes factors is carried out in functions
bf1, bf2, bf.c, bf.o, and bf.c.o,
which implement a multi-chain algorithm described in Doss (2012).
Author(s)
Deborah Burr
Maintainer: Deborah Burr <burr@stat.ufl.edu>
References
Burr, Deborah (2012). “bspmma: An R package for Bayesian semi-parametric models for meta-analysis.” Journal of Statistical Software 50(4), 1–23. http://www.jstatsoft.org/v50/i04/.
Doss, Hani (2012). “Hyperparameter and model selection for nonparametric Bayes problems via Radon-Nikodym derivatives.” Statistica Sinica 22, 1–26.
Compute Bayes Factors for Comparing Values of the Dirichlet Precision Parameter in the Conditional Dirichlet Model
Description
This function carries out the final step in computing Bayes factors for
comparing a sequence of values of the Dirichlet precision parameter
M for the conditional Dirichlet mixing model.
Usage
bf.c(df=-99, from=.4, incr=.1, to, cc, mat.list)
Arguments
df |
degrees of freedom for the |
from |
is the starting value for the sequence of values of
the precision parameter |
incr |
is the amount by which to increment the values
of |
to |
is the ending value for the sequence of values
of |
cc |
is the vector of nine constants computed by |
mat.list |
list of nine matrices of MCMC output produced by
|
Details
This function carries out the fourth and final step in the computation
of Bayes factors for the selection of M in the conditional
Dirichlet mixing model. In the current version of the package, the
Bayes factors for M are computed relative to
the model with M=4. The sequence of steps implements a
multiple-chain version of Equation (2.6) of Burr (2012); the details
of the multiple-chain algorithm are given in Doss (2012).
Previous steps are two calls to bf1 and a call to bf2,
as illustrated in the Examples section and in Burr (2012).
Value
A list with three named components, Mnew, y, and
yinfinity, needed to produce the plot of Bayes factors via the
function draw.bf. The vector Mnew is the sequence of
(finite) values of M. The vector y is the estimates of
the Bayes factors corresponding to the finite values of Mnew,
and the object yinfinity is the value of the Bayes factor for
M at infinity, that is, for the parametric model.
References
Burr, Deborah (2012). “bspmma: An R package for Bayesian semiparametric models for meta-analysis.” Journal of Statistical Software 50(4), 1–23. http://www.jstatsoft.org/v50/i04/.
Doss, Hani (2012). “Hyperparameter and model selection for nonparametric Bayes problems via Radon-Nikodym derivatives.” Statistica Sinica 22, 1–26.
Examples
## Not run:
## CPU times are from runs of the R command system.time() on an
## Intel $2.8$ GHz Q$9550$ running Linux.
## Preliminary steps
data(breast.17) # the breast cancer dataset
breast.data <- as.matrix(breast.17) # put data in matrix object
chain1.list <- bf1(breast.data) # 40.5 secs
cc <- bf2(chain1.list) # 1.6 secs
## Next get a second set of 9 chains, with a different seed
chain2.list <- bf1(breast.data,seed=2) # 40.4 secs
## Compute and plot the Bayes factors
breast.bfc <- bf.c(to=20, cc=cc, mat.list=chain2.list)
draw.bf(breast.bfc)
## End(Not run)
Compute Bayes Factors for Conditional vs. Ordinary Dirichlet Models
Description
This function carries out the final step in computing Bayes factors for
comparing conditional and ordinary Dirichlet mixing models, for a
sequence of Dirichlet precision parameters M.
Usage
bf.c.o(df=-99, from=.4, incr=.1, to, cc, mat.list)
Arguments
df |
degrees of freedom for the |
cc |
is the vector of nine constants computed by |
from |
is the starting value for the sequence of values of
the precision parameter |
to |
is the ending value for the sequence of values
of |
incr |
is the amount by which to increment the values
of |
mat.list |
list of nine matrices of MCMC output produced by
|
Details
This function carries out the fourth and final step in the computation
of Bayes factors for the conditional vs. ordinary Dirichlet mixing
models. It implements a multiple-chain version of Equation (2.7) of
Burr (2012); the details of the multiple-chain algorithm are given in
Doss (2012). Previous steps are two calls to bf1 and a call to
bf2, as illustrated in the Examples section and in Burr (2012).
Value
A list with two named components, Mnew and y. The
vector Mnew is the sequence of (finite) values of M.
