Hello Liu,

can you upload a graph / path diagram showing your model. Further: What do you and/or the reviewer consider as multicolinearity? And about which pairs of variables are we talking?

Best,

--Holger

You could look at the tolerance statistic (in SPSS under Linear Regression --> Statistics --> Collinearity diagnostics). The tolerance statistic is widely discussed in the regression literature (e.g., Cohen, Cohen, West, & Aiken, 2003).

Tolerance values close to 0 for a variable may indicate problems, especially if you get high standard errors for some of your regression coefficients and/or non-significant regression coefficients where you would expect them to be significant. In that case, the variable with low tolerance (which may be redundant) should perhaps be dropped. It does not sound like you have this problem though if your predictors are only moderately highly correlated. So your tolerance scores should be fine. You could report the tolerance statistics in the article (or your reply to the reviewers).

I agree with Holger Steinmetz the the key issue is which pairs of variables are supposed to be affected by multicolinearity. If your reviewer simply raised this as a general issue, then you might respond by incorporating the original correlation matrix into your paper.

I also agree with Christian Geiser that you could use ordinary least squares regression to examine the equations in your path model. In particular, mediation does not require any assumptions beyond OLS, it is simply a technique for interpreting direct and indirect effects.

Thank you Holger Steinmetz. I have uploaded my path analysis diagram.

Thank you David L Morgan for you advice.

Thank you Christian Geiser for suggestions.

I have decided to add VIF indicators when examining the effect of independent variables (i,e., grit, FLE, FLCA) on dependent variable (FLP).

Thank you.

For the following, I don't know, how PROCESS handles the expectable residual correlation between both mediators. So the following is just from a SEM perspective:

In a model with several mediators, there will be a certain correlation between the mediators. Hence, you have to come up with an assumption about the causes of this correlation. In a graph like that one you provided, you would simply assume that the solely reason for the correlation between both mediators is the common influence by the IV. This is often unreasonable. Hence if you think that there are other external common causes, this would be addressed by letting the errors of the mediators correlate.

Another scenario however is that there is an effect of one mediator on the other (instead or in addition). If you do not specify this effect, you will underestimate the indirect and total effect of x on y. Hence, this will bias these effects.

Now to the multicolinearity. Assume the "external common cause" aforementioned is correct, and you actually address this by estimating an error covariance, this will

1) lead to unbiased estimates of all parameters (x--> m1, x-->m2, m1 and m2 --> y)

2) With a rising influence of the external common cause (and hence, rising correlations and an increasing error correlation), the SE of the x-->m effects will increase (but not of the effects of the m's). Hence you loose power and you get wider confidence intervals (CI). The power issue is irrelevant once you have significant effects but the CI issue remains. Whether you call that "strong correlation" or "multicolinearity" depends on your definition. I tend to use the term for those cases of such high dependency that causes the algorithm to break down.

3) In my taste, the two much more serious problems of you model are

a) you have only one independent variable and no controls. So unobserved confounding of the x-m link, the m-y link and the x-y link opens the door for biased estimates.

b) a partial mediation structure opening the door to hundreds of equivalent models. Especially the latter is reason enough to never use PROCESS (or regression analysis) for testing mediation. The effects are completely uninformative.

See

Kline, R. B. (2015). The mediation myth. Basic and Applied Social Psychology, 37(4), 202-213. doi:10.1080/01973533.2015.1049349

Thoemmes, F. (2015). Reversing arrows in mediation models does not distinguish plausible models. Basic and Applied Social Psychology, 37(4), 226-234. doi:10.1080/01973533.2015.1049351

Antonakis, J., Bendahan, S., Jacquart, P., & Lalive, R. (2010). On making causal claims: A review and recommendations. The Leadership Quarterly, 21, 1086-1120. doi:10.1016/j.leaqua.2010.10.010

HTH

Holger

Dear All,

I have a problem somehow similar to Liu's. The problem is the multicollinearity of x on m (which is the mediator). The VIFs for these variables are around 20.

Here is the model:

x->m->y

the question is: is that a certified problem that the x and m variables are collinear?? or not?

I assume that as I am testing the regression effect of x on m so it is obvious that x should have a linear effect on m.

The problem is when going into the direct path with the model turn to y=x+m as x and m are multicollinear so the results do not contain an interpretable meaning and are somehow insignificant.

So, what should I do? Omit the "m" variable in the direct path? Holger Steinmetz

I would be thankful if you mind this question.

Hi Mostafa,

your first specification was uncomplete: When you have a partial mediation model, you have to clarify this from the start. I know, using path diagrams in the text field is impossible when you have more then one line. Hence always better ATTACH a small path diagram. Another possibility is to draw the graph with dagitty.net which allows you to "publish the graph" which only means that you get a link that you can post.

So now to your real question ;)

Multicolinearity as a label is much overused. Strictly speaking, it means that the software simply cannot estimate the effect of one variable because there is no specific information left due to a functional relationship between the two. In the extreme case, both correlate so highly that both are identical.

The point you refer to is, however, simply that the relationship between both leads to an increase of the standard errors (SE) of both predictors as the effect of one predictor is estimated while adjusting for the other. This is a continuous effect--that is within an increasing relationship, the SE continuously increase. Still the software does its job but you pay for that by getting more uncertainty.

