SEM The Musical 5

Here's the announcement for this year's musical!

We'll have a new song or two, plus we'll be singing some "oldies" from SEM the Musical 1, 2, 3, and 4 (just click directly on the numbers to access previous years' lyrics).

SEM Musical FIVE!
Lyrics by Alan Reifman (retread from last year)
(May be sung to the tune of “Let’s Get it Started,” Will Adams et al. for the Black Eyed Peas)

(Softly) The models keep runnin-runnin, and runnin-runnin, and runnin-runnin, and runnin-runnin, and runnin-runnin, and runnin-runnin, and runnin-runnin, and runnin-runnin, and...

We’re back again, to have some fun,
We’re gonna bust some rhyme, have a good time,
We’re gonna sing some songs, about SEM technique,
Access your inner geek, let your voices speak,
SEM is different, your measurement model’s explicit,
The whole model, gets tested for fit,
Is it identified? We know how hard you’ve tried,
Knowns and unknowns, side by side,
It takes you on a ride, finally you’re satisfied,
Your output’s now just fine, you’ve arrived, you can take pride…

NFI, TLI, CFI,
Calculate estimates, let it run, have some fun, yeah…
SEM Musical (FIVE!), SEM Musical (HERE!),
SEM Musical (FIVE!), SEM Musical (HERE!),
SEM Musical (FIVE!), SEM Musical (HERE!),
SEM Musical (FIVE!), SEM Musical (HERE!),
Yeah,

Build your constructs, get this straight,
Make sure the indicators, correlate,
Draw your pathways, residuals too,
Don’t leave out, the fixed 1 value,
Take your time, think it through,
Don’t worry if you’re new, we’ll walk with you,
Step by step, right up the pyramid,
For SEM, we’re really groovin,’
Hope you get an acceptable solution,
Submit your model and get it movin,’

NFI, TLI, CFI,
Calculate estimates, let it run, have some fun, yeah…
SEM Musical (FIVE!), SEM Musical (HERE!),
SEM Musical (FIVE!), SEM Musical (HERE!),
SEM Musical (FIVE!), SEM Musical (HERE!),
SEM Musical (FIVE!), SEM Musical (HERE!),
Yeah…

SEM Pyramid of Success (explanation)
Lyrics by Andrea Swenson
(May be sung to the tune of "Seasons of Love," Jonathan Larson, from the musical "Rent")

(Long opening on piano, about 40 seconds)

One hundred, thirty-nine thousand, two hundred seconds,
One hundred, thirty-nine thousand, moments to learn,
One hundred, thirty-nine thousand, two hundred seconds,
That is, how long, we sit in this class,*

It starts with, correlation,
Regression, and path an-al-y-sis,
E-F-A, builds into,
C-F-A, in time,

One hundred, thirty-nine thousand, two hundred seconds,
How, do you start? And, where do you go?

To get to, S.....E.....M.....
To get to, S.....E.....M.....
To get to, S.....E.....M.....
Measure it well....

Pyramid of.... (slow) success,
Pyramid of.... (slow) success,

One hundred, thirty-nine thousand, two hundred seconds,
One hundred, thirty-nine thousand, moments to learn,
One hundred, thirty-nine thousand, two hundred seconds,
That is, how long, we sit in this class,

Starting with, correlation,
Moving up to, regression,
In exploring, factors,
And confirming them,

It’s time now, to remember,
To bring it all together,
Let's, bring it all together, to do SEM,

Remember the pyramid (Oh you got to you got to remember the pyramid)
Remember the pyramid (You know that SEM is a starts from the r)
Remember the pyramid (regress, factor, SEM)
Assess the model (Learn, learn SEM)

Pyramid of success
Pyramid of success (that’s how we learn, learn SEM)

---
*Number of seconds in the class, based on 29 periods of 80 minutes each.


Hey, Hey, Heywood Cases
Lyrics by Nora "Felix" Phillips
(May be sung to the theme from "The Monkees," Boyce/Hart)

Let it run, the computations go through,
You get an error message, it leaves you feeling blue,

Hey Hey Heywood Cases!
Bringing, my AMOS, model down,
With your, negative variance,
You know that, isn't allowed,

Mis-specification,
Of the model, that you've drawn,
Or maybe, your own sample,
Was just, a tad bit, too small?

Hey Hey Heywood Cases!
I won't let you bring me down,
I can constrain, residuals,
To a, small positive, amount!

---

Nestedness
Lyrics by Alan Reifman
May be sung to the tune of “Yesterday” (Lennon/McCartney)

Nestedness,
It’s the way, models can be compared,
Should new paths be added in or spared?
The delta-test needs nestedness,

Can’t you see?
One model might have simplicity,
But more paths increase fidelity,
Which one to choose, the chi-square’s key,

Inside, the big one, the small one, is self-contained,
One has, extra paths, the other, does not maintain...

