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Gaussian mixtures are commonly used for modeling heavy-tailed error distributions in robust linear regression. Combining the likelihood of a multivariate robust linear regression model with a standard improper prior distribution yields an analytically intractable posterior distribution that can be sampled using a data augmentation algorithm. When the response matrix has missing entries, there are unique challenges to the application and analysis of the convergence properties of the algorithm. Conditions for geometric ergodicity are provided when the incomplete data have a “monotone” structure. In the absence of a monotone structure, an intermediate imputation step is necessary for implementing the algorithm. In this case, we provide sufficient conditions for the algorithm to be Harris ergodic. Finally, we show that, when there is a monotone structure and intermediate imputation is unnecessary, intermediate imputation slows the convergence of the underlying Monte Carlo Markov chain, while post hoc imputation does not. An R package for the data augmentation algorithm is provided.
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Addressing Monotone Likelihood in Duration Modelling of Political Events
This article provides an accessible introduction to the phenomenon of monotone likelihood in duration modeling of political events. Monotone likelihood arises when covariate values are monotonic when ordered according to failure time, causing parameter estimates to diverge toward infinity. Within political science duration model applications, this problem leads to misinterpretation, model misspecification and omitted variable biases, among other issues. Using a combination of mathematical exposition, Monte Carlo simulations and empirical applications, this article illustrates the advantages of Firth's penalized maximum-likelihood estimation in resolving the methodological complications underlying monotone likelihood. The results identify the conditions under which monotone likelihood is most acute and provide guidance for political scientists applying duration modeling techniques in their empirical research.
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- Award ID(s):
- 1737865
- PAR ID:
- 10184727
- Date Published:
- Journal Name:
- British Journal of Political Science
- ISSN:
- 0007-1234
- Page Range / eLocation ID:
- 1 to 18
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/S0007123420000071
