Title: Bridges between deterministic and probabilistic models for binary data
Authors: Gelman, Andrew ×
Leenen, Iwein
Van Mechelen, Iven
De Boeck, Paul
Poblome, Jeroen #
Issue Date: 2010
Publisher: Elsevier
Series Title: Statistical Methodology vol:7 issue:3 pages:187-209
Abstract: For the analysis of binary data, various deterministic models
have been proposed, which are generally simpler to fit and
easier to understand than probabilistic models. We claim that
corresponding to any deterministic model is an implicit stochastic
model in which the deterministic model fits imperfectly, with
errors occurring at random. In the context of binary data, we
consider a model in which the probability of error depends on the
model prediction. We show how to fit this model using a stochastic
modification of deterministic optimization schemes.
The advantages of fitting the stochastic model explicitly
(rather than implicitly, by simply fitting a deterministic model
and accepting the occurrence of errors) include quantification
of uncertainty in the deterministic model's parameter estimates,
better estimation of the true model error rate, and the ability to
check the fit of the model nontrivially. We illustrate this with
a simple theoretical example of item response data and with
empirical examples from archeology and the psychology of choice.
ISSN: 1572-3127
VABB publication type: VABB-1
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Quantitative Psychology and Individual Differences
Archaeology, Leuven
× corresponding author
# (joint) last author

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