Nestedness,
To the baseline, you can only add,
Or only subtract, paths you once had,
You can’t do both, for nestedness,

Inside, the big one, the small one, is self-contained,
One has, extra paths, the other, does not maintain...

Look, shall we?
One model could have, paths “A” and “B,”
They would nest in, model “A/B/C,”
A/B’s contained, in A/B/C…


Maximum Likelihood
Lyrics by Alan Reifman
May be sung to the tune of “Pink Houses” (John Mellencamp)

The computer, runs your model, looking for a solution,
It seeks to maximize, or maybe minimize,
Some function, seen in, a distribution,

You have least squares, which tries to put, the best-fit line near the dots,
But ML, seeks equations, so your findings, will come out on top,

Oh, maximum likelihood, that’s what we use,
Maximum likelihood, it tends to confuse,
Maximum likelihood, underlying values, that make your results, most probable,
And that’s, big news!

Sir Ronald Fisher, statistician,
Developed the, ML perspective,
It will iterate, till it’s really great,
But it’s so, calculation intensive,

For a long time, ML sat there,
Its steps were, so hard to reckon,
But computers, came along, and sped things up,
And now ML, runs in mere seconds,

Oh, maximum likelihood, that’s what we use,
Maximum likelihood, it tends to confuse,
Maximum likelihood, underlying values, that make your results, most probable,
And that’s, big news!

Instrumental

Well there are data, and more data,
What do they show?
With its complex math, on a tricky path,
ML tells you, what you, need to know,

Oh yeah,

Well some data, might be missing,
But there’s no need, for frustration,
’Cause you can, estimate the means, and intercepts,
To get ML, with full, information,

Oh, maximum likelihood, that’s what we use,
Maximum likelihood, tends to confuse,
Maximum likelihood, underlying values, that make your results, most probable,
And that’s, big news!

SEM The Musical 4

Below is a sneak peek at our new songs for this year. We'll also be singing some "oldies" from SEM the Musical 1, 2, and 3 (just click directly on the numbers to access previous years' lyrics).

SEM Musical FOUR!
Lyrics by Alan Reifman
(May be sung to the tune of “Let’s Get it Started,” Will Adams et al. for the Black Eyed Peas)

(Softly) The models keep runnin-runnin, and runnin-runnin, and runnin-runnin, and runnin-runnin, and runnin-runnin, and runnin-runnin, and runnin-runnin, and runnin-runnin, and...

We’re back again, to have some fun,
We’re gonna bust some rhyme, have a good time,
We’re gonna sing some songs, about SEM technique,
Access your inner geek, let your voices speak,
SEM is different, your measurement model’s explicit,
The whole model, gets tested for fit,
Is it identified? We know how hard you’ve tried,
Knowns and unknowns, side by side,
It takes you on a ride, finally you’re satisfied,
Your output’s now just fine, you’ve arrived, you can take pride…

NFI, TLI, CFI,
Calculate estimates, let it run, have some fun, yeah…
SEM Musical (FOUR!), SEM Musical (HERE!),
SEM Musical (FOUR!), SEM Musical (HERE!),
SEM Musical (FOUR!), SEM Musical (HERE!),
SEM Musical (FOUR!), SEM Musical (HERE!),
Yeah,

Build your constructs, get this straight,
Make sure the indicators, correlate,
Draw your pathways, residuals too,
Don’t leave out, the fixed 1 value,
Take your time, think it through,
Don’t worry if you’re new, we’ll walk with you,
Step by step, right up the pyramid,
For SEM, we’re really groovin,’
Hope you get an acceptable solution,
Submit your model and get it movin,’

NFI, TLI, CFI,
Calculate estimates, let it run, have some fun, yeah…
SEM Musical (FOUR!), SEM Musical (HERE!),
SEM Musical (FOUR!), SEM Musical (HERE!),
SEM Musical (FOUR!), SEM Musical (HERE!),
SEM Musical (FOUR!), SEM Musical (HERE!),
Yeah…

Once You Work in AMOS
Lyrics by Alan Reifman
(May be sung to the tune of “Once in Love with Amy,” Frank Loesser)

Once you work, in AMOS,
Find every quirk, in AMOS,
Construct by construct, you can draw your picture,
Using all the gadgets, is fun,

Learn the rules, in AMOS,
Use all the tools, in AMOS,
Circles and boxes, and you can add arrows,
Soon your model’s, ready to run,

The moving truck, the sizer, and the bubble,
Your choices, are vast,
And even if, you find yourself in trouble,
You can fix things fast,

So, once you work, in AMOS,
Find every quirk, in AMOS,
Each time you use it, your skills are expanded,
And you’ll understand, what you see,
Cause, in the end, it’s fixed, or it's free…

