Hello Nora,

first, reference to the terms "inner model" and "outer model" suggests you use PLS, right? Then I would recommend not speaking of SEM as these are different things.

second, multicolinearity concerns extremely high correlations between predictors or functional relationship between one predictor and a set of other predictors), not outcomes. Indicators are outcomes. They should correlate as highly as possible.

Strong correlations are no multicolinearity. With rising associations between predictors, the standard errors naturally increase as the amount of unique information is lower. Hence you need a larger sample size (which is the only remedy). Multicolinearity means that the estimation algorithm breaks down as there is simply no unique information to estimate an effect.

HTH

--Holger

Holger Steinmetz thank you for your response ,

yes Im using smart PLS , which provide the multicollinearity test in two tables , outer model (reflect the items and construct) the inner model (reflect the correlation between construct), based on your answer the inner model reflect the collinearity test needed, thanks a lot!

one more thing about the tolerance, can you explain it more , and how to get it through PLS , cause I couldn't

Hello Nora,

I have no clue what these tests in PLS represent. There is no cut off for multicolinearity in my point of view (like to be informed if otherwise). With rising depencies among predictors, their standard errors rise.

I did not understand what you mean with "tolerance"? Normally, multicolinearity is regarded with the variance inflation factor (VIF). Perhaps search for that term. There are various rules of thumb (as people are interested in clear guidelines which is understandable) but given the aforementioned relationship between dependency and standard errors they are built on shaky grounds.

As the usual criterion for hypothesis testing is significance, I would think about colinearity with a) high correlation among predictors, combined with b) substantial effects, combined with c) huge standard errors/nonsignificant effects.

I see, however, that this is a shallow way to go as beyond significant testing, we should be more concerned with efficiency of estimation (i.e., small confidence intervals)--which as noted before is strongly reduced with increasing colinearity.

Best,

--Holger

Hi Ms. Nora Ahmad, my reading recommendation for the report of both results in PLS-SEM:

Hair, J. F., Risher, J. J., Sarstedt, M., & Ringle, C. M. (2019). When to use and how to report the results of PLS-SEM. European Business Review.

Table 1 (p. 15):

Structural model - Collinearity (VIF)

- Probable (i.e. critical) collinearity issues when VIF > 5

- Possible collinearity issues when VIF  3-5

- Ideally show that VIF < 3

Formative measurement models

- Convergent validity (redundancy analysis) 0.70 correlation

Collinearity (VIF)

- Probable (i.e. critical) collinearity issues when VIF  5

- Possible collinearity issues when VIF  3-5

- Ideally show that VIF < 3

When to use and how to report the results of PLS-SEM

Article When to use and how to report the results of PLS-SEM

Hey,

Since OLS is applied to estimate regression equations with typically more than 1 independent variable when PLS mode B is used or the inner model is estimated by PLS, these estimates can suffer from multicollinearity. Hence, I would say it is worth to have a look at the VIF values for the path coefficients and the weights estimated by mode B.

Tolerance is 1/VIF so you do not get any additional insights by considering it.

Best regards,

Florian

Typically in PLS, we look at the measurement and structural model for collinearity isues in PLS. Among constructs, the formative masurement is more important as collineary has an impact on the weights and their statistical significance. (Exhibit 5.4 of Hair's A Primer on PLS).

For structural model, the same procedure is used as in the measurement model. (Exhibit 6.2 of the same book). If collinearity is indicated by the tolerance or VIF guideline, eliminate constructs by merging predictors into a single constructs or create higher oder construct to treat collinearity problems.

In PLS-SEM I analyze the inner VIF report to assess the collinearity among the constructs in a model, and values should be below 3.3:

"Kock (2015) suggests that the occurrence of a VIF greater than 3.3 is proposed as an indication of pathological collinearity, and also as an indication of common method bias (CMB)".

Kock, N. (2015). Common method bias in PLS-SEM: A full collinearity assessment approach. International Journal of e-Collaboration, 11(4), 1-10. doi:10.4018/ijec.2015100101

I have a higher order model, three endogenous constructs and one exogenous construct, after validating the measurement model of the lower order level and generating the latent variables, I have high collinearity (7.4, 6.4) between two of the endogenous constructs and the exogenous construct, is that fine as we are more concerned of collinearity between predictor constructs only?