Description Usage Arguments Details Value Author(s) References See Also Examples
This function generates a posterior density sample for a semiparametric ordinal linear mixed model using a Dirichlet Process or a Mixture of Dirichlet process prior for the distribution of the random effects.
1 2 3 |
fixed |
a two-sided linear formula object describing the
fixed-effects part of the model, with the response on the
left of a |
random |
a one-sided formula of the form |
prior |
a list giving the prior information. The list include the following
parameter: |
mcmc |
a list giving the MCMC parameters. The list must include
the following integers: |
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 ( |
data |
data frame. |
na.action |
a function that indicates what should happen when the data
contain |
This generic function fits an ordinal linear mixed-effects model with a probit link (see, e.g., Molenberghs and Verbeke, 2005):
Yij = k, if gammak-1 ≤ Wij < gammak, k=1,…,K
Wij | betaF, betaR , bi ~ N(Xij betaF + Zij betaR + Zij bi, 1), i=1,…,N, j=1,…,ni
thetai | G ~ G
G | alpha, G0 ~ DP(alpha G0)
where, thetai = betaR + bi, beta = betaF, and G0=N(theta| mu, Sigma). To complete the model specification, independent hyperpriors are assumed,
alpha | a0, b0 ~ Gamma(a0,b0)
beta | beta0, Sbeta0 ~ N(beta0,Sbeta0)
mu | mub, Sb ~ N(mub,Sb)
Sigma | nu0, T ~ IW(nu0,T)
A uniform prior is used for the cutoff points. Note that the inverted-Wishart prior is parametrized such that E(Sigma)= T^{-1}/(nu0-q-1).
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 (Escobar, 1994;
Escobar and West, 1998). The betaR parameters are sampled using
the epsilon-DP approximation proposed by Muliere and Tardella (1998), with
epsilon=0.01.
An object of class DPolmm
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 betaR
, betaF
, mu
, the elements of
Sigma
, the cutoff points, alpha
, and the number of clusters.
The function DPrandom
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 matrix of dimension (nsubjects)*(nrandom effects) giving the value of the random effects for each subject. |
bclus |
a matrix of dimension (nsubjects)*(nrandom effects) giving the value of the random
effects for each clusters (only the first |
cutoff |
a real vector defining the cutoff points. Note that the first cutoff must be fixed to 0 in this function. |
ss |
an interger vector defining to which of the |
beta |
giving the value of the fixed effects. |
mu |
giving the mean of the normal baseline distributions. |
sigma |
giving the variance matrix of the normal baseline distributions. |
Alejandro Jara <atjara@uc.cl>
Escobar, M.D. (1994) Estimating Normal Means with a Dirichlet Process Prior, Journal of the American Statistical Association, 89: 268-277.
Escobar, M.D. and West, M. (1995) Bayesian Density Estimation and Inference Using Mixtures. Journal of the American Statistical Association, 90: 577-588.
Escobar, M.D. and West, M. (1998) Computing Bayesian Nonparametric Hierarchical Models, in Practical Nonparametric and Semiparametric Bayesian Statistics, eds: D. Dey, P. Muller, D. Sinha, New York: Springer-Verlag, pp. 1-22.
Molenberghs, G. and Verbeke, G. (2005). Models for discrete longitudinal data, New York: Springer-Verlag.
Muliere, P. and Tardella, L. (1998) Approximating distributions of random functionals of Ferguson-Dirichlet priors. The Canadian Journal of Statistics, 26(2): 283-297.
DPrandom
,
DPlmm
, DPglmm
,
DPMglmm
, DPMlmm
, DPMolmm
,
PTlmm
, PTglmm
, PTolmm
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 | ## Not run:
# Schizophrenia Data
data(psychiatric)
attach(psychiatric)
# MCMC parameters
nburn<-5000
nsave<-10000
nskip<-10
ndisplay<-100
mcmc <- list(nburn=nburn,nsave=nsave,nskip=nskip,ndisplay=ndisplay)
# Initial state
state <- NULL
# Prior information
tinv<-diag(10,1)
prior<-list(alpha=1,nu0=4.01,tinv=tinv,mub=rep(0,1),Sb=diag(100,1),
beta0=rep(0,3),Sbeta0=diag(1000,3))
# Fitting the model
fit1<-DPolmm(fixed=imps79o~sweek+tx+sweek*tx,random=~1|id,
prior=prior,mcmc=mcmc,state=state,status=TRUE)
fit1
# Summary with HPD and Credibility intervals
summary(fit1)
summary(fit1,hpd=FALSE)
# Plot model parameters
plot(fit1)
# Plot an specific model parameter
plot(fit1,ask=FALSE,nfigr=1,nfigc=2,param="sigma-(Intercept)")
plot(fit1,ask=FALSE,nfigr=1,nfigc=2,param="ncluster")
# Extract random effects
DPrandom(fit1)
DPrandom(fit1,centered=TRUE)
# Extract predictive information of random effects
DPrandom(fit1,predictive=TRUE)
DPrandom(fit1,centered=TRUE,predictive=TRUE)
plot(DPrandom(fit1,predictive=TRUE))
plot(DPrandom(fit1,centered=TRUE,predictive=TRUE))
## End(Not run)
|
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