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Biometrika Advance Access originally published online on February 28, 2007
Biometrika 2007 94(1):153-165; doi:10.1093/biomet/asm009
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Copyright © 2007 Biometrika Trust

Articles

Modelling the effects of partially observed covariates on Poisson process intensity

Stephen L. Rathbun

Department of Health Administration, Biostatistics, and Epidemiology, University of Georgia, Athens, Georgia 30602, U.S.A.

Saul Shiffman

Department of Psychology, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, U.S.A.

Chad J. Gwaltney

Center for Alcohol and Addiction Studies, Box G-BH, Providence, Rhode Island 02912, U.S.A.

rathbun{at}uga.edu

shiffman{at}pitt.edu

gwaltney{at}brown.edu

Received for publication 1 October 2005. Revision received 1 June 2006.
  Abstract

We propose an estimating function for parameters in a model for Poisson process intensity when time- or space-varying covariates are observed for both the events of the process and at sample times or locations selected from a probability-based sampling design. We investigate the large-sample properties of the proposed estimator under increasing domain asymptotics, demonstrating that it is consistent and asymptotically normally distributed. We illustrate our approach using data from an ecological momentary assessment of smoking.

Key Words: ecological momentary assessment • increasing domain asymptotics • intensity function • modulated Poisson process • space-varying covariate • time-varying covariate


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