Probability Models for Duration: The Data Don′t Tell the Whole Story

Abstract

Probability models for duration have been applied to a wide range of individual-level and organizational phenomena. Seemingly similar models may, however, produce different results. Building on previous work by Morrison & Schmittlein (1980) and Schmittlein and Morrison (1983), we propose a hierarchy of models and show how an analysis of the results across models helps explain why different studies came to different conclusions. This analysis also leads to substantive insights that even the most complete model alone does not provide.

Estimating the SCAN⁎PRO model of store sales: HB, FM or just OLS?

“…step-wise, period-by-period approximation), the estimated variance for the mixing distribution (capturing the extent of heterogeneity) most often converges to zero. For example, Vanhuele, Dekimpe, Sharma, and Morrison (1995) found that the estimated variance for the mixing distribution, which captures the heterogeneity in the hazard-rate model, becomes small when they include time dummy variables and all the available covariates.…”

Rise and fall of stars: Investigating the evolution of star status in professional team sports

“…Given our definitions, each model will use only one rise observation and one fall observation for each athlete. In addition, many previous empirical studies (Gupta, 1991;Han & Hausman, 1990;Meyer, 1990;Vanhuele, Dekimpe, Sharma, & Morrison, 1995) have shown that not accounting for unobserved heterogeneity has more of an impact on the estimation of the time dependence (baseline hazard) than on the estimates of the covariates. Given our focus on the latter, we feel that not accounting for unobserved heterogeneity will not be too influential.…”

Long-Run Abstinence After Narcotics Abuse: What Are the Odds?

“…To incorporate covariates into the model, we first propose an expression for the hazard function, and subsequently use a general relationship between a distribution's hazard and survivor functions. Following Vanhuele et al (1995), we write the hazard function…”

“…To estimate the parameters of interest (l 0 , and an t b uc), expression for the survival function associated with the hazard function in Equation 2is needed. When the timevarying covariates are assumed to remain constant within a given month but are allowed to vary from month to month, it can be shown that (Vanhuele et al 1995) 0l…”

“…To correct for unobserved heterogeneity, we let l 0 be distributed according to a gamma mixing distribution with mean r/a and coefficient of variation r 01/2 (see Dekimpe and Degraeve 1997;Gupta 1991or Meyer 1990 for other applications of the gamma mixing distribution). This mixing distribution is quite flexible, and has been shown to result in the following closed-form solution for the loglikelihood function (Dekimpe and Degraeve 1997;Vanhuele et al 1995):…”