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I have a dataset (N=350) for which I would like to regress a neuropsychological test score (continuous) on age, education, symptom severity (continuous), and diagnosis (binary). Symptom severity is censored: symptom severity score was only generated if a participant passed a screening item. It appears that a tobit model would work for predicting symptom severity as the dependent variable, but is there a defensible method to include my left-censored variable as a predictor?

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    $\begingroup$ Asked and answered at stats.stackexchange.com/questions/1444/…. But the two questions look so different it makes sense to let them both stand, with these links between them. $\endgroup$
    – whuber ♦
    Commented Oct 9, 2012 at 22:04

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One option is to include a variable that is 1 if symptom severity was not measured and 0 otherwise, then code all the symptom severities that were not measured as 0. The coefficient on the 0/1 variable will represent the average test score for those that did not have the severity measured and the slope for the severity will be computed based on those that had severity measures.

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    $\begingroup$ Hi Greg, a long ago answer back to haunt you. I am having a bit of difficulty interpreting this. For example, if I have two variables y, and x, and x is missing below a certain level.(which i assume is due to censoring).. The coefficient of x (where y is regressed on x) is the same when using this technique of adding the dummy variable, as when using a complete case analysis when it was missing. Is this technique more for prediction rather than inference? Wont the x coefficient be biased using either technique? Thanks $\endgroup$
    – user20650
    Commented Oct 22, 2015 at 18:54
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    $\begingroup$ @user20650, with only 1 predictor variable you will see the same slope estimate (but the standard error could be different). If you have multiple predictors then this method may allow you to use points where most are observed. $\endgroup$
    – Greg Snow
    Commented Oct 22, 2015 at 19:00

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