Hi fellows,
Say I want to investigate the association between car preference and age. Then I have data from 100 people who like SUV, and another 100 who like classic models. As expected, A t-test shows that SUV lovers are significantly younger. The problems is that, apparently aging can change one's car preference but not vice versa, so age should logically be the IV and car preference the DV.
The issue may be simple as stat courses I've learned suggest a logistic regression, but recently I've seen the practice above (on some real variables) in several unpublished graduate-level manuscripts and would like to know whether there's any reason (that I do not know) to do this, or why even trained colleagues can fall into this trap.
Thanks
Meng
Hello Meng,
Yes, you may regress car preference on age via logistic regression. Establishment of a systematic relationship does not, of course, suffice as cause-effect evidence. Perhaps that is the "trap" to which you refer?
Good luck with your work!
Cause is not relevant in your example. That you demonstrate an association between car choice and age does not support a causal association in either direction, only an association. With such evidence one can assert that these two variables are related, which means that a significant amount of variance in car choice can be predicted from age, but it also means that a significant amount of the variance in age can be predicted from car choice. This may not be the logical way one might want to think about it, but the statistics you use to measure and test association are ignorant of such directionality.
Another, more technical, way to look at it is that you have a t that shows that age is significantly different between two groups constituted by those who like SUVs and Classic cars (with those who like SUVs with a younger mean). Let's change the question from difference to relationship. Rather than ask whether there is a difference in the age of those who prefer SUV and Classic cars, let's ask is there a relationship between car preference (SUV or Classic) and age. Further, let's code car preference as SUV=1 and Classic=2. Now, calculate a Pearson r between this car preference variable and age. You will see that these are the same statistically directionless questions, as the r yields the same information and p-value as the t you have calculated, for they are algebraically related as: t = SQRT((n - 2)*r2/(1 - r2)). I have selected "1" and "2", but, of course, it does not matter what values you use to represent car preference, and the sign of r will depend on which is larger, SUV or Classic. Here, because those who selected SUVs are younger and I selected a smaller number to represent them, the correlation will be positive.
Form observational data alone you can not conclude causality. From this point-of-view it is irrelevant if you model age by group (likes SUVs or not) or group by age.
If you want to predict the age of a person of which you know if this person likes SUVs or not, then modelling age by group would be helpful. If you know the age of a person and you want to predict of this person likes SUVs, then modellinig group by age is helpful.
A possible "trap" you are in is that the variable "likes SUV" (or "preferrs SUVs over classic models") may not be as good a variable as you hope:
First, it's dichotomous. It would be better ist this would be a gradual (ideally continuous) measure that puts a value on the "degree of preferrance".
Second, the terms SUV and "classic cars" may not be well defined. If you mean with "classic cars" actually modern cars, but not SUV-like cars, this might be misunderstood, particularily by younger people.
Third, not all people have a sufficiently solid knowledge in car types to judge what an SUV is or that there exist "classic cars" that they would much prefer over the SUVs they know too well see too often (you may get the answer that SUVs are preferred just because people are used to these types and think that anything else is "outdated", "unfashioned", "strange" or "exotic").
Forth, the usefulness (value) of that variable depends on how it is measured. If you ask people if they prefer SUVs, you have to take great care that their answer is not influenced by circumstances that you are not aware of (for instance, people may give answers that hey hope would impress the persons how do the survey, or they want to provoke, or they are scared to be honest etc).
Fifth, if the measure is self-reported, it may not at all be connected to any possibly relevant conclusion. For instance, younger people may say that they prefer SUVs, but they would not buy one. This is also an example for the fact that such judgements are always conditional, and the conditions need to be known and fixed in the survey (e.g., given amount of money to spend for a car, given running costs, given possibilities to park the car, given a use-case [driving to work, shopping, holidays; how long, what roads, etc]). The answers may very much depend on such conditions.
Try to address age as a confounder and try whether it has any effect on preference
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