SEM Episode 2: Path Analysis 

Rodrigo -- thanks for your nice comment. Dan and I hope these are of some use to you in your work. Take care -- patrick

Hi NJ -- thanks for the kind words. Glad you're finding these videos of some use. Dan and I hope to use quarantine to make some new ones, so hopefully we can do that sometime soon. Take care -- patrick

thanks so much for your kind words -- Dan and I have lots of fun doing these things, and it beats the heck out of working at our day jobs. Good luck with your work -- patrick

Hi Shuoyu -- thanks for your nice note. We also have a full 3-day workshop on introduction to SEM that is completely free-of-charge: see centerstat.org for details. Good luck with your grad applications!

Thanks for your very kind note -- Dan and I hope these videos might be of some use as you pursue your own research projects. Good luck with your work....patrick

@@centerstat I will share with my classmates

Hi Julie Anne -- thanks for the very kind words. If you're truly a glutton for punishment, Dan and I have a full 3-day workshop on the SEM that is completely free-of-charge (the beauty of both being tenured). See centerstat.org if you're interested. Good luck with your work -- Patrick

@@centerstat yes I already found it on your website! I’m very excited for it haha

​​@@centerstat I also look forward to attending! In the meanwhile I would appreciate a clarification. At about 5:32 you assume that the exogenous variables are correlated. Can you explain how this would happen considering they all point a collider? I thought the path was closed and the variables couldn't be associated...

@@domenicoscarpino3715 Thanks for the comment -- we always allow exogenous variables to freely correlate, either in the SEM or in any form of the GLM, because this allows the regression coefficients to be partialed for all other predictors (that is, the relation between one predictor and the outcome above and beyond all other predictors). Substantively why we do this is to represent the shared causes that might exist from things outside of our model that led to the predictors being correlated in the first place. I hope this helps -- patrick

@@centerstat please correct me if I'm wrong. If we don't include correlated exogenous variables in the model we would also incur in a confounding case scenario.

Thanks for the very nice words. New Zealand is one of my very favorite places in the world -- you gotta love a place that has more sheep than people. I'm really glad you found the video helpful. If you're a true glutton for punishment, Dan Bauer and I have a full 3-day workshop on the SEM that is completely free -- see centerstat.org/introduction-to-structural-equation-modeling-async/ Good luck with your work -- Patrick

​@@centerstat Thanks so much! it is very generous of you to off the course for free, I will have a look.... glad you enjoyed your time here! ... we do have the odd sheep, also lots of need for your type of research & LOTS of jobs if you ever wanted to join us! :)

Thanks, Patrick! Again, I can't help let you know how helpful these videos are. Gonna share them to friends who want to learn SEM. Wish you more good work from you! Cheers!

Bollen, K. A. (1989). Structural equations with latent variables. New York : Wiley.

Dear Patrick, thanks so much for your explanation, that was very clear!

Hi Ahmed -- thanks for your question and your kind words. We actually estimate all variances for all variables, whether they be exogenous or endogenous. If they are exogenous, the estimates simply take on their sample values (assuming there are no missing data); if they are endogenous, the variances are conditional given the effects of the predictors and are thus disturbances (or residuals). These are extremely important parameters in the model and should always be estimated. If you obtain a negative variance (or Heywood case), then that is a reflection of a problem elsewhere in the model that needs to be diagnosed and fixed. Citations for a couple of papers that might be of interest are below. Good luck with your work -- patrick Chen, F., Bollen, K. A., Paxton, P., Curran, P. J., & Kirby, J. B. (2001). Improper solutions in structural equation models: Causes, consequences, and strategies. Sociological methods & research, 29(4), 468-508. Cooperman, A. W., & Waller, N. G. (2021). Heywood you go away! Examining causes, effects, and treatments for Heywood cases in exploratory factor analysis. Psychological Methods. Kolenikov, S., & Bollen, K. A. (2012). Testing negative error variances: Is a Heywood case a symptom of misspecification?. Sociological Methods & Research, 41(1), 124-167.

