4,456 research outputs found
Bayesian comparison of latent variable models: Conditional vs marginal likelihoods
Typical Bayesian methods for models with latent variables (or random effects)
involve directly sampling the latent variables along with the model parameters.
In high-level software code for model definitions (using, e.g., BUGS, JAGS,
Stan), the likelihood is therefore specified as conditional on the latent
variables. This can lead researchers to perform model comparisons via
conditional likelihoods, where the latent variables are considered model
parameters. In other settings, however, typical model comparisons involve
marginal likelihoods where the latent variables are integrated out. This
distinction is often overlooked despite the fact that it can have a large
impact on the comparisons of interest. In this paper, we clarify and illustrate
these issues, focusing on the comparison of conditional and marginal Deviance
Information Criteria (DICs) and Watanabe-Akaike Information Criteria (WAICs) in
psychometric modeling. The conditional/marginal distinction corresponds to
whether the model should be predictive for the clusters that are in the data or
for new clusters (where "clusters" typically correspond to higher-level units
like people or schools). Correspondingly, we show that marginal WAIC
corresponds to leave-one-cluster out (LOcO) cross-validation, whereas
conditional WAIC corresponds to leave-one-unit out (LOuO). These results lead
to recommendations on the general application of the criteria to models with
latent variables.Comment: Manuscript in press at Psychometrika; 31 pages, 8 figure
Semiparametric Bayesian inference in smooth coefficient models
We describe procedures for Bayesian estimation and testing in cross-sectional, panel data and nonlinear smooth coefficient models. The smooth coefficient model is a generalization of the partially linear or additive model wherein coefficients on linear explanatory variables are treated as unknown functions of an observable covariate. In the approach we describe, points on the regression lines are regarded as unknown parameters and priors are placed on differences between adjacent points to introduce the potential for smoothing the curves. The algorithms we describe are quite simple to implement - for example, estimation, testing and smoothing parameter selection can be carried out analytically in the cross-sectional smooth coefficient model. We apply our methods using data from the National Longitudinal Survey of Youth (NLSY). Using the NLSY data we first explore the relationship between ability and log wages and flexibly model how returns to schooling vary with measured cognitive ability. We also examine a model of female labor supply and use this example to illustrate how the described techniques can been applied in nonlinear settings
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