I have a survey data where respondents were asked if they or an immediate family member had previously used a lawyer and, for those who said yes, they were then asked if they had ever sued.

I want to estimate the likelihood of suing using a logit or probit model but I am concerned that my estimates will be biased because answers to question are only observed for those who have used a lawyer (I believe this would be a case of "incidental or indirect selection" as described by Berk, 1983).

Of course it is possible to sue without a lawyer - small claims court - thus the screening question asking about previous use of a lawyer is not an appropriate screen but the data are what they are I have to make the most of them.

Do I attempt to address this using a heckman type adjustment or can I safely ignore it and proceed with logit/probit? Is there a better alternative?

Reference Berk, R. A. (1983). An introduction to sample selection bias in sociological data. American Sociological Review, 48(3): 386-398.


Censoring is a special type of missing data. You are describing missing data, but not censoring. Censoring refers to time-to-event outcomes where there is an interval of time in which the outcome of interest may or may not have happened: you don't know.

You are right in saying that there may be some small proportion of the sample who has sued not using a lawyer. Furthermore, the proportion of respondents who did use a lawyer for any reason, cannot in any way be taken to be representative of those who did not use a lawyer. Therefore, this is a kind of "missing not an random" problem, so it is basically impossible to borrow information across groups in anyway.

Rather than going about some complex kind of methodology which is heavily dependent on modelling assumptions, why not just refine your question? You can confidently, instead, answer the question, "What is the likelihood of suing given an individual has some history of consulting a lawyer?" This is an accurate representation of the data. You can go on further to report, "X.X% of the sample reporting some history of consulting a lawyer." And "We believe that those whose family has used a lawyer are most likely to sue, so that overall the likelihood to sue is at most Y.Y% regardless of family legal history."

I would not believe the assumptions behind the Heckman correction, and I would review such an analysis critically saying that you are trying to answer questions that are not available in the data.

  • $\begingroup$ Thanks for the superb answer. I agree, in retrospect it isn't censoring. I think the original designers were thinking of this like wages - they're only observed for those who choose to enter to work force. My original thought was to reframe the meaning of the estimated parameter as you have suggested but my concern was that the estimate would still be biased. $\endgroup$ – whauser Nov 9 '15 at 19:01
  • $\begingroup$ @whauser technically speaking, you're right that it's biased. But as Donald Rumsfeld said, "It's a known unknown." In these situations, it's important to present the unbiased estimate (aka the prob of suing given lawyer), and then describe how the actual question was not answered, but that the results insinuate it's in the following range: Lower= Prob(Lawyer)*Prob(Sue|Lawyer), upper = Prob(Sue|Lawyer). $\endgroup$ – AdamO Nov 9 '15 at 19:36

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