Mixture Models for the Analysis of Repeated Count Data

Abstract

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Bias properties of Bayesian statistics in finite mixture of negative binomial regression models in crash data analysis

“…This is because the FMNB-2 model was considered more useful and parsimonious than the finite mixture of Poisson regression models (termed as a FMP-K models; K represents the number of components). The FMP-K models often produce too many components (Van Duijn and Böckenholt, 1995), making it difficult to apply. For this purpose, a Monte Carlo simulation is conducted using various sample sizes under different sample-mean values.…”

Mixture Models for Mixed Poisson Processes with Baseline Counts in Randomized Controlled Trials

“…, m, with the conditioning ni0 ≥ c as well. With c = 0, the bivariate distribution ofÑi becomes negative trinomial (Bates and Neyman, 1951;Cameron and Trivedi, 1998;Winkelmann, 2003;Zelterman, 2006;van Duijn, 1993;Iwasaki and Yeom, 2007), which should be identical to two independent Poisson when α → ∞. The probability mass function for this truncated distribution is λ0, λ1, β, δ, γ0, γ1) and Pr…”

“…All of them consist of two random effect components representing the patient heterogeneity in terms of baseline and pre-post change. For the latter, we used log-normal or discrete random effect parameters, both of which have been widely used for expressing the inter-subject heterogeneity in the analysis of over-dispersed data (Tango, 1989;van Duijn and Bockenholt, 1995;McLachlan and Peel, 2000;Booth et al, 2003;Farewell and Sprott, 1988;Diggle et al, 2002).…”

Negative Binomial Factor Analysis

“…The Poisson factor analysis corresponds to the case of a;=0 and E(Xij I O ,• )= Var(Xi; I ei, • ). The term a;h in (5) is the extra-Poisson or overdispersion variation (see e.g., Engel, 1984 ;Van Duijn, 1993) contributed by the "specific factor" 7)ij when given ei.…”

“…In the extended models of Rasch's multiplicative Poisson model (Rasch, 1960(Rasch, / 1980 for subjects by tests frequency tables (e.g., Jansen & Van Duijn, 1992 ;Van Duijn, 1993 ;Ogasawara, 1996b), the Poisson parameter (see (2)) takes the form such as ai/3j=exp(lnai+ln/3j)=exp(ai+/3;).…”