DPMmeta {DPpackage} | R Documentation |
This function generates a posterior density sample for a semiparametric linear mixed effects meta-analysis model using a Dirichlet Process Mixture of Normals prior for the distribution of the random effects.
DPMmeta(formula,prior,mcmc,state,status,data=sys.frame(sys.parent()), na.action=na.fail)
formula |
a two-sided linear formula object describing the
fixed-effects part of the model, with the response on the
left of a ~ operator and the terms, separated by +
operators, on the right.Both effect and variance must be included
in the LHS of the formula object |
prior |
a list giving the prior information. The list include the following
parameter: a0 and b0 giving the hyperparameters for
prior distribution of the precision parameter of the Dirichlet process
prior, alpha giving the value of the precision parameter (it
must be specified if a0 and b0 are missing, see details
below), tau01 and tau02 giving the hyperparameters of the
inverted gamma prior distribution for the variance of the normal
kernel, mb and Sb giving the hyperparameters
of the normal prior distribution for the mean of the normal
baseline distribution, mub giving the value of the mean of the
centering distribution (it must be specified if
mb and Sb are missing),
tau11 and tau12 giving the hyperparameters of the
inverted gamma prior distribution for the variance of the normal
baseline distribution, sigmab giving the value of the variance
of the centering distribution (it must be specified if
tau11 and tau12 are missing), and
beta0 and Sbeta0 giving the
hyperparameters of the normal prior distribution for the fixed effects
(must be specified only if fixed effects are considered in the model). |
mcmc |
a list giving the MCMC parameters. The list must include
the following integers: nburn giving the number of burn-in
scans, nskip giving the thinning interval, nsave giving
the total number of scans to be saved, and ndisplay giving
the number of saved scans to be displayed on screen (the function reports
on the screen when every ndisplay iterations have been carried
out). |
state |
a list giving the current value of the parameters. This list is used if the current analysis is the continuation of a previous analysis. |
status |
a logical variable indicating whether this run is new (TRUE ) or the
continuation of a previous analysis (FALSE ). In the latter case
the current value of the parameters must be specified in the
object state . |
data |
data frame. |
na.action |
a function that indicates what should happen when the data
contain NA s. The default action (na.fail ) causes
DPMmeta to print an error message and terminate if there are any
incomplete observations. |
This generic function fits a semiparametric linear mixed effects meta-analysis model:
yi ~ N(thetai+ Xi beta, sigma2ei), i=1,...,n
sigma^-1 | tau01, tau02 ~ Gamma(tau01/2,tau02/2)
thetai | G, sigma ~ int N(mu,sigma)G(d mu)
G | alpha, G0 ~ DP(alpha G0)
where, G0=N(mu| mub, sigmab). To complete the model specification, independent hyperpriors are assumed,
alpha | a0, b0 ~ Gamma(a0,b0)
beta | beta0, Sbeta0 ~ N(beta0,Sbeta0)
mub | mb, Sb ~ N(mb,Sb)
sigma^-1_b | tau11, tau12 ~ Gamma(tau11/2,tau12/2)
The precision or total mass parameter, α, of the DP
prior
can be considered as random, having a gamma
distribution, Gamma(a0,b0),
or fixed at some particular value. When alpha is random the method described by
Escobar and West (1995) is used. To let alpha to be fixed at a particular
value, set a0 to NULL in the prior specification.
The computational implementation of the model is based on the marginalization of
the DP
and on the use of MCMC methods for conjugate priors
for a collapsed state of MacEachern (1998).
The average effect is sampled using the epsilon-DP approximation proposed by Muliere and Tardella (1998), with epsilon=0.01.
An object of class DPMmeta
representing the linear
mixed-effects model fit. Generic functions such as print
, plot
,
summary
, and anova
have methods to show the results of the fit.
The results include beta
, sigma
, mub
, sigmab
, \alpha
, and the
number of clusters.
The function DPMrandom
can be used to extract the posterior mean of the
random effects.
The list state
in the output object contains the current value of the parameters
necessary to restart the analysis. If you want to specify different starting values
to run multiple chains set status=TRUE
and create the list state based on
this starting values. In this case the list state
must include the following objects:
ncluster |
an integer giving the number of clusters. |
alpha |
giving the value of the precision parameter |
b |
a vector of dimension (nrec) giving the value of the random effects for each subject. |
mu |
a vector of dimension (nrec) giving the value of the mean
of the normal kernel for each cluster (only the first ncluster are considered to start the chain). |
ss |
an interger vector defining to which of the ncluster clusters each subject belongs. |
beta |
giving the value of the fixed effects. |
sigma |
giving the variance of the normal kernel. |
mub |
giving the mean of the normal baseline distributions. |
sigmab |
giving the variance of the normal baseline distributions. |
Alejandro Jara <ajarav@udec.cl>
Escobar, M.D. and West, M. (1995) Bayesian Density Estimation and Inference Using Mixtures. Journal of the American Statistical Association, 90: 577-588.
MacEachern, S.N. (1998) Computational Methods for Mixture of Dirichlet Process Models, in Practical Nonparametric and Semiparametric Bayesian Statistics, eds: D. Dey, P. Muller, D. Sinha, New York: Springer-Verlag, pp. 23-44.
Muliere, P. and Tardella, L. (1998) Approximating distributions of random functionals of Ferguson-Dirichlet priors. The Canadian Journal of Statistics, 26(2): 283-297.
DPMrandom
,
DPmeta
DPMglmm
, DPMolmm
,
DPlmm
, DPglmm
, DPolmm
## Not run: ################################################################## # Data on the effectiveness of silver sulfadiazine coating # on venous catheters for preventing bacterial colonisation of # the catheter and bloodstream infection. # Veenstra D et al (1998) "Efficacy of Antiseptic Impregnated # Central Venous Catheters in Preventing Nosocomial Infections: # A Meta-analysis" JAMA 281:261-267. # # Note that -Inf and Inf have been replaced by NA. ################################################################## studies <- c("Tennenberg","Maki","vanHeerden", "Hannan","Bach(a)","Bach(b)", "Heard","Collins","Ciresi","Ramsay", "Trazzera","George") logOR <- c(-1.5187189,-0.7136877,-1.3217558,-0.1910552, NA,-2.2005195,-0.5057461,-2.3538784,-0.3643810, -0.5371429,-0.7608058,-2.1400662) varlogOR <- c(0.4157541,0.2632550,0.6739189,0.3727788,NA, 0.7623470,0.2306169,0.7477891,0.3645463,0.2291839, 0.3561542,0.5190489)^2 names(logOR) <- studies names(varlogOR) <- studies y <- cbind(logOR,varlogOR) colnames(y) <- c("logOR","varlogOR") # Prior information prior<-list(alpha=1, tau01=20, tau02=10, tau11=20, tau12=10, mb=0, Sb=100) # Initial state state <- NULL # MCMC parameters nburn<-20000 nsave<-10000 nskip<-20 ndisplay<-100 mcmc <- list(nburn=nburn, nsave=nsave, nskip=nskip, ndisplay=ndisplay) # Fit the model: First run fit1<-DPMmeta(formula=y~1,prior=prior,mcmc=mcmc, state=state,status=TRUE) fit1 # Summary with HPD and Credibility intervals summary(fit1) summary(fit1,hpd=FALSE) # Plot model parameters (to see the plots gradually set ask=TRUE) plot(fit1,ask=FALSE) plot(fit1,ask=FALSE,nfigr=2,nfigc=2) ## End(Not run)