In the idealized logistic model, we obtain an S-shaped curve linking each continuous IV to the DV. But in practice this infrequently happens, making the logistic approach seem a little less superior for such types of data. Of course predicted probabilities that each observation will be "1" on the DV are usable in logistic and not in OLS regression, since in the latter these probabilities can exceed the bounds of [0,1]. But, for exploratory purposes, how sound is it to use OLS to see which IV have strong vs. moderate vs. weak relationships with the DV? Wouldn't this amount to a sort of multivariate version of point-biserial correlation? (Standardized regression coefficients, not to mention collinearity statistics and partial plots, are all I think more easily obtained in OLS than in logistic.)
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If the explanatory variables have values over the entire real line it makes little sense to express an expectation that is a proportion in $[0,1]$ as a linear function of variable defined over the entire real line. If the sigmoid shape of the logit transformation doesn't describe the shape then perhaps it is best to search for a different transformation that maps $[0,1]$ into $(-∞ , ∞)$. |
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