I’m performing a binary logistic regression and my linearity of logit assumption for one of my independent variables (total scores) is not being met.
My only option that doesn’t require very complicated statistics is to transform my variable. However, I’m worried now that interpreting the results would be very difficult.
1. Should I bother meeting the assumption if the results are the same? As in if I meet the assumption or if I don’t I still get the same end result.
2. From my understanding you should not perform a Box-Tidwell transformation to test the linearity of logit on variables that contain values of 0 or negative numbers. However if I Log(natural) transform my variable to fix the assumption not being met, I end up with values of 0 and therefore not being able to perform the Box-Tidwell transformation to check if the assumption is met. So what would I do in this instance?
Any help would be much appreciated I don’t have access to a statistician to ask. Also I’m using SPSS, and my data has over 600 participants.
Linearity of the right hand side does not mean of the predictors but rather of the regression coefficients. As long as you don't have a term that's nonlinear in the regression coefficient eg sin(b)*x1 you have nothing to worry about.. Best wishes, David Booth
Hello Tara Chammas
Please take a look at the link below.
https://www.statisticssolutions.com/free-resources/directory-of-statistical-analyses/assumptions-of-logistic-regression/
https://www.ibm.com/docs/en/spss-statistics/24.0.0?topic=option-choosing-procedure-binary-logistic-regression
I have also sent you a PDF file of a webinar. It has useful content.
Abolfazl Ghoodjani I just read through the links, in the last link, the webinar states "Don’t worry about the significant interaction if the sample sizes are large.". This is very interesting, do you know where I can find a reference for that? As I have not seen that statement being made in any textbook I have searched.
David Eugene Booth Thank you for your reply. I am only a beginner with statistics and unfortunately I don't understand what you mean. How do I check If I don't have a nonlinear regression coefficient?
Tara in your case it doesn't matter is what I said. David Booth. NB Monash university was R.A. Fisher's last professor appointment. ,He is buried there.
I do not think that you have said how do you know that the underlying relation on the logit scale is non-linear. How so? The logit model is already non-linear so often it is sufficient.
If you want to be re-assured you can fit a GAM model; the output is essentially a graph which will show you the degree of non-linearity it is available in the freely available R software.
https://datascienceplus.com/generalized-additive-models/
For background see
Article “Moving Out of the Linear Rut: The Possibilities of Generali...
Article Generalized Additive Models, Graphical Diagnostics, and Logi...
@Kelven I think she meant she had a b*x"x term on the RHS. David Booth
Kelvyn Jones Thank you for your answer, from my understanding prior to progressing with my logistic regression there needs to be a linear relationship between any continuous independent variables and the logit transformation of the dependent variable. To test this assumption I used the the Box-Tidwell procedure. I added an interaction term between my continuous predictor and the natural log transformed version of that predictor. My interaction term was significant in the model, therefore the assumption of linearity of logit was not met.
Thanks to the two of you, now understood a bit more, but Tara said at the outset she was unable to fit the additional variable with a transform.
the GAM is useful as it is a much more flexible procedure than a quadratic.
Kelvyn, I absolutely agree with you about GAMs. However I suggest that if we are having difficulties with one x**2 term perhaps a GAM is not yet feasible.. I learned GAMs with the Michaelis and Menten model of enzyme kinetics and found it somewhat difficult. I still suggest we do our best with x**2 and perhaps go from there. Best wishes to all, David Booth
Tara Chammas , I am confused. What is your dependent variable (I assume it is binomial, perhaps even binary) and what is your model? You said one of your variables isn't linear. As Kelvyn Jones says, you could allow a more flexible model and in particular allow this one variable to be more flexible (google splines).
Quoting from the first line of the original question (and adding emphasis):
I’m performing a binary logistic regression...
;-)
As long as we doing this, Kelvyn as you have often said here logistic regression is a linear model. It has nothing to do with the logit function. David Booth
Tara
this is a free online course that may help your understanding of the binary logit model and the interpretation of results
http://www.bristol.ac.uk/cmm/learning/online-course/course-topics.html#m06
David Eugene Booth, I am trying to understand how a binary logistic regression model, aka., a binary logit model, i.e., a generalized linear model with a binomial error distribution and a logit link function, has "nothing to do with the logit function". Can you clarify what you mean? Thank you.
@Bruce, please look at my last post previous to the one you comment on. The question was about a quadratic term in a linear model .that question has little to do with a logit function. Should you still be concerned about my current opinion on logistic regression you will find it in the attached authors proof. I believe that you have had an opportunity to view earlier versions in that discussion about why stepwise regression doesn't work. Perhaps you could review my thoughts on that subject and questions are always welcome here. David Booth
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