The vector y is the estimates of the Bayes factors
corresponding to Mnew.
References
Burr, Deborah (2012). “bspmma: An R package for Bayesian semiparametric models for meta-analysis.” Journal of Statistical Software 50(4), 1–23. http://www.jstatsoft.org/v50/i04/.
Doss, Hani (2012). “Hyperparameter and model selection for nonparametric Bayes problems via Radon-Nikodym derivatives.” Statistica Sinica22, 1–26.
Examples
## Not run:
## CPU times are from runs of the R command system.time() on an
## Intel $2.8$ GHz Q$9550$ running Linux.
## Preliminary steps
data(breast.17) # the breast cancer dataset
breast.data <- as.matrix(breast.17) # put data in matrix object
chain1.list <- bf1(breast.data) # 40.5 secs
cc <- bf2(chain1.list) # 1.6 secs
## Next get a second set of 9 chains, with a different seed
chain2.list <- bf1(breast.data,seed=2) # 40.4 secs
## OR load the chains and constants saved earlier
load("breast-rdat-2lists-1000")
load("breast-rdat-2lists-1000")
## Compute and plot the Bayes factors
breast.bfco <- bf.c.o(to=20, cc=cc, mat.list=chain2.list) # 107 secs
draw.bf(breast.bfco)
## End(Not run)
Compute Bayes Factors for Comparing Values of the Dirichlet Precision Parameter in the Ordinary Dirichlet Model
Description
This function carries out the final step in computing Bayes factors for
comparing a sequence of values of the Dirichlet precision parameter
M for the ordinary Dirichlet mixing model.
Usage
bf.o(df=-99, from=.4, incr=.1, to, cc, mat.list)
Arguments
df |
degrees of freedom for the |
from |
is the starting value for the sequence of values of
the precision parameter |
incr |
is the amount by which to increment the values
of |
to |
is the ending value for the sequence of values
of |
cc |
is the vector of nine constants computed by |
mat.list |
list of nine matrices of MCMC output produced by
|
Details
This function carries out the fourth and final step in the computation
of Bayes factors for the selection of M in the ordinary
Dirichlet mixing model. In the current version of the package, the
Bayes factors for M are computed relative to
the model with M=4. The sequence of steps implements a
multiple-chain version of Equation (2.7) of Burr (2012); the details
of the multiple-chain algorithm are given in Doss (2012).
Previous steps are calls to bf1, bf2, and bf1
again, in that order, as illustrated in the Examples section and in
Burr (2012).
Value
A list with three named components, Mnew, y, and
yinfinity, needed to produce the plot of Bayes factors via the
function draw.bf. The vector Mnew is the sequence of
(finite) values of M. The vector y is the estimates of
the Bayes factors corresponding to the finite values of Mnew,
and the object yinfinity is the value of the Bayes factor for
M at infinity, that is, for the parametric model.
References
Burr, Deborah (2012). “bspmma: An R package for Bayesian semi-parametric models for meta-analysis.” Journal of Statistical Software 50(4), 1–23. http://www.jstatsoft.org/v50/i04/.
Doss, Hani (2012). “Hyperparameter and model selection for nonparametric Bayes problems via Radon-Nikodym derivatives.” Statistica Sinica 22, 1–26.
Examples
## Not run:
## CPU times are from runs of the R command system.time() on an
## Intel $2.8$ GHz Q$9550$ running Linux.
## Preliminary steps
data(breast.17) # the breast cancer dataset
breast.data <- as.matrix(breast.17) # put data in matrix object
chain1.list <- bf1(breast.data) # 40.5 secs
cc <- bf2(chain1.list) # 1.6 secs
## Next get a second set of 9 chains, with a different seed
chain2.list <- bf1(breast.data,seed=2) # 40.4 secs
## Compute and plot the Bayes factors
breast.bfo <- bf.o(to=20, cc=cc, mat.list=chain2.list) #51 secs
draw.bf(breast.bfo)
## End(Not run)
Generate Chains for Computation of Bayes Factors
Description
Generate nine matrices of MCMC output under the ordinary Dirichlet
model, for nine fixed values of the precision parameter M.
This MCMC output is needed for computing Bayes factors.
