I am currently studying the effect of atrophy of a muscle on the clinical outcome of joint injury. There is actually another muscle that was previously well established to have an effect on clinical outcome, and both these 2 muscles are closely related. The aim of the study was to shed some light on the previously ignored muscle to see if there is anything that can be done to help improve clinical outcomes in that aspect.
While doing univariate analysis, i wasnt sure if i should include the previously established muscle as well and when i included it into the multi-linear regression model, the initially significant primary variable became insignificant. I was thinking if this could be due to co-linearity but the VIF value was not high enough to show significant co-linearity in the two variables. (GVIF ^(1/(2*Df))=1.359987)
My question is, should these 2 variables be included in the same model if they are both highly correlated (clinically and mathematically) but was not determined to have co-linearity, or should these 2 variables be evaluated separately?
Bryan Soh, your question is a good one. I think it's necessary to be familiar with the nature of your variables (which it seems you are). Unfortunately, I'm not, but might I suggest that you conduct your analyses both ways, look at the results, then think carefully about which results are likely to be most valid.
I also think it is a good idea to present both sets of results if that's permissible. As you are obviously aware, the world of research isn't black and white, and making other researchers, and consumers of research, aware of that could well be helpful. About 20 years ago, I read an article in a top psychological journal in which the author analysed her data in more than one way (from memory, it was more than only two ways), and she discussed the ins and outs intelligently and with insight. It was, for me, much more enlightening that the run-of-the-mill articles that seem to report unambiguoous results but leave the reader wondering how much cleaning up and manipulation, and obscuring, occurred to obtain those results.
Every good wish as you plough on!
Bryan Soh, your question is a good one. I think it's necessary to be familiar with the nature of your variables (which it seems you are). Unfortunately, I'm not, but might I suggest that you conduct your analyses both ways, look at the results, then think carefully about which results are likely to be most valid.
I also think it is a good idea to present both sets of results if that's permissible. As you are obviously aware, the world of research isn't black and white, and making other researchers, and consumers of research, aware of that could well be helpful. About 20 years ago, I read an article in a top psychological journal in which the author analysed her data in more than one way (from memory, it was more than only two ways), and she discussed the ins and outs intelligently and with insight. It was, for me, much more enlightening that the run-of-the-mill articles that seem to report unambiguoous results but leave the reader wondering how much cleaning up and manipulation, and obscuring, occurred to obtain those results.
Every good wish as you plough on!
You say that the two variables are correlated both clinically and mathematically. If, by "clinical correlation" you mean that some underlying process has a role in generating the atrophy of both muscles, then a variable transformation may help you understand the results. That is, if instead of using "level of atrophy" (however measured) in your two muscles, you can create a variable that reflects the impact of the underlying process on the two muscles jointly (sorry for the bad pun!!), and then have your second variable be the differential atrophy of the muscle of interest, you may be able to understand your results a little more clearly. Note that because this change of variable is assumed to be linear, you are not actually "doing" anything mathematically, but now if your differential variable comes back insignificant, you have failed to reject the hypothesis that it is the underlying process that matters, not the separate levels of atrophy of the two muscles individually. And if the differential variable comes back significant, you really know something.
One more thing: My experience is that the rules of thumb for VIFs are too generous. Some say "4 is OK"; if what I'm trying to do is measure differential impact of two variables, I get really nervous with a VIF over 2.
Hi Bryan,
I would definitely drop one of the two variables, as you have a high multicollinearity in your model, which is against the basic principles of correlation analysis. If you have this large correlation among your explanatory variables, your coefficient estimates will be quite biased, which leads to biased interpretations as well. You could include an interaction of your two variables in the model and then inspect your model. This should absorb this correlation a bit. Often, one of your coefficients will then be statistically insignificant and can be left out easily. Also try out different models and compare them, e.g. by AIC, BIC, AICc. At the least your model won't be the most efficient one.
Best!
There is a very simple test to assess multicollinearity in your regression model. The variance inflation factor (VIF) identifies correlation between independent variables and the strength of that correlation. Statistical software calculates a VIF for each independent variable. VIFs start at 1 and have no upper limit. A value of 1 indicates that there is no correlation between this independent variable and any others. VIFs between 1 and 5 suggest that there is a moderate correlation, but it is not severe enough to warrant corrective measures. VIFs greater than 5 represent critical levels of multicollinearity where the coefficients are poorly estimated, and the p-values are questionable. Use VIFs to identify correlations between variables and determine the strength of the relationships. Most statistical software can display VIFs for you. Assessing VIFs is particularly important for observational studies because these studies are more prone to having multicollinearity.
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