193,061 research outputs found
Estimation in Dirichlet random effects models
We develop a new Gibbs sampler for a linear mixed model with a Dirichlet
process random effect term, which is easily extended to a generalized linear
mixed model with a probit link function. Our Gibbs sampler exploits the
properties of the multinomial and Dirichlet distributions, and is shown to be
an improvement, in terms of operator norm and efficiency, over other commonly
used MCMC algorithms. We also investigate methods for the estimation of the
precision parameter of the Dirichlet process, finding that maximum likelihood
may not be desirable, but a posterior mode is a reasonable approach. Examples
are given to show how these models perform on real data. Our results complement
both the theoretical basis of the Dirichlet process nonparametric prior and the
computational work that has been done to date.Comment: Published in at http://dx.doi.org/10.1214/09-AOS731 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Linear Mixed Models with Marginally Symmetric Nonparametric Random Effects
Linear mixed models (LMMs) are used as an important tool in the data analysis
of repeated measures and longitudinal studies. The most common form of LMMs
utilize a normal distribution to model the random effects. Such assumptions can
often lead to misspecification errors when the random effects are not normal.
One approach to remedy the misspecification errors is to utilize a point-mass
distribution to model the random effects; this is known as the nonparametric
maximum likelihood-fitted (NPML) model. The NPML model is flexible but requires
a large number of parameters to characterize the random-effects distribution.
It is often natural to assume that the random-effects distribution be at least
marginally symmetric. The marginally symmetric NPML (MSNPML) random-effects
model is introduced, which assumes a marginally symmetric point-mass
distribution for the random effects. Under the symmetry assumption, the MSNPML
model utilizes half the number of parameters to characterize the same number of
point masses as the NPML model; thus the model confers an advantage in economy
and parsimony. An EM-type algorithm is presented for the maximum likelihood
(ML) estimation of LMMs with MSNPML random effects; the algorithm is shown to
monotonically increase the log-likelihood and is proven to be convergent to a
stationary point of the log-likelihood function in the case of convergence.
Furthermore, it is shown that the ML estimator is consistent and asymptotically
normal under certain conditions, and the estimation of quantities such as the
random-effects covariance matrix and individual a posteriori expectations is
demonstrated
Modelling the distribution of health related quality of life of advancedmelanoma patients in a longitudinal multi-centre clinical trial using M-quantile random effects regression
Health-related quality of life assessment is important in the clinical
evaluation of patients with metastatic disease that may offer useful
information in understanding the clinical effectiveness of a treatment. To
assess if a set of explicative variables impacts on the health-related quality
of life, regression models are routinely adopted. However, the interest of
researchers may be focussed on modelling other parts (e.g. quantiles) of this
conditional distribution. In this paper, we present an approach based on
quantile and M-quantile regression to achieve this goal. We applied the
methodologies to a prospective, randomized, multi-centre clinical trial. In
order to take into account the hierarchical nature of the data we extended the
M-quantile regression model to a three-level random effects specification and
estimated it by maximum likelihood
Profiled deviance for the multivariate linear mixed-effects model fitting
This paper focuses on the multivariate linear mixed-effects model, including
all the correlations between the random effects when the marginal residual
terms are assumed uncorrelated and homoscedastic with possibly different
standard deviations. The random effects covariance matrix is Cholesky
factorized to directly estimate the variance components of these random
effects. This strategy enables a consistent estimate of the random effects
covariance matrix which, generally, has a poor estimate when it is grossly (or
directly) estimated, using the estimating methods such as the EM algorithm. By
using simulated data sets, we compare the estimates based on the present method
with the EM algorithm-based estimates. We provide an illustration by using the
real-life data concerning the study of the child's immune against malaria in
Benin (West Africa)
Pseudo Bayesian Estimation of One-way ANOVA Model in Complex Surveys
We devise survey-weighted pseudo posterior distribution estimators under
2-stage informative sampling of both primary clusters and secondary nested
units for a one-way ANOVA population generating model as a simple canonical
case where population model random effects are defined to be coincident with
the primary clusters. We consider estimation on an observed informative sample
under both an augmented pseudo likelihood that co-samples random effects, as
well as an integrated likelihood that marginalizes out the random effects from
the survey-weighted augmented pseudo likelihood. This paper includes a
theoretical exposition that enumerates easily verified conditions for which
estimation under the augmented pseudo posterior is guaranteed to be consistent
at the true generating parameters. We reveal in simulation that both approaches
produce asymptotically unbiased estimation of the generating hyperparameters
for the random effects when a key condition on the sum of within cluster
weighted residuals is met. We present a comparison with frequentist EM and a
methods that requires pairwise sampling weights.Comment: 46 pages, 9 figure
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