Usage
bf1(data,seed=1,ncycles=2000,d=c(.1,.1,0,1000),K=10,burnin=1000)
Arguments
data |
is a two-column matrix with a row for each study in the meta-analysis. The first column is the log of estimate of relative risk, often a log(odds ratio). The second column is the true or estimated standard error of the log(odds ratio). |
seed |
is the value of the seed for starting the random number
generator, which will be used before each of the nine calls to the
function |
ncycles |
is the number of cycles of the Markov chain. |
d |
is a vector of length four with the values of the
hyperparameters, in order, the location and scale of the Gamma
inverse prior, mean and variance multiplier for the normal prior
on |
K |
is the number of summands to include when one uses
Sethuraman's (1994) representation for getting the parameter
|
burnin |
is the number of Markov chain cycles to drop. |
Details
Doss (2012) describes a method for estimating Bayes
factors for many M values in a Dirichlet mixing model;
the method requires judicious selection of multiple hyperparameter
points at which to estimate the posterior distribution by MCMC under
the ordinary Dirichlet model. The function bf1 is used for
estimating Bayes factors for conditional vs.\ ordinary Dirichlet
models, and for comparing values of M in the conditional
model or in the ordinary model, for a range of the precision parameter
M which cover the range of values of interest in most
practical problems. The function bf1 generates the MCMC
output for a hard-wired selection of hyperparameters which work
well to give low-variance estimates of Bayes factors of interest
in practice. Chains are generated for nine values of the Dirichlet
precision parameter M:
.25, .5, 1, 2, 4, 8, 16, 32,
and 64.
The rest of the Dirichlet model is specified by the parameters of the
normal/inverse Gamma prior, which by default are
\vec{d} = (.1,.1,0,1000).
Value
List with nine matrix components. Each matrix has
nr rows and nc columns, where
nr= ncycles - burnin,
nc= (number of studies) + 4 for the row label,
the individual study parameter values, and the three overall
parameters, \mu, \tau, and \eta.
References
Doss, Hani (2012). “Hyperparameter and model selection for nonparametric Bayes problems via Radon-Nikodym derivatives.” Statistica Sinica, 22, 1–26.
Sethuraman, J. (1994). “A constructive definition of Dirichlet priors.” Statistica Sinica 4, 639–650.
Examples
## Not run:
## Set up the data.
data(breast.17) # the breast cancer dataset
breast.data <- as.matrix(breast.17) # put data in matrix object
## Default values ncycles=2000, burnin=1000, seed=1
## CPU time is given from a run of the R command system.time() on an
## Intel $2.8$ GHz Q$9550$ running Linux
chain1.list <- bf1(breast.data) # 40.5 secs
## Next get a second set of 9 chains, with a different seed
chain2.list <- bf2(breast.data, seed=2) # 40.4 secs
## Perhaps save for another time.
save(chain1.list,chain2.list,file="breast-rdat-2lists-1000",compress=TRUE)
## later session
load("breast-rdat-2lists-1000")
## End(Not run)
Compute Constants for Multi-Chain Algorithm to Compute Bayes Factors
Description
This function computes nine constants needed in the multi-chain
algorithm for Bayes factors comparing conditional and ordinary
Dirichlet mixing models, and for Bayes factors comparing Dirichlet
precision parameter (M) values for the conditional model,
or for the ordinary model.
Usage
bf2(chain.list)
Arguments
chain.list |
is a list of nine matrices of MCMC output produced by function bf1 |
Details
This function computes the constants needed for the denominator of the left-side of Eqn. (2.5) of Doss (2012). This is the step in which Radon-Nikodym derivatives are evaluated for each line of MCMC output and then averaged to estimate the constants. The actual algorithm is a little more complicated than that to make use of output from multiple chains. Nine constants are computed in this way.
Value
A vector of nine constants which is needed in the next step of the computation of the Bayes factors. Burr (2012) gives detailed explanations of the algorithm and illustrates the steps in the algorithm.
References
Burr, Deborah (2012). “bspmma: An R package for Bayesian semi-parametric models for meta-analysis.” Journal of Statistical Software 50(4), 1–23. http://www.jstatsoft.org/v50/i04/.
Doss, Hani (2012). “Hyperparameter and model selection for nonparametric Bayes problems via Radon-Nikodym derivatives.” Statistica Sinica, 22, 1–26.
