Ordinary least squares is the regression subset of the General Linear Model. The GLM is a beautiful statistical structure unlike any other in our discipline. It provides a consistent theory and methods for regression, Analysis of Variance, Analysis of Covariance, and--through its use to generate results for other analyses--many other statistical methods (David Booth notes that SEM is one of these). Simple results such as t-test and F-tests are just special cases. In addition, it provides a wealth of diagnostic tools that apply across the board to all of these methods. Leverage, influence measures, partial regression plots, and residual analyses all make it more likely that a carefully performed GLM analysis will be valid and intelligible. Methods that rely on computations that are too complex to be visible can't do that. You are stuck with a P-value and some coefficients and no insight into what might really be going on in your data.

My advice:

* Plot your data

* Re-express if relationships are not linear

* Remove outliers, split your data into subgroups if they are not a consistent whole.

* Fit OLS models carefully. Be willing to entertain alternative models--there often is not a single "best" model and alternative models can be informative.

* Diagnose your models: examine leverage, influence measures, plots of residuals, partial regression plots for the coefficients of interest, and other related tools.

* Then--and only then--if everything looks good and you think there is still more to learn about your data, try one of the other methods.

I'll bet you rarely get to that last step.

The Gauss-Markov theorem and the properties of a normal distribution. For details see a linear statistical models book. SEM is just a dressed up version of least squares as is PLS-SEM. Best wishes, David Booth. PS in the old days i.e. when I was a student all of the SEM and Path Analysis calculations were done with ordinary least squares regression - no special programs. See Oscar Kempthorne's book, An Introduction to Genetic Statistics to see how path analysis was originally done.

I suggest you read these articles.

Hayes, A. F. (2009). Beyond Baron and Kenny: Statistical mediation analysis in the New Millennium.

Hayes, A. F., & Rockwood, N. J. (2017). Regression-based statistical mediation and moderation analysis in clinical research: Observations, recommendations, and implementation.

Hi,

The following attached papers may be of help to you.

Thank you and have a nice time.

Ordinary least squares is the regression subset of the General Linear Model. The GLM is a beautiful statistical structure unlike any other in our discipline. It provides a consistent theory and methods for regression, Analysis of Variance, Analysis of Covariance, and--through its use to generate results for other analyses--many other statistical methods (David Booth notes that SEM is one of these). Simple results such as t-test and F-tests are just special cases. In addition, it provides a wealth of diagnostic tools that apply across the board to all of these methods. Leverage, influence measures, partial regression plots, and residual analyses all make it more likely that a carefully performed GLM analysis will be valid and intelligible. Methods that rely on computations that are too complex to be visible can't do that. You are stuck with a P-value and some coefficients and no insight into what might really be going on in your data.

My advice:

* Plot your data

* Re-express if relationships are not linear

* Remove outliers, split your data into subgroups if they are not a consistent whole.

* Fit OLS models carefully. Be willing to entertain alternative models--there often is not a single "best" model and alternative models can be informative.

* Diagnose your models: examine leverage, influence measures, plots of residuals, partial regression plots for the coefficients of interest, and other related tools.

* Then--and only then--if everything looks good and you think there is still more to learn about your data, try one of the other methods.

I'll bet you rarely get to that last step.