I am interested in a relationship between adolescents' thoughts about cigarettes (e.g., how many times have you thought about cigarettes in the past day?) and cigarette use (e.g., how many cigarettes did you smoke in the past month?), where both measures are continuous. With a longitudinal study (e.g., three-wave study), it would be possible to examine if cigarette thought would predict cigarette use, cigarette use would predict cigarette thoughts, or both (i.e., a reciprocal relationship).
However, if I conduct a cross-section study, where I would measure the above two variables and some demographic variables (e.g., gender, ethnicity, etc.), could I do more than a correlational analysis??
For example, would it be reasonable to conduct two multiple regression analyses with cigarette thought as DV, cigarette use, gender, and ethnicity as IVs in one model, and then switch DV and one of IV (i.g., cigarette use <-> cigarette thoughts) in a next model? I am aware that you should stop at a correlational analysis when you do not have a specific hypothesis about two variables; however, I feel that even within a context of a cross-sectional study, it may be fine to run two multiple regression analyses to examine different predictable relationships between two variables as long as you do not talk about a 'causal relationship.'
Is this reasoning wrong? Any inputs would be greatly appreciated.
Best Answer
In the linear regression model, it is assumed the independent variable, $X$, is measured exactly and the dependent variable, $Y$, is observed with measurement error. The measurement error in $Y$ is accounted for with the $\epsilon$ term in the model. Therefore in most cases it is clear which variable is $X$ and which is $Y$.
If you do perform a regression where $X$ is not measured exactly you must account for this in the model! Ordinary linear regression no longer suffices...