Hi,

Multicollinearity is a common issue in statistical modeling that can arise when there are high correlations among the predictors or factors in the model. In SmartPLS, there are several ways to evaluate the model fit in the presence of multicollinearity issues and address their potential consequences on the validity and reliability of your results.

One approach is to examine the Variance Inflation Factor (VIF) values for each variable in the model. The VIF measures how much the variance of the estimated regression coefficient is inflated due to multicollinearity, with values above 5 indicating a potential problem with multicollinearity. If high VIF values are observed, you can consider removing one of the correlated variables or combining them into a single variable to reduce the impact of multicollinearity.

Another approach is to use Partial Least Squares Path Modeling (PLS-PM) algorithms that are less sensitive to multicollinearity issues than other regression-based methods. PLS-PM algorithms allow for modeling the relationships between variables based on their covariance structure, rather than directly estimating regression coefficients.

Ignoring multicollinearity issues can lead to biased and unstable parameter estimates, lower statistical power, and inflated standard errors, which can result in a loss of accuracy and reliability in the model. In addition, it can also affect the interpretation and generalization of the results, leading to erroneous conclusions and misguided actions. Therefore, it is important to address multicollinearity issues appropriately to ensure the validity and reliability of your SmartPLS model.

Regards,

Uday Bhale

Partial least squares regression uses principal component analysis to create a set of uncorrelated components to include in the model. LASSO and Ridge regression are advanced forms of regression analysis that can handle multicollinearity.

OLS estimators are BLUE (i.e. they are linear, unbiased and have the least variance among the class of all linear and unbiased estimators). Amidst all this, one should not forget the Gauss-Markov Theorem (i.e. the estimators of OLS model are BLUE) holds only if the assumptions of OLS are satisfied.

Under OLS assumptions, OLS estimator is BLUE (least variance among all linear unbiased estimators). Therefore, it is the best (efficient) estimator.

https://365datascience.com/tutorials/statistics-tutorials/ols-assumptions/

1. The Gauss-Markov Theorem and “standard” assumptions

2. Recovering the OLS estimator

3. Proof under what conditions the OLS estimator is unbiased

4. Unbiased and Consistent Variance estimators of the OLS estimator, under different conditions

5. Proof under standard GM assumptions the OLS estimator is the BLUE estimator

6. Connection with Maximum Likelihood Estimation

7. Wrap-up and Final Thoughts

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