  The premise of independence among subjects in the same cluster/group often
fails in practice, and models that rely on such untenable assumption can
produce misleading results. To overcome this severe deficiency, we introduce a
new regression model to handle overdispersed and correlated clustered counts.
To account for correlation within clusters, we propose a Poisson regression
model where the observations within the same cluster are driven by the same
latent random effect that follows the Birnbaum-Saunders distribution with a
parameter that controls the strength of dependence among the individuals. This
novel multivariate count model is called Clustered Poisson Birnbaum-Saunders
(CPBS) regression. As illustrated in this paper, the CPBS model is analytically
tractable, and its moment structure can be explicitly obtained. Estimation of
parameters is performed through the maximum likelihood method, and an
Expectation-Maximization (EM) algorithm is also developed. Simulation results
to evaluate the finite-sample performance of our proposed estimators are
presented. We also discuss diagnostic tools for checking model adequacy. An
empirical application concerning the number of inpatient admissions by
individuals to hospital emergency rooms, from the Medical Expenditure Panel
Survey (MEPS) conducted by the United States Agency for Health Research and
Quality, illustrates the usefulness of our proposed methodology.
