Proc LOGISTIC - meaning of UNITS statement

[pink_poodle]

Hi,

This can be tested experimentally, but I would like to prime the work with some discussion of variable distributions and primitive vs. advanced normalization. I have a distribution of times to be used in logistic regression. Majority of the times are short, so the distribution is skewed. I want to rank the times (i.e., bin them into groups of equal size) and use them as an ordinal variable.

• Is it the same as setting a unit change in time to group size in the UNITS statement?
• Ranked times will have a uniform distribution - is it legit to use such variable in PROC LOGISTICS?
• Should I be setting some sort of a reference level, or can I use the ranked time as a continuous-ordinal variable?

Many thanks!

[Reeza]

Personally, I would try regularization/standardization for variables before binning. 

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@pink_poodle wrote:

Hi,

This can be tested experimentally, but I would like to prime the work with some discussion of variable distributions and primitive vs. advanced normalization. I have a distribution of times to be used in logistic regression. Majority of the times are short, so the distribution is skewed. I want to rank the times (i.e., bin them into groups of equal size) and use them as an ordinal variable.

• Is it the same as setting a unit change in time to group size in the UNITS statement?
• Ranked times will have a uniform distribution - is it legit to use such variable in PROC LOGISTICS?
• Should I be setting some sort of a reference level, or can I use the ranked time as a continuous-ordinal variable?

Many thanks!

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[pink_poodle]

@Reeza, could you please be more specific?

[Reeza]

Are you familiar with the concept of variable standardization and why having variables with various different units are problematic?

https://statisticsbyjim.com/regression/standardize-variables-regression/

[pink_poodle]

Thank you, this is a very nice website. The times are all in minutes. If I subtract the mean from times to center them, many will be negative.

[Reeza]

A negative standardized value, means it's less than the average, which is informative in terms of comparisons and predictions, but may not make intuitive sense initially. For explanations and odds ratio, you could convert it back to the original scale though the non linear relationship makes it difficult to explain.

There are various standardization methods, not all would cause you to have negative values, e.g using a RANGE method. Here's a few from the PROC STDIZE documentation.
https://documentation.sas.com/doc/en/pgmsascdc/9.4_3.3/statug/statug_stdize_details01.htm

Are you looking to build a model for predictive power?

[pink_poodle]

I already built it with a continuous variable. Just trying to determine if there are additional benefits to be had from using time as an ordinal variable.

[Reeza]

Typically you lose information when binning/categorizing variables as already mentioned by @StatDave.

[StatDave · Accepted solution]

If you are saying that your question is about how to use a continuously-valued but positively skewed variable, TIME, as a predictor in a logistic regression model, then I suggest you simply use the variable, as is, in your model. Logistic regression makes no assumption on the distribution of the predictors. And categorizing a continuous variable simply throws away information that can be used to better model its effect. If the association between TIME and your response is complex, you can even use a spline on TIME (in the EFFECTS statement) to allow for as much flexibility as needed, or you could simply add higher order polynomial terms like quadratic, cubic, and so on. That cannot be done if the variable is categorized and used in the CLASS statement. Regarding the UNITS statement, that is only used to modify the odds ratio estimates computed after the model is fitted. The UNITS statement has no effect on how a predictor is used in the model.