This essentially means that attrition is probably not affected by observables. I ran probit regressions using different sets of lagged outcomes (such as lagged costs, hospitalization status, disability status etc.)and none of the models predicted >10% variation in non-attrition. They call the lagged outcomes as auxillary variables. Fitzgerald and Moffit (1998) developed an indirect method to test attrition bias in panel data by using lagged outcomes to predict non-attrition. If there is no way to determine MAR, will it be fine to use a weighting procedure based on the theory of selection on observables ? For e.g. SES, maternal characteristics, family income etc.). Key characteristics that could affect attrition are not observed in my data (e.g.

I get your point about the criteria for MAR, that the missigness should not depend on the value of the datum. Thanks for clarifying about the incidental parameters problem. вЂњ Logistic Regression in Rare Events Data.вЂќ Political Analysis 9 (2001): 137-163. You can learn more about penalized likelihood in my seminar Logistic Regression Using SAS. Does anyone have a counter-argument? If so, IвЂ™d like to hear it. In fact, a case could be made for always using penalized likelihood rather than conventional maximum likelihood for logistic regression, regardless of the sample size. Unlike exact logistic regression (another estimation method for small samples but one that can be very computationally intensive), penalized likelihood takes almost no additional computing time compared to conventional maximum likelihood. In the case of logistic regression, penalized likelihood also has the attraction of producing finite, consistent estimates of regression parameters when the maximum likelihood estimates do not even exist because of complete or quasi-complete separation. Also called the Firth method, after its inventor, penalized likelihood is a general approach to reducing small-sample bias in maximum likelihood estimation. Their method is very similar to another method, known as penalized likelihood, that is more widely available in commercial software. WhatвЂ™s the solution? King and Zeng proposed an alternative estimation method to reduce the bias. So even with a sample size of 100,000, if there are only 20 events in the sample, you may have substantial bias.

And the degree of bias is strongly dependent on the number of cases in the less frequent of the two categories. The problem is that maximum likelihood estimation of the logistic model is well-known to suffer from small-sample bias. ThereвЂ™s nothing wrong with the logistic model in such cases. If your sample has 100,000 cases with 2000 events, youвЂ™re golden. If you have a sample size of 10,000 with 200 events, you may be OK. If you have a sample size of 1000 but only 20 events, you have a problem. The problem is not specifically the rarity of events, but rather the possibility of a small number of cases on the rarer of the two outcomes. Although King and Zeng accurately described the problem and proposed an appropriate solution, there are still a lot of misconceptions about this issue. Prompted by a 2001 article by King and Zeng, many researchers worry about whether they can legitimately use conventional logistic regression for data in which events are rare. Logistic Regression for Rare Events FebruBy Paul Allison

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