Logistic regression

[div44]

Hello,

I am performing logistic regression using binary dependent variable. However, one of my independent variable is continuous in nature and has an inverted-U shaped distribution with my dependent variable. Since the association is not linear, I am unable to figure out how do I incorporate the desired independent variable in the model. One option is to categorize the continuous variable, but I want to avoid that.

Thank you.

[Reeza]

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@div44 wrote:

However, one of my independent variable is continuous in nature and has an inverted-U shaped distribution with my dependent variable. Since the association is not linear, I am unable to figure out how do I incorporate the desired independent variable in the model. 

Please clarify in detail, what assumption for logistic regression model are you concerned with and why do you think your data does not meet this assumption.

[div44]

Hello Reeza,

I am manily concerned with the non-linear association between my dependent variable and independent variable. The independent variable shows an inverted - U shaped distribution when plotted against the dependent variable. As for data which is right-skewed (cost data in general), log transformation are used to model costs as independent variables, however I am unaware of any such transformations whih are used to model data which is U-shaped or inverted-U shaped. 

A classic example I can think of is that of a disease affecting middle aged population the most, then elderly population and young population the least. If age was my independent variable, it would have led to an inverted - U shaped distribution.

I hope this is clear.

Than you

[Reeza]

Is that an assumption for logistic regression? I don't believe it is.

[pbwn]

i think dose response is often modelled using logistic regression so you might check that literature, eg they speak about biphasic dose response which i guess can be an inverted-U shape?

[Reeza]

The log odds need to be linearly related to your variable, not the two variables. So after conversion what does the relationship look like?

http://www.statisticssolutions.com/assumptions-of-logistic-regression/

[Ksharp]

Check EFFECT statement of proc logistic. 

You can use spline curve to fit the nonlinear relationship.

Calling @Rick_SAS

[StatDave · Accepted solution]

Adding an EFFECT statement that defines a spline effect for your independent variable is certainly one possibility if a simple polynomial model form (squared, cubed, etc.) isn't adequate. Another easy to implement approach is to use a Generalized Additive Model in either PROC GAM or the newer (available in SAS 9.4 TS1M3) PROC GAMPL. See the examples of using these procedures in the SAS/STAT User's Guide.

[stat_sas]

Hi,

You will get U shape distribution because you are plotting continuous variable against a binary variable which has only two values. A useful plot to detect nonlinear relationship is plot of the empirical logits in logistic regrssion.

[pbwn]

they couldn\t possibly obtain a U shape if they are plotting against a dichotomous variable, i would assume theyre are plotting against logit(y)