336 research outputs found
Efficient estimate of Bayes factors from Reversible Jump output
We exend Meng and Wong (1996) identity from a fixed to a varying dimentional setting. The identity is a very powerful tool to estimate ratios of normalizing constants and thus can be used to evaluate Bayes factors. The extention is driven by the reversibler jump algorithm so that the output from the semplar can be directly used to efficiently estimate the required Bayes factor. Two applications, involving linear and logistic regression models, illustrate the advantages of the suggested approach with respect to alternatives previously proposed in the literature.Bayes factor; Bayesian modeel choice; Marginal likelihood; Markov chain Monte Carlo; Reversible jump
Bayesian inference through encompassing priors and importance sampling for a class of marginal models for categorical data
We develop a Bayesian approach for selecting the model which is the most
supported by the data within a class of marginal models for categorical
variables formulated through equality and/or inequality constraints on
generalised logits (local, global, continuation or reverse continuation),
generalised log-odds ratios and similar higher-order interactions. For each
constrained model, the prior distribution of the model parameters is formulated
following the encompassing prior approach. Then, model selection is performed
by using Bayes factors which are estimated by an importance sampling method.
The approach is illustrated through three applications involving some datasets,
which also include explanatory variables. In connection with one of these
examples, a sensitivity analysis to the prior specification is also considered
Assessment of school performance through a multilevel latent Markov Rasch model
An extension of the latent Markov Rasch model is described for the analysis
of binary longitudinal data with covariates when subjects are collected in
clusters, e.g. students clustered in classes. For each subject, the latent
process is used to represent the characteristic of interest (e.g. ability)
conditional on the effect of the cluster to which he/she belongs. The latter
effect is modeled by a discrete latent variable associated with each cluster.
For the maximum likelihood estimation of the model parameters we outline an EM
algorithm. We show how the proposed model may be used for assessing the
development of cognitive Math achievement. This approach is applied to the
analysis of a dataset collected in the Lombardy Region (Italy) and based on
test scores over three years of middle-school students attending public and
private schools
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