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Thread: Violation of linearity assumptions - binary logistic regression - what to do?

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    Angry Violation of linearity assumptions - binary logistic regression - what to do?




    I am running a binary logistic regression with SPSS and unfortunately the assumption of linearity (Box-Tidwell procedure) are not met for the continous variables. Also transforming the data does not remedy this problem.

    I could build categories for the continous variables, however, building logical groups seems rather impossbile. Even if I build categories I can not interpret with regrad to the hypothesis.

    Do you know any scientific source that allows me to let the assumption of linearity unconsidered? If there is any way my hypothesis are met and it is easier for me to interpret the results.

    Looking forward to you response.

    Best,

    Chris

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    Re: Violation of linearity assumptions - binary logistic regression - what to do?

    It's been a while since I worked with logit, but I believe it primarily rests on the following assumptions: (a) lack of multicollinearity, and (b) independence of irrelevant alternatives (IIA). Correct me if I am wrong, but it really does not need a linear relationship between the dependent and independent variables, because it applies a non-linear log transformation to the predicted odds ratio.

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    Re: Violation of linearity assumptions - binary logistic regression - what to do?

    There are a number of non-linear regressions. All are very complex in my opinion and I don't know if they work with binary response variables. Splines are one way to deal with non-linearity, but they do not unfortunately generate parameters (or none that I know of do anyway).
    "Very few theories have been abandoned because they were found to be invalid on the basis of empirical evidence...." Spanos, 1995

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    Re: Violation of linearity assumptions - binary logistic regression - what to do?

    Thank you very much for the answer.

    You know any scientific paper who neglected the assumption of linearity? That would solve my problem

    Best,

    Simon

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    Re: Violation of linearity assumptions - binary logistic regression - what to do?

    Quote Originally Posted by beatoctane View Post
    Thank you very much for the answer.

    You know any scientific paper who neglected the assumption of linearity? That would solve my problem

    Best,

    Simon
    I am sure there are many....but it wouldn't solve your problem. In honesty very few of the papers using regression I have seen even comment on testing or correcting for errors. So it is impossible to know if in fact they did.

    Generalized Additive Models (GAM) address non-linearity but they are (in my humble opinion) complex and in some cases do not generate parameters (I believe this includes non-linear results). In that case they analyze the data through splines or similar approaches. I do not know if they address bivariate response variables.

    There is apparently a special form of logistic regression that is non-linear, but I have never heard of it.
    http://www.mathworks.com/help/stats/...egression.html

    Are you sure you have tried all the transformations suggested for non-linearity?
    "Very few theories have been abandoned because they were found to be invalid on the basis of empirical evidence...." Spanos, 1995

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    Re: Violation of linearity assumptions - binary logistic regression - what to do?

    You can use a generalized additive model (GAM) (search for it). (I don't know if spss can do that.) Then the continuous variable will be non-linearly related to the logit dependent variable. But it will be piecewise linear in the parameters. You will get nice graphs and significance tests.

    Edit:
    How about: Beyond Linearity by default: GAM

    Do google scholar search and lots of papers (and introductions) will be found. It is a big area.

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    Re: Violation of linearity assumptions - binary logistic regression - what to do?

    Some transformations to deal with non-linearity in case you missed one of these
    http://people.revoledu.com/kardi//tu...sformation.htm
    "Very few theories have been abandoned because they were found to be invalid on the basis of empirical evidence...." Spanos, 1995

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    Re: Violation of linearity assumptions - binary logistic regression - what to do?

    Quote Originally Posted by GretaGarbo View Post
    You can use a generalized additive model (GAM) (search for it). (I don't know if spss can do that.) Then the continuous variable will be non-linearly related to the logit dependent variable. But it will be piecewise linear in the parameters. You will get nice graphs and significance tests.
    In SAS you get nice graphs (such as splines) but you don't get parameters you can test for the non-linear variables. Of that is how I understood it when I read this topic. Whether this is generic to GAM, no parameters for non-linear relationships, or this is only the case in SAS, I am not clear on.
    "Very few theories have been abandoned because they were found to be invalid on the basis of empirical evidence...." Spanos, 1995

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    Re: Violation of linearity assumptions - binary logistic regression - what to do?

    thank you very much for your answers!

    It would extremely help me, when you can provide a paper when the assumption of linearity was neglected.
    If you have any reference I would appreciate that highly =)

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    Re: Violation of linearity assumptions - binary logistic regression - what to do?

    Quote Originally Posted by beatoctane View Post
    thank you very much for your answers!

    It would extremely help me, when you can provide a paper when the assumption of linearity was neglected.
    If you have any reference I would appreciate that highly =)
    Very few papers note they tested at all. You could go to almost any journal on logistic regression and use that. But that would be wrong because 1) someone else doing it wrong does not eliminate the problem and 2) they might have tested it and not reported this in the journal which has strict space limits. A better way to handle this would be to find a logistic regression in a journal that is in a similar area to yours and ask them how they addressed this issue.

    Or if you are at a university, which is my guess, you could talk to one of your colleagues in the STATS department. I am guessing they will point you to Generalized Additive Models. They might be willing to give you guidance how to actually do that if they are really nice. Its not for the faint of heart.
    "Very few theories have been abandoned because they were found to be invalid on the basis of empirical evidence...." Spanos, 1995

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    Re: Violation of linearity assumptions - binary logistic regression - what to do?


    Beat,


    What is your hypothesis? Does it include that variable?


    I would recommend running at least one GAM with a spline and look at the graph. That graph will help you understand the relationship and perhaps find appropriate cut-points (at the knots) for possible groupings of the variable or possibly address your hypothesis.
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