# Does control get us closer to or farther from causation?

In logistic regression with an N of 40,000, purchase decision is unrelated to price. However, with certain demographic variables controlled, price can show a positive coefficient of meaningful strength. (Searches for 2-, 3-, and 4-way interactions involving price have yielded nothing.)

The goal here is to maximize the leverage one can get out of discounting. There seems to be a real risk of confusing the "real" relationship with one that, in the words of Elazar Pedhazur, has an "air of fantasy about it" due to statistical manipulation (regression control). Any suggestions as to how to proceed?

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Alternatively, one could interpret the initial results of no relation as the "statistical fantasy," because the subsequent "meaningful" relationships found upon controlling for demographics suggest the original model was a bad fit to the data. What results do your goodness-of-fit tests and other model diagnostic tests show? –  whuber Feb 17 '12 at 18:08
Over many regression trials on subgroups, here's a fairly typical set of results when only price was used as a predictor vs. when 4 other vars were controlled: N=2958, -2LL= 2534 vs. 2210, Chi-Square= 6 vs. 329, p = .02 vs. <.0001, Cox&Snell pseudo RSQ= .002 vs. .11, correct classification rate= .846 (same as in null model) vs .841 (!). Actually in most cases the latter did improve a little. Please let me know if you were looking for other indicators. –  Karl2 Feb 17 '12 at 22:29
That sure looks like including the covariates has improved things, but it's hard to say. Hosmer & Lemeshow describe several ways to check for approximate linearity of the logit versus the independent variables: that would be useful to do here. You might want to apply some robust methods, too, and see whether things change much (in both models) when you exclude outliers and high-leverage data. –  whuber Feb 17 '12 at 22:33
Thanks. Would checking for linearity between the logit and the Xs be akin to doing visual checks of scatterplots between Y and each X? Because those didn't reveal any nonlinearity. –  Karl2 Feb 17 '12 at 22:44
Re the question in the question text, causation cannot be obtained from any type of analysis, logistic regression or otherwise, it is based on study design. –  Michelle Feb 19 '12 at 18:53
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