On the Problem of Identification in Multiplicative Intensity-Rate Models with Multiple Interactions

On the Problem of Identification in Multiplicative Intensity-Rate Models with Multiple Interactions In this paper we examine a multiplicative intensity model in which a covariate interacts with two other covariates in the same model. We demonstrate, analytically, that in such situations a log-linear parameterization based on two pairs of baseline levels cannot be transformed, uniquely, to the, otherwise equivalent, multiplicative parameterization. We show that the problem lies in an oversight of the conditional independence between the two covariates interacting with a common third covariate. As a solution, therefore, we propose an approach that takes due account of such dependence. Our proposed approach uses a common baseline level for the three covariates involved in interaction while estimating the corresponding relative intensities. The issues addressed are illustrated with a demographic data set involving the estimation of rates of transition to parenthood. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quality & Quantity Springer Journals

On the Problem of Identification in Multiplicative Intensity-Rate Models with Multiple Interactions

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Publisher
Kluwer Academic Publishers
Copyright
Copyright © 1999 by Kluwer Academic Publishers
Subject
Social Sciences; Methodology of the Social Sciences; Social Sciences, general
ISSN
0033-5177
eISSN
1573-7845
D.O.I.
10.1023/A:1004347705806
Publisher site
See Article on Publisher Site

Abstract

In this paper we examine a multiplicative intensity model in which a covariate interacts with two other covariates in the same model. We demonstrate, analytically, that in such situations a log-linear parameterization based on two pairs of baseline levels cannot be transformed, uniquely, to the, otherwise equivalent, multiplicative parameterization. We show that the problem lies in an oversight of the conditional independence between the two covariates interacting with a common third covariate. As a solution, therefore, we propose an approach that takes due account of such dependence. Our proposed approach uses a common baseline level for the three covariates involved in interaction while estimating the corresponding relative intensities. The issues addressed are illustrated with a demographic data set involving the estimation of rates of transition to parenthood.

Journal

Quality & QuantitySpringer Journals

Published: Oct 19, 2004

References

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