There are several independent variables and several dependent variables. I want to see how those independent variables affect the dependent variables. In other words, I want analyze:
[y1, y2, y3] = [a1, a2, a3] + [b1, b2, b3]*x1 + [c1, c2, c3]*x2 + [e1, e2, e3]
The main problem is that y1, y2, y3 are correlated. y1 increases may have lead to decrease of y2 and y3. In this situation, what multivariate multiple regression models can I use? And what assumptions of those models?
BTW, the purpose is to get good estimation of [b1, b2, b3] and [c1, c2, c3].
Hello Jialing,
The fact that DVs are correlated is often one argument for choosing a multivariate method to analyze the data rather than generating a univariate model for each individual DV.
If what you are saying is that, causally or temporally, is that Y1 influences Y2, then perhaps you'd be better off evaluating a path model which incorporates such proposed relationships rather than simply allowing for correlations/covariances other than zero among the DV pairs in the multivariate regression.
Good luck with your work.
Thank you for your answer! May I ask what are common multivariate methods? My goal is to get good estimation for the coefficient of interest.
This may help:
https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&cad=rja&uact=8&ved=2ahUKEwj19pWl5aL4AhUDNhoKHe57BgQQFnoECCMQAQ&url=https%3A%2F%2Fstatisticsbyjim.com%2Fregression%2Fchoosing-regression-analysis%2F&usg=AOvVaw3Bf2dmhFtFt2YH3XwaV5vA
Oluwaseyi Ayorinde Mohammed , Adeyemi Oluwole , David Morse
Thank you for your answers. But I don't think multinomial regression model will work. Because y1, y2, y3 are not categories of y. They are three separate dependent variables. There are three multiple regressions and I just wrote them in the matrix form. My independent variable x will affect all of the y1, y2, y3. And I am trying to get the coefficients of how x affects y1, y2, y3.
I am considering to use instrumental variable regression to see how x affects y1, y2, y3. But since y1, y2, y3 are correlated with each other, I am not exactly sure if the coefficients are biased if I apply the regression separately. Therefore, I am considering how multivariate multiple regressions can help solve the problem.
Hello again Jialing,
Without knowing more, it's difficult to understand how seeking instrumental variable(s) for your IVs will help alleviate anything with respect to whether the DVs correlate or not.
You asked about multivariate methods in your response. Again, given that your DVs are not independent, multivariate methods are the preferred approach, in my opinion. For data sets such as yours, I suggest the most likely options would be:
1. multivariate regression (your original plan); or
2. canonical correlation; or
3. manova (which duplicates information in #1 and #2).
The goals of each differ, so the choice may hinge on your specific research aims.
If you wanted to know what pair of linear combinations of variables: one for the IVs and one for the DVs, yielded the highest correlation, then canonical correlation will give you this result. Yes, collinearity among either variable set can and will influence the estimated regression coefficients for a set of variables.
Your original query and follow-ups make it sound as if multivariate regression would still be the preferred method. It yields estimated coefficients for each IV on each DV...further, if desired, you may statistically compare the regression coefficient for a given IV for equality across any pair of DVs. So, the concern about DVs being correlated still doesn't raise any flags to me for trying to achieve this outcome.
Good luck with your work.
Your question (here in the comments) is rather broad ("May I ask what are common multivariate methods?"). Try STAT750 Multivariate Analysis (3 Credits) at your university. Or google.
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