We are in the process of analyzing some data to see if a combination of pre-existing factors and factors associated with the current condition of a patient help to predict severity of current medical condition/disease (example: If previous exposure to tobacco smoke [pre-existing factor]; and current signs on physical exam and histological pattern [factors associated with current condition] help to predict severity of lung tumor).
We had two continuous variables, and a bunch of categorical variables as predictors; and a categorical variable as the outcome. All independent variables are significant predictors in univariate analyses. When we include two continuous as well as other categorical variables together in a logistic regression model, only two continuous variables turn out to be significant predictors. If we remove either of those two and run the model again, then at least three categorical variables show significance. When we transform two continuous variables in categorical ones, then also we get other variables as significant besides these two. None of the predictors shows collinearity.
My supervisor asked me- Is it possible that any of the continuous variables mask the effects of other predictors? If it is the case, how can we address the issue? If we remove any of the continuous variables, how can we justify that? If we transform continuous variables into categorical ones, what will be the explanation for that? I am not able to find satisfactory answers to these questions. It will be great if you can help answer these questions.
A couple of (I hope) at least someone relevant, if not helpful, notes:
1) It is vitally important to distinguish between statistical significance (in the sense of p values and whatnot) and predictive power, or at least to understand how these relate and what they mean. For example, I can probably perfectly predict that, given a person who doesn't drink water, that person won't be an alcoholic. I can likewise show that drinking water and alcoholism are (statistically significantly) correlated. However, I cannot build a model that predicts alcoholism given that a person drinks water. This is why null hypothesis significance testing (the "if p
I see that you have checked the collinearity between predictors. If no multicollinearity exist (shown if VIF higher than 10), I don't think any such masking would occur. If you still think the masking exist and don't want to eliminate other predictors, I suggest you to employ factor analysis prior to the regression and use the factors as predictors since factor analysis should produce (near) uncorrelated factors.
A couple of (I hope) at least someone relevant, if not helpful, notes:
1) It is vitally important to distinguish between statistical significance (in the sense of p values and whatnot) and predictive power, or at least to understand how these relate and what they mean. For example, I can probably perfectly predict that, given a person who doesn't drink water, that person won't be an alcoholic. I can likewise show that drinking water and alcoholism are (statistically significantly) correlated. However, I cannot build a model that predicts alcoholism given that a person drinks water. This is why null hypothesis significance testing (the "if p
That sounds like "negative confounding". Usually, people think of confounding as masking (or attenuating) the true association. But in some cases, a confounder can have the opposite effect. Try Googling . Also take a look at this article by MacKinnon et al.
http://link.springer.com/article/10.1023/A:1026595011371
HTH.
Aakash - I would be hesitant to transform continuous variables to categorical ones, as it would seem to me to be throwing away possibly some of your best information. Looking at the interesting comments above, I have a few observations: I'm not big on VIF factors or significance because they are rather nebulous. (A p-value is a function of sample size, so changing your sample size can change your conclusions.) Scatterplot graphs are very informative. Negative confounding does sound like an interesting topic to research. - Finally, I think you may want to look at the impact your proposed model changes have on the variance of the prediction error. Graphing those results may be very informative. - Thanks - Jim
@Andrew Messing: I would give 7 up-votes :)
One more advice: In models with continuous predictors it is recommended to use the centered (or even standardized) values, especially when interactions are part of the model.
And a least advice: Consult a statistician.
As Rafael indicated, it would be interesting to hear something about sample sizes used here.
Dear Aakash
You did not mention about the sample size. For any study, the size of the sample is very important. As we know in many studies the fallacy of small sample size is not considering. If your sample size is very small and when distributing that to different cells, the cell value will be very small. I think both way you have to think. One is multicollinearity and the other is sample size.
Yes. A confounding variable is a variable which is a risk factor for the disease (response) and is associated with the risk factor but is not a consequence of the risk factor. When this confounding variable is not adjusted for the association between the risk factor and disease can be highlighted or masked.
One more point. One can have multiple association without multiple co-linearity. One must check for linearity (or any other assumptions) in the final model that is produced. And, as others have stated, prediction is not the same as causation. The current issue of the American Statistician has a series of articles on Simpson's paradox which is well worth reading.
Why do not you try using multimodel inference based on, for example, Akaike criterion? Having competing models you might have estimated relative importance of each variable, averaged estimates of function slopes and confidence intervals... and you would not need to calculate P values. Moreover, you would be able to see how variables behave in different models.
One question more. How did you check multicollinearity between categorical variables? What I would have done first, is building simple logistic regression models between continuous covariates and independent categorical variables to see if they respond in similar way as your original dependent variable (inication of redundancy in dataset).
You may want to look into the effects of "suppressor variables" here. I have attached an excerpt from an excellent multivariate statistics book by Tabachnick and Fidell that discusses the role of suppression in multiple regression models.
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