Examples
## Not run:
## Get the two sets of chains saved from runs of bf1 from
## the breast cancer example in the help file for bf1.
load("breast-rdat-2lists-1000")
## Default values ncycles=2000, burnin=1000
## CPU time is from a run of the R command system.time() on an
## Intel $2.8$ GHz Q$9550$ running Linux.
cc <- bf2(chain1.list) #1.6 secs
## Perhaps save for another time.
save(cc,file="breast-rdat-constants",compress=TRUE)
## Next session
load("breast-rdat-constants")
## End(Not run)
Aspirin and Breast Cancer: 17 studies
Description
This dataset gives log odds of breast cancer for long-term aspirin users, and its standard error, derived from 17 cohort and case-control studies.
Usage
data(breast.17)Format
A data frame with seventeen rows, corresponding to the seventeen
papers. There are two columns: psi.hat (numeric, the log odds ratio),
and se.psi.hat (numeric, estimated SE of the log odds ratio).
The rownames attribute gives the first author of the paper
and the citation number of the study in Harris et.\ al. (2005).
Source
Harris, R., Beebe-Donk, J., Doss, H., and Burr, D. (2005). “Aspirin, ibuprofen, and other non-steroidal anti-inflammatory drugs in cancer prevention: A critical review of non-selective COX-2 blockade (Review).” Oncology Reports 13 559-583.
References
Gonzalez-Perez, A., Rodriguez, L., and Lopez-Ridaura, R. (2003). “Effects of non-steroidal anti-inflammatory drugs on cancer sites other than the colon and rectum: a meta-analysis.” BMC Cancer 3 28.
Khuder, S. and Mutgi, A. (2001). “Breast cancer and NSAID use: a meta-analysis.” British Journal of Cancer 84, 1188–1192.
CAPRIE Study: Three Risk Groups
Description
From the CAPRIE study comparing clopidogrel versus Aspirin, this dataset gives risk ratios and their SEs separately for patients who had stroke, heart attack (myocardial infarction or MI), and peripheral arterial disease (PAD).
Usage
data(caprie.3grps)Format
A data frame with three rows, corresponding to the three risk groups. There are three columns: study (character, for the risk groups), psi.hat (numeric, the log odds ratio, and se.psi.hat (numeric, estimated SE of the log odds ratio).
Source
CAPRIE Steering Committee (1996), A randomized, blinded trial of clopidogrel versus aspirin in patients at risk of ischaemic events (CAPRIE), Lancet, 348, 1329–1339.
Burr and Doss (2005) state how the SEs for the log odds ratios for the three risk groups are obtained from data on p.\ 1334 of the CAPRIE article.
References
Burr, D. and Doss, H. (2005). A Bayesian semi-parametric model for random effects meta analysis. The Journal of the American Statistical Association,100, 242–251.
Decontamination of the Digestive Tract Mortality, Short Dataset
Description
This dataset gives number of deaths and number of subjects in treatment vs. control groups in 14 studies from a meta-analysis of studies on antiobiotics to reduce infection in intensive-care units.
Usage
data(ddtm.s)Format
A data frame with fourteen rows, corresponding to fourteen different, unidentified studies. There are four columns: number of deaths in the treatment group, sample size in the treatment group, number of deaths in the control group, sample size in the control group.
Burr and Doss (2005) give the background for this dataset.
Source
Selective Decontamination of the Digestive Tract Trialists' Collaborative Group (1993). “Meta-analysis of randomised controlled trials of selective decontamination of the digestive tract.” British Medical Journal 307 525–532.
References
Burr, D. and Doss, H. (2005). “A Bayesian semiparametric model for random-effects meta-analysis.” Journal of the American Statistical Association 100 242–251.
Brief summary statistics of the posterior for convenient comparison of several models
Description
Compute, print posterior means and posterior P(odds ratio < 1) for the individual study parameters and hyperparameters of the model.
Usage
describe.post(mcout,burnin=1000)
Arguments
mcout |
is a list. Each item in the list is a matrix of MCMC
output, corresponding to different values of |
burnin |
is the number of initial chains to omit from the estimates. |
Value
List with two named components, means.table and probs.table, returned invisibly.