In your partial mediation model, this happens when estimating the direct effect--which implies that the mediator is adjusted for. Hence, with an increasing effect of x on m, the SE of the x->y effect slightly increase. I just tried that with a small/quick Monte-Carlo simulation. The increase however, is as mentioned only slightly.

The situation is dramatically different when you have a simple regression model with to correlating predictors (x1, x2). In this case, rising correlation between both will strongly increase the SE of each of their effect on y.

So no problem in your mediation model.

(I did not understand the sentence beginning with "the problem...". Perhaps you can clarify. Again, a path diagram would help)

All the best,

Holger

Dear Holger,

First of all, thank you for the time you advocated for the answer.

Here I have attached the model I was talking about. Also, I bring the exact model and its results for clarification:

1- first path: m= x + Control variables + e

The result for the effect of "x" on "m"

coeff            se             t             p          LLCI          ULCI

x          .358614      .002584   138.768931      .000000      .353546      .363683

2- Direct path: y= x + m + Control variables + e

- Results of the direct path using Hayes mediation test :

Direct effect of X on Y

       Effect            se             t             p   LLCI   ULCI      -.009145      .002859    -3.198993      .001402     -.014751     -.003538

3- INDIRECT EFFECT:  x        ->    m       ->    y                  Effect       BootSE     BootLLCI     BootULCI             .008206      .003036      .002139      .014198

which is statistically significant for not having the appearance of null of zero between BootLLCI and BootULCI.

My problem is: when testing the multicollinearity of variables using the VIF test, I face the result of VIF of above 20 for both variables of "m" and "x" (FYI the correlation between "x" and "m" is also at a high level which is 0.972).

I just want to know that the high level of multicollinearity between "x" and "m" is a problem for interpreting the results or no it is a normal result because we were expecting collinearity, as "m" is somehow defined by "x" according to the first path?

Holger Steinmetz

Sorry, I forgot to mention you in the previous message and unfortunately, researachgate doesn't have a feature to add a mention in the edit mode!

Hi Mostafa,

regarding the last comment: I would further suggest also to add code or outputs of a model always in an attached txt file that allows you to use courier new as a fond. But your output is not complex so I could read it.

As I said, the issue is not on multicolinearity. The direct effect is significant which in addition to the results of my simulation yesterday shows that the SE are not the problem. The question is rather on causal misspecification. I would like to know whether the negative direct effect makes sense to you. It is often a strange result in partial mediation models that the indirect effect is positive and then there is this strange negative direct effect. This always rings my alarm bells because this is a typical result of confounding bias of the m-y link. The only way to solve this is to instrument m--that is find one or better 2 predicators of m which don't have an effect on y. This will allow running a TSLS regression or an SEM. Please do yourself a favor and avoid this PROCESS macro.

One side comment: Control variables have to be part of a model and thus graph., see

Tennant, P. W. G., Murray, E. J., Arnold, K. F., Berrie, L., Fox, M. P., Gadd, S. C., . . . Ellison, G. T. H. (2020). Use of directed acyclic graphs (DAGs) to identify confounders in applied health research: review and recommendations. International Journal of Epidemiology, 1-13. doi:10.1093/ije/dyaa213

Best,

Holger

Hi Holger,

Holger Steinmetz

I am asking you to guide me with my research analysis, your help will be highly appreciated.

My problem came from seeing different approaches used in how to analyze mediation with multicollinearity between the independent variables, where I can't remove or combine these variables together:

I conclude at this moment, that I shall start with the Multicollinearity test to observe VIF ( the previous researchers found VIF between independent around 18-24), Thus, I expected to have the same.

Then, I will analyze the model by using path analysis as a causal model.

My issue is deciding which method to use: Baron and Kenny's Procedures, soble test, etc.

and why some researchers used conformance testing instead of using path analysis to analyze the mediation. and how they select the approach and methods.

Hello Ahmad.

As always, it is very helpful to clearly differentiate between causal identification (which refers to the population level) and estimation (which refers to the sample level).

Lets first consider it with regard to identification:

When your independent variables correlate, the estimated effect on v5 will be adjusted for that. Whether this is problematic depends on the cause their correlations. When you specify the model as you did, you tell me that your suspicion is that the correlation (e.g., between v1 and v3) is due to ommitted common causes. If this is correct than you adjustment will work (of course you should really think about whether there are omitted confounders of the various links between the predictors and the mediator and outcome. You can use dagitty especially for that.

If however, the correlation between v1 and v3 is not due to omitted confounders but stems from one variable causing the other than you will "overcontrol" a distal variables total effect on v5. Again: You have to come upt with your assumptions.

Now let's switch to the sample (and the multicolinearity issue). As said, if the model above is correct than you will causally identify the parameter with population data. Unfortunately you have only a sample and the estimator has to come up with a guess. With a rising correlation, the unique covariance information associated with each predictor gets smaller creating uncertainty about the estimate. This is reflected in rising standard errors. Hence, your estimate will be consitent and unbiased but inefficient/uncertain. The only remedy is to increase the sample size. In addition, I guess (being no expert) that a Bayes estimation with a definitive prior (if that is defendable) can be a help.

HTH

Holger

Holger Steinmetz

Thanks for your reply. The calculated sample size was 190 people. I already increased it to 250, shall I increase it more? noting that the population size is only 550 employees.

Regarding the method, which one shall I use?

Hi.. did you find the answer to this question.. i am having same problem.