Testing for Unobserved Heterogeneity in Censored Duration Models: EM Approach

2026-09-29

AI Summary

This study addresses the failure of standard asymptotic theory caused by non-regularity in testing for unobserved heterogeneity within censored duration models. To overcome this, we propose an EM algorithm-based approach for testing heterogeneity in Weibull models. The core contribution lies in constructing a test statistic that possesses an analytical asymptotic null distribution, thereby eliminating the need for simulation or bootstrap methods to compute critical values while accommodating arbitrary covariate-dependent censoring mechanisms. Empirical evaluations demonstrate that the proposed method maintains accurate size properties in large samples and achieves superior practical power compared to conventional likelihood ratio tests. Furthermore, an application to heart transplant data robustly rejects the homogeneity assumption, confirming the method’s effectiveness in real-world settings.

Abstract

Ignoring unobserved heterogeneity in duration models biases parameter estimates and invalidates inference, but testing for it is non-regular: the null hypothesis lies on the boundary of the parameter space and some parameters are unidentified under the null. These features render standard asymptotic theory inapplicable. This paper develops an EM test for unobserved heterogeneity in censored Weibull duration models, building on the EM approach of Li, Chen, and Marriott (2009). The test statistic has an asymptotic null distribution equal to the square of max{0, N(0,1)}, hence critical values require neither simulation nor bootstrap, and the test accommodates covariate-dependent censoring of arbitrary form. Monte Carlo simulations compare the EM test with the likelihood ratio test (LRT) of Cho and White (2010), information matrix tests, and Lagrange multiplier tests. The EM test has empirical size close to the nominal level for sample sizes of 500 or more, where the LRT remains markedly conservative and the other tests over-reject. Its size-adjusted power is comparable to that of the LRT and higher than that of the other tests. Because size adjustment requires knowledge of the data-generating process and is unavailable in practice, the EM test attains higher power than the LRT in most designs as the tests would actually be applied. In an application to the Stanford Heart Transplant data, the EM test rejects homogeneity in every covariate specification, whereas the LRT's conclusion depends on a user-chosen set of admissible parameter values and on the specification.

Problem

• unobserved heterogeneity
• censored duration models
• non-regular testing
• Weibull model
• EM test

Innovation

• EM test
• Unobserved heterogeneity
• Censored duration models
• Non-regular testing
• Weibull model