Examples
## Not run:
## Set up the data.
data(breast.17) # the breast cancer dataset
breast.data <- as.matrix(breast.17) # put data in matrix object
## Generate at least two chains, from models which are the same except
## for different \eqn{M} values.
set.seed(1) # initialize the seed at 1
breast.c1 <- dirichlet.c(breast.data, ncycles=4000, M=5)
breast.c2 <- dirichlet.c(breast.data,ncycles=4000, M=1000)
## Create list object.
breast.c1c2 <- list("5"=breast.c1$chain, "1000"= breast.c2$chain)
## Decide on some number of initial runs to omit from the analysis.
describe.post(breast.c1c2, burnin=100)
## End(Not run)
Mixture of Conditional Dirichlet Model
Description
MCMC generation of posterior distributions for the
conditional Dirichlet mixing distribution model, using
m+1-cycle Gibbs sampler
Usage
dirichlet.c(data, ncycles=10, M=1,d=c(.1,.1,0,1000),
start=NULL)
Arguments
data |
is a two-column matrix with a row for each study in the meta-analysis. The first column is the log of estimate of relative risk, often a log(odds ratio). The second column is the true or estimated standard error of the log(odds ratio). |
ncycles |
is the number of cycles of the Markov chain. |
M |
is the precision parameter of the Dirichlet process prior. |
d |
is a vector of length four with the values of the
hyperparameters, in order, the location and scale of the Gamma
inverse prior, mean and variance multiplier for the normal prior
on |
start |
is an optional vector containing starting values for the
parameters, |
Details
This function generates MCMC output for the posterior distribution for
the parameters \psi_i, i=1, \ldots, m
where m is the number of
studies in the meta-analysis, \mu and \tau,
in the conditional Dirichlet mixing model for random-effects
meta-analysis. Notation is taken from Burr (2012),
Model 4.
The MCMC algorithm for estimating the posterior under this model is
given in Burr and Doss (2005). The chain is a
(m+1)-cycle Gibbs sampler which cycles through
the vector of \psi_i's and the pair \mu,
\tau, and
the main part of the computational burden is in the first part of the
cycle, the generation of the vector of \psi_i's.
If starting values are not specified via the argument start,
the default values are used, which are based on the data. The study
estimates are the starting values for the \psi_i, i=1, \ldots,m,
and the mean and standard deviation of the study estimates are the
starting values for \mu and \tau, respectively.
Value
call |
the call that resulted in this object |
ncycles |
the number of cycles in the Markov chain |
M |
the value of the precision parameter for the conditional Dirichlet model |
prior |
the vector length four of hyperparameters |
chain |
A matrix with |
start.user |
logical, TRUE if the user supplied initial values of
the parameter vector, FALSE if input argument |
start |
vector of initial parameter values used in the MCMC algorithm, whether this was the default or was user-supplied |
References
Burr, Deborah (2012). “bspmma: An R package for Bayesian semi-parametric models for meta-analysis.” Journal of Statistical Software 50(4), 1–23. http://www.jstatsoft.org/v50/i04/.
Burr, D. and Doss, H. (2005). “A Bayesian semiparametric model for random-effects meta-analysis.” Journal of the American Statistical Association 100 242–251.
Sethuraman, J. (1994). “A constructive definition of Dirichlet priors.” Statistica Sinica 4, 639–650.
Examples
## Not run:
data(breast.17) # the dataset
breast.data <- as.matrix(breast.17) # put data in matrix object
set.seed(1) # initialize the seed at 1 for test purposes
breast.c1 <- dirichlet.c(breast.data, ncycles=4000, M=5)
breast.c2 <- dirichlet.c(breast.data,ncycles=4000, M=1000)
## End(Not run)
Mixture of Ordinary Dirichlet Model
Description
MCMC generation of posterior distributions for the
usual (unconditional) Dirichlet mixing distribution model, using
an m+1-cycle Gibbs sampler
Usage
dirichlet.o(data, ncycles=10, M=1,d=c(.1,.1,0,1000),
start=NULL,K=100)
Arguments
data |
is a two-column matrix with a row for each study in the meta-analysis. The first column is the log of estimate of relative risk, often a log(odds ratio). The second column is the true or estimated standard error of the log(odds ratio). |
ncycles |
is the number of cycles of the Markov chain. |
M |
is the precision parameter of the Dirichlet process prior. |
d |
is a vector of length four with the values of the hyperparameters, in order, the location and scale of the Gamma inverse prior, mean and variance multiplier for the normal prior on mu. |
start |
is an optional vector containing starting values for the
parameters, |
K |
is the number of summands to include when one uses
Sethuraman's (1994) representation for getting the parameter
|
Details
This function generates MCMC output for the posterior distribution for
the parameters \psi_i, i=1,...,m where m is the number of
studies in the meta-analysis, \mu, \tau, and \eta
in the ordinary Dirichlet mixing model for random-effects
meta-analysis. Notation is taken from Burr (2012),
Model 2 and 3.
