Writing Up SEM Findings

The SEMNET e-mail discussion listserv had some useful references recently on how to write up SEM findings (thanks to Debbi Bandalos, Mbaye Fall Diallo, Jonathon Little, Amin Mousavi, Christian M. Ringle):

Bandalos, D.L., & Finney, S.J. (2010). Factor analysis: Exploratory and confirmatory. In G.R. Hancock & R.O. Mueller (Eds.), The reviewer’s guide to quantitative methods in the social sciences (pp. 125-155). New York: Routledge.

Boomsma, A. (2000). Reporting analyses of covariance structures (Teacher's Corner). Structural Equation Modeling, 7, 461-83.

Boomsma, A., Hoyle, R. H., & Panter, A. T. (2012).  The structural equation modeling research report.  In R. H. Hoyle (Ed.), Handbook of structural equation modeling (pp. 341-358).  New York: Guilford Press.

Gefen, D., Rigdon, E. E., & Straub, D.W. (2011). Editor's comment: An update and extension to SEM guidelines for administrative and social science research. MIS Quarterly, 35, iii-xiv.

Hoyle, R. H., & Panter, A. T. (1995). Writing about structural equation models. In R. H. Hoyle (Ed.), Structural equation modeling: Concepts, issues and applications (pp. 158-176). Thousand Oaks, CA: Sage.

Jackson, D. L., Gillaspy J. A., & Purc-Stephenson R. (2009). Reporting practices in confirmatory factor analysis: An overview and some recommendations. Psychological Methods, 14, 6–23.

Mueller, R. O., & Hancock, G. R. ( 2010). Structural equation modeling. In G. R.Hancock & R. O.Mueller ( Eds.), The reviewer's guide to quantitative methods in the social sciences (pp. 371– 383). New York: Routledge.

Raykov, T., Tomer, A., & Nesselroade, J. R. (1991). Reporting structural equation modeling results in Psychology and Aging: Some proposed guidelines. Psychology and Aging, 6, 499-503.

Schreiber, J. B., Nora, A., Stage, F. K., Barlow, E. A., & King, J. (2006). Reporting structural equation modeling and confirmatory factor analysis results: A review. Journal of Educational Research, 99,  323-337.

SEM The Musical 6


UPDATE May 10.  SEM The Musical 6 is now on the books. Shown below are the new songs written this year, along with some photos of the performances (thanks to Chris Bedard and Xiaohui Tang for the pictures).

We had a surprise "visit" via video feed from three friends of the musical who moved last August from Texas Tech to Virginia Tech: Professor Anisa Zvonkovic (below, center), now department chair at VT; Kyung-Hee Lee (left), who finished her Ph.D. at TTU and is now a post-doc at VT; and Andrea "Hermione" Swenson (right), who finished her Master's at TTU and is studying for her Ph.D. at VT. The song they wrote is shown further down the page.


We also sang several songs from the previous five musicals (links: 1, 2, 3, 4, 5). For the first time ever, we ran a poll (see right-hand column) to help determine which songs from previous years to sing. The song "Parsimony," from SEM The Musical 1, is always what we close the show with, so it was not included in the poll. That's enough background. Here are this year's new songs...

Let’s Sing About It
Lyrics by Alan Reifman
(May be sung to the tune of “Tell Her About It,” Billy Joel)

Listen all you, SEM users,
It’s our yearly, singing day,
To review the things we’ve learned, this semester,
In a most unusual, way,

From your model fit,
To max-i-mum likelihood,
You’ve learned practices that,
Expert modelers should,

Listen all you, SEM users,
You’ve really come, a long way,
From regression, correlation, and pathways,
Through factors and CFA,

From constraining paths,
And checking, delta chi-square,
To run multi-groups and,
Seeing what paths, they share,

Let’s sing about it,
Cover, all the things, we do,
So that, all the concepts,
Now seem old, although they’re new,

Let’s sing about it,
From the blueprint, to the fit,
How to judge, a model,
Knowing how, to interpret,

(brief interlude)

Listen all you, SEM users,
You can run a model, now,
You can draw the boxes, circles, and arrows,
Those are things, that you know how,

But to understand,
In depth, is what we seek,
To make each, of you,
A real, SEM geek,

Let’s sing about it,
Cover, all the things, we do,
So that, all the concepts,
Now seem old, although they’re new,

Let’s sing about it,
From the blueprint, to the fit,
How to judge, a model,
Knowing how, to interpret,

So, now and then, you get an error,
Cause you’ve drawn, something in AMOS, that is wrong,
Make sure to use, the correct tools,
So figuring out the right way, won’t take long,

Listen all you, SEM users,
You’ve, really, come, a long way,
From regression, correlation, and pathways,
Through factors and CFA,

From constraining paths,
And checking, delta chi-square,
To run multi-groups and,
Seeing what paths, they share,

Let’s sing about it,
Cover, all the things, we do,
So that, all the concepts,
Now seem old, although they’re new,

Let’s sing about it,
From the blueprint, to the fit,
How to judge, a model,
Knowing how, to interpret,

Let’s sing about it!
Sing about what, you’ve learned here,
We’ve got to, all sing about it,
How degrees-of-freedom work,
We’ve got to, all sing about it,
Finding out the, errors that lurk,
We’ve got to, all sing about it,
We’ve all got, models to run
We’ve got to, all sing about it
You know, we want to have fun,
We got to, all sing about it… 

You Have Not Shown It’s Causal
Lyrics (and performance) by Devin DuPree
(May be sung to the tune of “When You Say Nothing at All,” Overstreet/Schlitz, popularized by Alison Krauss)


Sometimes you may want, to show how, two constructs relate,
And you may want to show, that B’s caused by A.
Try as you may, it is hard to define,
If Y causes X, or if X causes Y.

