Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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.

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The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex