Christiansen, C. L. and Morris, C. N. (1997). Hierarchical Poisson regression modeling.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....has focused on detecting fraud within a single account. A large network of accounts may be accommodated by embedding MMPP parameters in a hierarchical model. The exponential family priors used in Section 4 make construction of a hierarchical model straightforward using existing theory (e.g. Christiansen and Morris, 1997). Parameter estimation for a hierarchical model describing a network of accounts requires less prior information than the current model for a single account because multiple criminal intrusions can be observed. In particular, accounts examined by fraud investigators can provide information about ....

Christiansen, C. L. and Morris, C. N. (1997). Hierarchical Poisson regression modeling.

....element is 2 ( i Gamma j ) 2 16 i j . As a consequence, this suggests a choice of the constant when using the uniform shrinkage prior for 2 in these models. We might choose the harmonic mean of the variances of the logits of ij s, evaluated at = 0 (see e.g. Daniels, 1999 or Christiansen and Morris, 1997 for a discussion of choosing these constants) This form also illustrates a problem when any of the are equal: the variance is infinite, since the ij are no longer unique. For example, it is known that there is not a unique rotation matrix for the identity matrix. Acknowledgments We would ....

Christiansen CL, Morris, CN (1997) Hierarchical Poisson regression modeling. Journal of the American Statistical Association. 92:618-632.

.... Aguilar and West (1998b) and West and Aguilar (1997) arise from motivating applications in institutional assessment and monitoring, and involve multivariate hierarchical models evolving in time, adding structured time series components to more standard hierarchical models used in this field (e.g. Christiansen and Morris 1997; Normand, Glickman and Gatsonis 1997) Here we are dealing with a large number of related time series of conditionally binomial counts, and adopt multi 14 West et al. variate, latent factor dynamic models for vectors of parameters defining the sets of binomial outcome probabilities. Components of ....

Christiansen, C.L. and Morris, C.N. (1997). Hierarchical Poisson regression modeling. J. Amer. Statist. Assoc. 92, 618-632.

....providing some correction for hospital monitor specific case mix and characteristics of patient population profiles. Further details appear in Burgess, Christiansen, Michalak and Morris (1996 and in related unpublished work) who discuss aspects of data analysis and hierarchical modelling (Christiansen and Morris 1997) in this context. Our study is concerned with evaluating ffl patterns of variability over time, in hospital monitor and area specific performance measures across a selection of quality monitors, and ffl patterns of dependencies between sets of monitors, in addition to and in combination with ....

Christiansen, C.L., and Morris, C.N. (1997) Hierarchical Poisson regression modeling, Journal of the American Statistical Association, 92, 618632.

....on the monitors separately, guided by the previous work of M C. These authors have developed a variety of Bayesian hierarchical models for the observed outcomes, including regressions on the DRG predictor and hospital specific parameters drawn from a hospital population prior (Burgess et al. 1996, Christiansen and Morris 1997). These are customised versions of standard random effects generalised linear models with Bayesian interpretations and motivations. We explore some such models for the three Monitors M20, M21 and M22 of interest here, currently restricting attention to 152 of the hospitals that have complete ....

....on the exact conditional binomial sampling distributions. ffl Poisson approximations. In cases where n i is large and p i is small, appeal to Poisson approximations to the binomial sampling model leads M C to the class of PRIMM regression models in which z i is conditionally Poisson with mean n i (Christiansen and Morris 1997). In such cases the logistic regression is approximated by a loglinear regression with i = x fi 1 i j i where j i = exp(ff i ) The PRIMM models of M C adopt gamma distributions for the hospital population priors of the random effects j i : We note that the low p i large n i condition is ....

Christiansen, C.L., and Morris, C.N. (1997) Hierarchical Poisson regression modeling, Journal of the American Statistical Association, 92, 618-632.

....of the j s. Nevertheless our results suggest that some strategy based on intelligent selection of the hyperparameters may be superior to the vague prior approach. This recommendation appears to be at variance with what is currently preferred in the literature on hierarchical models, see e.g. Christiansen and Morris (1997). 8 CONCLUSIONS The main purpose of this paper has been to argue that theoretical comparisons of Bayesian predictive procedures are both possible and worthwhile. Comparisons may be decision theoretic using one of a variety of loss functions, or based on the coverage probability bias of prediction ....

Christiansen, C.L. and Morris, C.N. (1997), Hierarchical Poisson regression modeling.

....care must be taken using these prior distributions as many are improper and thus, can lead to improper posterior distributions. Additionally, in small samples, these priors can be informative . In this paper, we investigate a proper vague prior, the uniform shrinkage prior (Strawderman, 1971; Christiansen and Morris, 1997). We discuss its properties and show how posterior distributions for common hierarchical models using this prior lead to proper posterior distributions. We also illustrate the attractive frequentist properties of this prior for a normal hierarchical model including testing and estimation. To ....

.... priors have been discussed by many authors (e.g. Jeffreys, 1961; Box and Tiao, 1973; Berger and Deely, 1988; Berger and Bernardo, 1992) The purpose of this paper is to investigate a prior, the uniform shrinkage prior, first suggested by Strawderman (1971) and later generalized by Morris (e.g. Christiansen and Morris, 1997). In Section 2, we derive and discuss properties of the uniform shrinkage prior. We give examples of some common hierarchical regression models with corresponding shrinkage priors and show that the posteriors are proper in section 3. Frequentist procedures based on this prior are explored in ....

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Christiansen C.L., and Morris, C.N. (1997). Hierarchical Poisson Regression Modeling. Journal of the American Statistical Association, 92, 618-632.

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Christiansen, C. L. and Morris, C. N. (1997). Hierarchical Poisson regression modeling.

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