Even with a, significant correlation,
There are two other things, you need to, show causation,
Time ordering and, ruling out third variables...

And without that,
You have not shown, it’s causal.

There's a link between, breast implants and suicide,
The risk for women, who do is, three times as high.
Is this because, they don’t like, what they’ve done,
Or are both, caused by, body dis-affection?

Even with a, significant correlation,
There are two other things, you need to, show causation,
Time ordering and, ruling out third variables...

And without that,
You have not shown, it’s causal...

Theory on Your Screen
Lyrics by Alan Reifman
(May be sung to the tune of “Music of the Night,” Lloyd Webber/Hart, from Phantom of the Opera)

(SLOWLY and SOFTLY)
Thinking over, every implication,
Direct pathways, maybe mediation,
Carefully consider, and overcome your jitter,
You have to convey, all that you mean,
For you record, the theory on your screen,

Slowly, gently, contemplate each linkage,
Parsimony, compels one, to shrinkage,
Draw the paths you say, underlie the works at play,
Think of every type of route, though serpent-teen,
And listen to, the theory on your screen,

Close your eyes and surrender to creative schemes!
Push notions beyond, what you’ve read before!
Close your eyes, let your thinking start to soar!
And draw something, that gets right to the core!

Constructs, measures, hypotheses surround you ...
Hear them, feel them, closing in around you ...
Open up your mind, new ideas let it find,
Try to make sense, of what all these things can mean,
The beauty of, the theory on your screen,

Try and model a journey, through a strange, new world!
Go beyond what, the world has known before!
Let arrows, fill in what you think you see!
Only then can you let the paths run free!

Theories, concepts, find your inspiration!
Later, check your, identification!
Let it calculate, the paths that you estimate,
Find the fruits, of the ideas, that you glean,
The power of, the theory on your screen,

ORCHESTRA CRESCENDO

You have to convey, all that you mean,
For you record, the theory on your screen...

S-E-M
Lyrics by Anisa Zvonkovic and Kyung-Hee Lee
(May be sung to the tune of "Edelweiss," Rodgers/Hammerstein, from The Sound of Music)

S-E-M, S-E-M,
Every model, we're building,

Small but right, fit and tight,
Keeps us happy, analyzing,

Helping our vitas, to bloom and grow,
Bloom and grow, for tenure,

Texas Tech, Virginia Tech,
Bless Dr. Reifman, forever

Ways to Treat Single-Indicator Variables

(Updated March 25, 2015)

Often, a researcher will have one or more single-indicator variables within his or her model. It could be a demographic variable such as gender or age, or a total scale score for some social/psychological questionnaire (e.g., Rosenberg Self-Esteem Scale).

With multiple manifest indicators for a latent construct, the construct is automatically rendered "error-free," with measurement error segregated out into each indicator's residual "tiny bubble." Relations between constructs will be stronger when they are error free. Single-indicator variables, when left to stand alone, usually have measurement error, but are assumed to be perfectly measured.

Here are five scenarios in which a researcher was interested in studying self-esteem (thanks to CRO for the photograph of the board).


As shown in the photo, reliability-corrected single-indicator constructs are a way to account for measurement error in single-indicator variables (lower-right). The following is a quote from Choi et al. (2011): “To account for imperfect reliability of the scale scores, we created latent variables to represent the … constructs with each latent variable being measured by its corresponding scale score and the residual variance of the scale score fixed to (1-scale reliability) * scale variance (Hayduk, 1987).” Cronbach's alpha (internal consistency) is often used as the reliability value. A made-up example of this procedure is shown in the photo.

I previously created the following graphic to illustrate further the difference between keeping single variables as they are and using reliability correction.


References and Resources

Choi, K. H., Bowleg, L., & Neilands, T. B. (2011). The effects of sexism, psychological distress, and difficult sexual situations on U.S. women's sexual risk behaviors. AIDS Education and Prevention, 23(5), 397-411. (LINK)

Cole, D. A., & Preacher, K. J. (in press). Manifest variable path analysis: Potentially serious and misleading consequences due to uncorrected measurement error. Psychological Methods. (LINK)

Hayduk L. A. (1987). Structural equation modeling with LISREL: Essentials and advances. Baltimore, MD, USA: Johns Hopkins University Press. 

Table of Contents from September 2013 Psychological Methods (item-parcel debate)