Logit Transform

 

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Logit is a common transformation for linearizing sigmoid distributions of proportions (Armitage and Berry, 1994). The logit is defined as the natural log ln(p/1-p) where p is a proportion. For example, the number of insects killed by the log dose of an insecticide might describe a sigmoid relationship, which is a rectangular hyperbolic relationship to the non-log transformed dose. This sort of quantal response situation is often treated as a linear problem after logit transformation. Logistic regression uses these principles.

 

You can supply proportions or discrete data for logit transformation. If you specify discrete data then StatsDirect converts these to proportions by taking each value as a proportion of the maximum of the supplied data. The results are stored in a new column that is marked Logit:<name> where <name> is the original column label.

 

StatsDirect marks indeterminable values as missing data, i.e. p=0 or p=1. StatsDirect logistic regression, on the other hand, provides a more complex treatment for this situation whereby p=0 or p=1 contribute to the overall regression.

 

Another definition of a logit is 0.5*ln(p/1-p), this just brings values numerically closer to probits.

 

An attractive feature of logits, which has contributed to the popularity of logistic regression, is that the difference between two logits can be seen as an odds ratio. This situation arises when comparing points on fitted logistic regression lines.