*apologies for cross-posting*
During the PDW "Succeeding as Researcher II: Common Methodological Pitfalls in Research", which was sponsored by the IM and BPS divisions, at the AOM 2015 meeting there were several articles that were mentioned by Dr. Glenn Hoetker.
As promised, professor Glenn Hoetker was kind enough to share with us those references along with additional commentary, which we think are providing valuable insights to all AOM members that plan to use Limited Dependent Variable models in their research:
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During the Succeeding as Researcher II: Common Methodological Pitfalls in Research PDW, I mentioned several papers that I felt had advanced the discussion of logit and probit models recently. Here are the full citations for those papers, along with some additional commentary for context.
1.Hoetker G. 2007. The use of logit and probit models in strategic management research: Critical issues. Strategic Management Journal 28(4): 331-343
Girigorios was kind enough to reference my 2007 SMJ paper on logit and probit models in management research. This is just the full cite of that paper.
2. Zelner B. 2009. Using simulation to interpret results from logit, probit, and other nonlinear models. Strategic Management Journal 30(12): 1335-1348.
Drawing on work done in political science, Zelner offers an alternative approach to interpreting coefficients from logit, probit and other nonlinear models. Among other things, it allows one to represent the uncertainty of the estimated coefficients without the complex calculations required to calculate the s.e.'s, particularly in the case of interactions.
3. Williams R. 2009. Using heterogeneous choice models to compare logit and probit coefficients across groups. Sociological Methods and Research 37(4): 531-559
While Zelner offers an alternative means of interpreting the results of standard logit/probit estimation, Williams offers an alternative model, which "explicitly specify the determinants of heteroskedasticity in an attempt to correct for it". Among other things, this offers a flexible approach to the problem of comparing coefficients across groups in logit and probit models. He also offers useful critique of Allison's (1999) approach and suggests that the qualified endorsement of Allison's approach that I offered in my 2007 SMJ paper was overly optimistic. Williams has made Stata code that implements the methods of this paper available as the oglm package.
4. Norton EC, Wang H, Ai C. 2004. Computing interaction effects and standards errors in logit and probit models. Stata Journal 4(2): 154-167
This paper and associated work in Economics Letters (Ai CR, Norton EC. 2003. Interaction terms in logit and probit models. Economics Letters 80(1): 123-129) seeks to "present the correct way to estimate the magnitude and standard errors of the interaction effect in nonlinear models." Particularly since the authors provide accompanying Stata code, the methods in the paper have become fairly prevalent. Unfortunately, leading lights in the modelling of discrete variable have rasied serious concerns about these papers. Specifically, William Greene concludes that
"The preceding does not fault Ai and Norton's (2003) suggested calculations. Rather, we argue that the process of statistical testing about partial effects, and interaction terms in particular, produces generally uninformative and sometimes contradictory and misleading results. The mechanical reliance on statistical measures of significance obscures the economic, numerical content of the estimated model." page 295 of Greene W. 2010. Testing hypotheses about interaction terms in nonlinear models. Economics Letters 107(2): 291-296.
Patrick Puhani demonstrates that the quantity calculated by Ai, Wang and Norton's is not the relevant quantity when one wishes to understand treatment effects in non-linear models, although it is relevant to other cases. (Puhani PA. 2012. The treatment effect, the cross difference, and the interaction term in nonlinear "difference-in-differences" models. Economics Letters 115(1): 85-87). Interestingly, the discussion paper that proceeded the published paper (Puhani PA. 2008. The treatment effect, the cross difference, and the interaction term in nonlinear "difference-in-differences" models. IZA Working Paper No. 3478, http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1136279 ) is more bluntly critical.
Based on the subsequent critique, I'd probably avoid the method of Ai and Norton, not because it is "wrong" in terms of the underlying mathematics, but because the output it provides is in many cases uninformative or even mis-informative for the types of questions we often ask. At a minimum, one should have a clear understanding of the concerns raised by Greene and Puhani before deciding to use it.
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Grigorios Livanis, Ph.D.
Assistant Professor
International Business and Strategy
D'Amore-McKim School of Business
Northeastern University
319 Hayden Hall
Boston, MA 02115
617.373.4801