Thanks for your kind words. Yes...if the predictors are correlated, then the regression coefficients are the partial effect of each predictor above-and-beyond all other predictors. If the predictors are uncorrelated (or "orthogonal") then no statistical control is necessary -- the coefficient is simply the relation between the predictor and the outcome. However, even if you simulate data to be uncorrelated, you may still get small chance correlations among predictors and they will rarely if ever be truly uncorrelated unless you have a massively large sample of data. Hope that helps - - good luck with your work.

@@centerstat Ahhhh! I get it now. Thank you, Patrick.

Hi Wajdy -- thanks for the comment. This is a tricky question because it depends on your theoretical question, the development of the instrument, and the purpose of your study. That said, if prior validity studies have been conducted on your instrument, you typically do not need to re-do this for your own study. however, if this is a brand new instrument that you've developed, it's important to establish that it is measuring what it purports to measure in a valid and reliable way. I hope this helps -- good luck with your project -- patrick

Hi Larissa -- thanks for the note. At its core, SEM assumes independence -- no two residuals are any more or less related than any other two residuals. But as you note, more and more designs involve nested structures -- siblings nested in families, patients nested within physician, etc. There are two ways of handling this in the SEM. The first is to ignore nesting in the analysis itself, but then "adjust" the standard errors and test statistics for violations of independence. The second is to model the dependence directly, and this is often referred to as a multilevel SEM -- these models are challenging to estimate and procedures continue to be developed and perfected. Finally, some prefer to side-step the SEM entirely and bolt together tests of mediation directly within the multilevel model (that is naturally built for nesting). A few exemplar cites are below, but there is much more wonderful work on this topic out on the intertube. Good luck with your work -- Patrick McNeish, D., Stapleton, L. M., & Silverman, R. D. (2017). On the unnecessary ubiquity of hierarchical linear modeling. Psychological methods, 22(1), 114. Preacher, K. J., Zyphur, M. J., & Zhang, Z. (2010). A general multilevel SEM framework for assessing multilevel mediation. Psychological methods, 15(3), 209. Zhang, Z., Zyphur, M. J., & Preacher, K. J. (2009). Testing multilevel mediation using hierarchical linear models: Problems and solutions. Organizational Research Methods, 12(4), 695-719. Zigler, C. K., & Ye, F. (2019). A comparison of multilevel mediation modeling methods: recommendations for applied researchers. Multivariate Behavioral Research, 54(3), 338-359.

Thanks for the nice words. Briefly, the parameters are what we hypothesize relates the variables to one another in the population; that is, we are trying to recreate the multivariate distribution of observed measures based on our hypothesized model structure, and the parameters create this structure. But we never have the actual parameters themselves as these only exist in the population. Instead, we get sample estimates of the parameters. Different types of parameters include regression coefficients, intercepts, residual variances, among others. I hope this helps -- patrick

@@centerstat Thank you so so much. this is very helpful. Could you please explain the differences between (free, fixed, and constrained)? why do we choose one over another? what conditions for each one? Thank you

@@user-jz8sf4yk7f Good morning -- A free parameter takes on the best estimate from the sample data, and a fixed or constrained parameter is set to a given value or set to be a function of some other parameter. If you're interested, we actually have a completely free 3-day online workshop in structural equation modeling. Go to centerstat.org and you can register for video lectures and PDFs of lecture notes and computer demonstrations. Hope this helps -- patrick

@@centerstat you are so nice thank you so so much. Definitely I will take that course. Appreciate it

Most typically, in a CFA you set a single factor loading to a value of 1.0 to set the scale of the latent factor. However, this is not required. You can instead freely estimate all factor loadings but fix the variance of the latent factor to 1.0. Either way, you need to impose one restriction to set the scale of the latent variable.