The MCMC algorithm for estimating the posterior under this model is
given in Burr and Doss (2005). The chain is a
(m+1)-cycle Gibbs sampler which cycles through
the vector of \psi_i's and the triple \mu, \tau,
\eta, and the main part of the computational burden is in the
first part of the cycle, the generation of the vector of
\psi_i's.
Value
call |
the call that resulted in this object |
ncycles |
the number of cycles in the Markov chain |
M |
the value of the precision parameter for the conditional Dirichlet model |
prior |
the vector length four of hyperparameters |
chain |
A matrix with |
start.user |
logical, TRUE if the user supplied initial values of
the parameter vector, FALSE if input argument |
start |
vector of initial parameter values, whether default or user-supplied |
References
Burr, Deborah (2012). “bspmma: An R package for Bayesian semi-parametric models for meta-analysis.” Journal of Statistical Software 50(4), 1–23. http://www.jstatsoft.org/v50/i04/.
Burr, D. and Doss, H. (2005). “A Bayesian semiparametric model for random-effects meta-analysis.” Journal of the American Statistical Association 100 242–251.
Sethuraman, J. (1994). “A constructive definition of Dirichlet priors.” Statistica Sinica 4, 639–650.
Examples
## Not run:
data(breast.17) # the dataset
breast.data <- as.matrix(breast.17) # put data in matrix object
set.seed(1) # initialize the seed at 1
diro <- dirichlet.o(breast.data, ncycles=4000, M=5)
## a short description of the model and Markov chain
print(diro1)
## the last mcmc cycle
diro$mcmc[4001,]
## End(Not run)
Plot Function for Bayes Factors
Description
This function plots the output from function bf.c.o.
Usage
draw.bf(obj,line.lwd=2, ...)
Arguments
obj |
is a list with two elements, the vectors x and y to be
plotted in a scatterplot, which are produced by function |
line.lwd |
graphical parameter; the relative thickness of the plotted line |
... |
additional graphical parameters for the overall plot |
Overlapping Plots of Posterior Distributions for Several Models
Description
Draw overlapping kernel density estimates of the posterior
distributions of the parameters of the conditional or ordinary
Dirichlet model, where the posteriors arise from different values
of the Dirichlet precision parameter M.
Usage
draw.post(mcout,burnin=1000,ind.par=NULL,adjust=1,...)
Arguments
mcout |
is a list. Each item in the list is a matrix of MCMC
output, corresponding to different values of |
burnin |
is the number of initial chains to omit from the
estimates, must be no larger than |
ind.par |
an integer vector, containing indices of which columns
of |
adjust |
is the bin width argument for the call to the R base package function density. |
... |
additional arguments to plot may be supplied. |
Examples
## Not run:
## Conditional Dirichlet model
## Set up the breast cancer dataset.
data(breast.17)
breast.data <- as.matrix(breast.17) # Data must be a matrix object.
## Generate at least two chains, from models which are the same except
## for different \eqn{M}{M} values.
set.seed(1) # initialize the seed at 1 for test purposes
breast.c1 <- dirichlet.c(breast.data, ncycles=4000, M=5)
breast.c2 <- dirichlet.c(breast.data,ncycles=4000, M=1000)
## Create list object.
breast.c1c2 <- list("5"=breast.c1$chain, "1000"= breast.c2$chain)
## Decide on some number of initial runs to omit from the analysis.
draw.post(breast.c1c2, burnin=100) # plots for hyperparameters only
## End(Not run)
printing method for objects of class dir.cond
Description
gives limited info
Usage
## S3 method for class 'dir.cond'
print(x,digits=max(3,getOption("digits") -3),...)
Arguments
x |
object of class dir.cond |
digits |
positive integer, number of digits for printing |
... |
place holder |
printing method for objects of class dir.ord
Description
gives limited info
Usage
## S3 method for class 'dir.ord'
print(x,digits=max(3,getOption("digits") -3),...)
Arguments
x |
object of class dir.ord |
digits |
positive integer, number of digits for printing |
... |
place holder |