arXiv subjects

Luna Fazio

Publications and source records attributed to Luna Fazio.

3 recordsLinked to original sources

arXiv2026

Latent Variable Models for Distributional Features

Analyzing the mean response of study subjects in psychological research is a standard, well-justified practice. However, theoretical arguments and empirical evidence also suggest that there is value in investigating other aspects of the distribution of such responses, such as their variability or skewness. A particular challenge that practitioners face is statistical modeling of associations between distributional features and other outcomes of interest. The most common approach is to perform estimation in two steps: distributional features are estimated first, and then those estimates are used as predictors for the relevant outcomes. Such an approach is most amenable to implementation in standard statistical software, but it ignores estimation error and can therefore lead to biased estimates and increased error rates. We introduce Distributional Feature Latent Variable Models (DFLVM), a general framework that represents between-person difference in distributional features as random intercepts. These intercepts can be simultaneously used as predictors for downstream outcomes and their associations estimated in a single estimation step. We compare the performance of our approach against two-step procedures in a simulation study and through a re-analysis of a real dataset.

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arXiv2024

Primed Priors for Simulation-Based Validation of Bayesian Models

Simulation-based calibration (SBC) is a method for validating inference algorithms and model implementations through repeated inference on data simulated from a generative model. For a model to be generative, one must specify proper priors. However, in all but the simplest of cases, choosing priors for every model parameter is a nontrivial task. In particular, priors that are too broad can produce numerical issues due to extreme parameter values while overly narrow ones can exclude precisely those regions of the parameter space where legitimate problems in the implementation would have manifested. When the data to be analyzed is already available, the issue can be sidestepped by checking calibration on the corresponding posterior, but that is not always a viable option. In this paper, we adapt the framework of catalytic priors, which have been recently proposed for construction of data-based prior distributions, and propose primed priors, which do not require real data and can therefore facilitate prior specification in SBC. We discuss relevant connections of primed priors to the theory of catalytic priors and show their use for SBC in three simulation studies.

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arXiv2024

Gaussian distributional structural equation models: A framework for modeling latent heteroscedasticity

Accounting for the complexity of psychological theories requires methods that can predict not only changes in the means of latent variables -- such as personality factors, creativity, or intelligence -- but also changes in their variances. Structural equation modeling (SEM) is the framework of choice for analyzing complex relationships among latent variables, but the modeling of latent variances as a function of other latent variables is a task that current methods only support to a limited extent. In this paper, we develop a Bayesian framework for Gaussian distributional SEM which broadens the scope of feasible models for latent heteroscedasticity. We use statistical simulation to validate our framework across four distinct model structures, in which we demonstrate that reliable statistical inferences can be achieved and that computation can be performed with sufficient efficiency for practical everyday use. We illustrate our framework's applicability in a real-world case study that addresses a substantive hypothesis from personality psychology.

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