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A frailty model for interaction between multiple events

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  • Cuzick, Jack
  • Yang, Zihua

Abstract

Most models for categorical data rely on linear models in which higher order interactions are limited, usually to second order terms. Here we explore a dataset where second order interactions lead unavoidably to high order interactions. However in certain cases these interactions have a simple form which can be explained by population heterogeneity or ‘frailty’ and the Rasch model which uses a logistic structure is one such model. However its parameters are difficult to interpret. When event probabilities are low, we develop a simple model based on a multiplicative structure and a one-parameter gamma frailty model is developed to accommodate this sort of data. Moment estimators estimates are also provided for more general cases and goodness of fit statistics are given. An example involving 35 different human papillomavirus types in 33614 women with normal cervical cytology smears (stratified by age) is explored.

Suggested Citation

  • Cuzick, Jack & Yang, Zihua, 2013. "A frailty model for interaction between multiple events," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 133-147.
    • Handle: RePEc:eee:jmvana:v:122:y:2013:i:c:p:133-147
    DOI: 10.1016/j.jmva.2013.07.012
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    References listed on IDEAS

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    1. Svend Kreiner & Karl Christensen, 2011. "Item Screening in Graphical Loglinear Rasch Models," Psychometrika, Springer;The Psychometric Society, vol. 76(2), pages 228-256, April.
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