I have some difficulties to understand the practical solutions for the collinearity problem in mediation analysis.
In my model I have collinearity problem between X and M. X explains about 86% of the variance in M with positive association between them. In the path analysis, X has positive direct relatiionship with Y. Contrary to my expectation, M has negative and significant relationship with Y. I guess this is becouse of collinearity. I guess my result is misleading and not correct. How can I solve this problem? In path analysis, can I test a mediation hypothesis without the direct relationship between X and Y to avoid collinearity problem?
Thank you in advance
Best regards
It is imperative to do Data screening. The process involves checking for and dealing with missing data, which can be done by checking for the frequencies or using the “COUNTBLANK” function in excel.
You need to check for the engaged and ungagged respondents to determine outliers. Then check for normality, Linearity, Homoscedasticity, and Multicollinearity.
For details on the above, check the link below.
http://statwiki.kolobkreations.com/index.php?title=Data_screening
Regards
It may be due to normal distribution problems of the instruments in AMOS you can perform the mahalanobis distance to remove the atypical data.
Hello Abdallah,
colinearity concerns several predictors in one equation and the simple or aggregate relationship. This makes it difficult to identify unique estimates with a resulting higher standard error (expressing this uncertainty).
So the strong relationship between X and M does not explain the negative relationship between M and Y.
Given the unsually strong rsq of the first equation, perhaps the model is misspecified? What's the correlation between M and Y?
Best,
Holger
Dear @Holger Steinmetz
Thank you for your answer. The correlation between X and M is about 0.83. When I examined the relationship between M and Y controlling for X, the coffecient of M becomes negative and significant.
Hi, I asked for the correlation between M and Y?
It may be that in the equation of Y predicted by X and M together, colinearity might be an issue. But as I wrote, this strongly increases the SE which will ususally lead to non-significant effects.
Can you present a) the N and b) the full correlation matrix (attached in a word file)?
Best,
Holger
Holger Steinmetz This is the correlation matrix and the regression analysis.
Dear Abdallah,
of course I am no magician, but I created / simulated a scenario that would lead to your situation. I would be interested how you judge that scenario with regard to its theoretical plausibility.
According to my hypothesis and simulation, your correlation matrix and the behavior of the coefficients in the regression model very nicely concurs with an underlying data generating model, in which
a) M causes Y and X (!)
b) Y causes X
In simple words, Y is the mediator in the relationship between M and X.
Based on such a model, I simulated a data set that very closely resembles your observations--both with regard to the correlation matrix and the regression results. In the regression, I did not quite recreate the strong coefficient concerning the relationship between X and Y, however. I could imagine that there is an additional confounding variable involved increasing the relationship but that's another story.
I attached a word file that contains the R code. Download R (https://cran.r-project.org/bin/windows/base/R-3.6.3-win.exe) and simply run the code to understand the data.
So why does this happen? The answer is given by graph theory (Judea Pearl). Below I attached a paper in case you want to learn the principles (I highly recommend that).
The keyword is "collider bias". A collider is a variable in a causal system/model/graph that receives effects of at least two other variables such as A --> B
@Holger Steinmetz. Thank you very much for this answer. It is a very deep answer. I have to read about collide variables and correct my model if theoretically applicable.
Abdallah Alsaad, what I forgot is: If you take my data (and surely yours, too), and estimate the mediation model as i suggested, all parameters are positive, substantial and significant.
As I wrote, the question is whether such a model structure is complete nonsense from a theoretical point of view...
Best,
Holger
Dear Alsaad,
The structure of the diagram should be drawn, so that the relationship between variables can be seen, meaning the framework of thought. So when there is a discrepancy with the results of the calculation, it does not mean a mistake. Sorry this is just my feeling. thanks.
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