Here are some newly written songs (including one by a student) for SEM The Musical 3, which we'll perform on Wednesday. We'll also do some "oldies" from the first and second annual musicals.

The SEM Way
Lyrics by Alan Reifman
(May be sung to the tune of “Let’s Live for Today,” Mogol/Shapiro/Julien, popularized by the Grass Roots)

You’ve got your sets of measures, some constructs they could form,
Plus, indices of fitness, to compare to a norm,
You draw yourself a model, with circles, squares, and paths,
The AMOS program handles, the complicated math,
If you get too many errors, you can express your wrath,

1-2-3-4

Analyze your work, the SEM way,
Analyze your work, the SEM way,
Don’t forget to, check your RM-SEA,
Analyze your work, the SEM way…

AMOS is Ideal
Lyrics by Susan Murray
(May be sung to the tune of “Jesus, Take the Wheel,” James/Lindsey/Sampson, popularized by Carrie Underwood)

She was working last Friday on her laptop battery,
On homework to achieve,
Her constructs were getting muddy, with her model nowhere near complete,
Fifty specs to go and she was running low on patience and caffeine,

It was complex and unclear,
She had a constraint and the software caused the tension,
But they say SAS is unsurpassed,
Before she knew it she was closing down that darn software SAS,

She saw the latent variables flash before her eyes,
She didn’t even have time to imply,
She was so impaired,
She suddenly was aware,

AMOS is ideal,
Take causation from my hands,
‘Cause I can’t do this on my own,
I’m letting go,

No coding song and dance,
To learn about the population,
AMOS is ideal,

A cross-lagged panel model she pulled out of the folder,
And like Emeril she went BAM! nonstop,
She cried like a baby when she saw the RMSEA drop,
Her hypothesis and all the parameters,
She now could weigh,
She could model all day,
In a Paula Abdul light,
Software to exchange,
Arbuckle already did the fight,

AMOS is ideal,
Take causation from my hands,
‘Cause I can’t do this on my own,
I’m letting go,

No coding song and dance,
SAS I won’t depend upon,
Oh, AMOS is ideal,
SAS, I’m saying no,

No coding song and dance
SAS I won’t depend upon,
My loyalty is withdrawn,
AMOS is ideal,

Oh, don’t you take it from me,
Find my μ

Equal
Lyrics by Alan Reifman
(May be sung to the tune of “Mercy,” Duffy/Booker)


A-A-A, B-B-B, C-C-C, D-D-D

I’ve got two, paths that you can view,
I think their strength, might be the same, and that’s the frame,
You’ve got, to see through,

Let’s run the model free, paths can be any sized,
Then run equalized,

We need a way to choose, a way to compare,
Test delta chi-square,

You’ve got me constrained to be equal,
Why won’t you release me?
You’ve got me constrained to be equal,
Why won’t you release me?
Can’t you rele-e-e-e-ase me?

Lower chi-square, will always be there,
When you let the paths go free, but you must see,
True sig-nif-i-cance,

When the chi-square’s non-sig, the one to retain,
Is where you constrain,

But if the change is big, p’s under oh-five,
Free paths shall survive,

You’ve got me constrained to be equal,
Why won’t you release me?
You’ve got me constrained to be equal,
Why won’t you release me?
Can’t you rele-e-e-e-ase me?

It’s Still SEM to Me
Lyrics by Alan Reifman
(May be sung to the tune of “It’s Still Rock and Roll to Me,” Billy Joel)

It’s a way to show, inter-relations,
In a set of, latent constructs,
It gives you, some global fit statistics,
Does your model, really stack up?
Squares and circles, now you’re off and you’re running,
Will your results, be routine or be stunning?

LISREL, M-PLUS, EQS, or AMOS,
It’s still SEM to me…..

Yoona Chin, a newly minted Ph.D. recipient from our department, will be giving a guest presentation today on differences between AMOS, the program we've been using in class, and Mplus, an increasingly popular program. She's put together a very elaborate PowerPoint slide show, a few key graphics I wanted to put online (with Yoona's permission). You may click on the following images to enlarge them.







Professor Judy Fischer will also be with us in class today, presenting some recent multiple-group findings from her research.

Today we will take up the topic of dyadic analysis in SEM, particularly something known as the Actor-Partner Interdependence Model (APIM). We will draw upon the following article, which is available via the TTU library.

Popp, D., Laursen, B., Burk, W. J., Kerr, M., & Stattin, H. (2008). Modeling homophily over time with an Actor-Partner Interdependence Model. Developmental Psychology, 44, 1028-1039.

The notes from my Methods class on unit of analysis may be helpful for this topic.

An important issue is whether the two partners in a dyad are distinguishable (i.e., non-exchangeable), as opposed to being indistinguishable (exchangeable). See David Kenny's webpage on dyadic analysis (particularly Topic 3). As Kenny, Kashy, and Cook (2006) state in their book Dyadic Data Analysis:

When dyad members are distinguishable, we estimate the path model or CFA model for each of the two members combined in a single model... However, when members are indistinguishable, it is less clear exactly how to do the analysis. The use of SEM with indistinguishable or exchangeable dyad members has generally been viewed pessimistically... (p. 111).

A suggested reference in this regard is:

Olsen, J. A., & Kenny, D. A. (2006). Structural equation modeling with interchangeable dyads. Psychological Methods, 11, 127-141.

As another example of an APIM-type model, see Hye-Sun Ro's dissertation in the online collection to the right.

One of our students this semester, Susan Murray, came up with a way to present model fit statistics that Kristina (the TA) and I both thought was very effective. With Susan's permission, here is the tabular format she came up with. The listed criteria for desirable values come from the Garson and Kenny documents in the links section to the right.

As I alluded to recently, if one wanted to re-analyze a model from the published literature (or propose an entirely new specification of a model), one could directly type a correlation matrix (ideally with standard deviations) from an article into AMOS. In this way, SEM analyses can be done on a data set without having the actual raw data. We'll discuss this in class today. The necessary information can be found in the AMOS program, by going to the "Help" area and looking up: "To reformat a text file of sample moments."

Today, we'll begin learning about full structural models, with an accompanying assignment being distributed. Over the last couple of years, I've developed several graphics for illustrating how to work with full SEM's. These, as well as the Keiley et al. chapter, will guide us through.

This graphic illustrates where the variances are located in full SEM's.

This one summarizes how to calculate degrees of freedom in a full SEM.

For the assignment, you'll have to engage in comparative model testing, for which we'll need to learn the concepts of model nestedness and delta-chi square difference testing.

The assignment will also involve some difficulties in the data (an outlier in the raw data and a Heywood Case in the SEM, which may be related), and we'll discuss how to overcome them.

ADDENDUM: The following image can be a guide in drawing your model for the assignment. Once you get the model to run successfully, you'll be testing the overall fit of models with and without the red-dashed pathway.

To summarize what we did today and provide easy access to the links, see the following:

1. We introduced the SEM Pyramid of Success (link).

2. We reviewed the Pearson correlation coefficient (link). We also looked at a graphical depiction of the least-squares criterion (link).

3. We transitioned from correlation to multiple-regression, with a focus on standardized and unstandardized relationships (link). We also looked at a picture (the second one down) of how an unstandardized regression equation would be depicted (link).