Prof. Reifman
Lyrics by Kim Corson and Janis Henderson
(May be sung to the tune of "Fernando," Ulvaeus, Andersson, & Anderson, for ABBA)

Can you hear the songs, Prof. Reifman?
We remember long ago, in intro stats you sang like this,
At the front of class, Prof. Reifman,
You were humming to yourself, and softly strumming air guitar,
We could hear the distant drums,
And suddenly, the answers didn't seem so far,

We’re much closer now, Prof. Reifman,
Every box, every circle, seems to make more sense to us,
We are not afraid, Prof. Reifman,
We sit here so full of life; all of us are prepared to try,
And we're not ashamed to say,
The songs of SEM the Musical 4 helped us get by,

There was something in the air that day,
The fog went away, Prof. Reifman,
He was talking about SEM,
And our heads didn't swim, Prof. Reifman,

Though we never thought that we would grasp, degrees of freedom,
We can calculate them now, in fact, we just subtract, Prof. Reifman,
We can calculate them now, in fact, we just subtract, Prof. Reifman,

When we're old and grey, Prof. Reifman,
And for many years we haven't played in your "rock band,"
We'll still hear the strums, Prof. Reifman,
And we'll recall learning AMOS, like Emeril, can go "Bam!",
And we'll still call point-0-0-0 "Paula Abdul significance,"

There was something in the air that day,
The fog went away, Prof. Reifman,
He was talking about SEM,
And our heads didn't swim, Prof. Reifman,

Though we never thought that we would grasp, under-identification,
We now see it's when a model's flown, with too much unknown, Prof. Reifman,

There was something in the air that day,
The fog went away, Prof. Reifman,
He was talking about SEM,
And our heads didn't swim, Prof. Reifman,

Though we never thought that we would grasp, degrees of freedom,
We can calculate them now, in fact, we just subtract, Prof. Reifman,
We can calculate them now, in fact, we just subtract, Prof. Reifman,

Graphics Programs for Drawing SEM Diagrams

On the SEMNET discussion listserv around April 3-4, 2010, someone asked about graphics programs for drawing structural-equation-model diagrams, and other participants sent in suggestions. I, personally, find AMOS and PowerPoint to be good. However, if anyone wants to examine additional programs, here are some:

GraphViz

Concept Draw

Concept Map (perhaps more appropriate for illustrating theory construction than actual SEM drawing)

Easy Draw (seems like a very general graphic-arts program)

ADDED 6/10/2017: PowerPoint Tips for Displaying SEM Models

Further Issues for Full Structural Models

Now that we've learned the basics of full structural models, we'll be taking up the following topics in the coming weeks:

Maximum Likelihood Estimation

Equivalent models

Handling single-indicator variables

Negative variances (Heywood Cases)

Mediation

Equality constraints (these lecture notes also touch briefly on longitudinal models and multiple-group analyses)

Longitudinal (panel) models

Multiple-Group Modeling (see notes on equality constraints above; Kyle Gillett dissertation in links section to the right; and this article, which we'll revisit from when we learned about measurement and structural models)

Dyadic analysis in SEM (Actor-Partner Interdependence Model)

Running an AMOS model off of a published correlation/covariance matrix from the literature

Software comparison: AMOS vs. Mplus

Advanced Applications

Latent Growth Modeling (here and here)

Compared to the more piecemeal/incremental cross-lagged panel models for longitudinal analysis, latent growth models test for predictors and correlates of respondents' long-term growth trajectories (see cannon-ball analogy). Thanks to Tim and Xiaohui for photographing the board after class on May 1, 2012. Some illustrative references on latent growth modeling are:

Barnes, G. M., Reifman, A. S., Farrell, M. P., & Dintcheff, B. A. (2000). The effects of parenting on the development of adolescent alcohol misuse: A six-wave latent growth model. Journal of Marriage and the Family, 62, 175-186.

Wampler, R. S., Munsch, J., & Adams, M. (2002). Ethnic differences in grade trajectories during the transition to junior high. Journal of School Psychology, 40, 213-237.

Partial Least Squares (Alternative to Conventional SEM for Small Samples)

University-Quality Assignment

The following is the model for the new assignment. You will run the model twice, once without the three red-dashed paths and once with them. We will learn about comparative model testing.



Here's a direct link to the figure we recently looked at regarding where variances are located in full structural models, as well as how degrees of freedom are determined in a full structural model.

The model also makes salient the issue of outliers, in particular that Harvard's endowment (and to a lesser extent those of a few other institutions) are so much larger than most others. Harvard and these other elite universities have endowments in the billions, whereas many other schools have endowments well under 1 billion. This document discusses approaches to handling outliers; in the past we've used winsorizing, but this year, we'll use a square-root transformation (already implemented in the data set).

There is some evidence that the depressed economy may be "winsorizing" Harvard's endowment, but this didn't occur early enough to be reflected in the data set.

UPDATE (2014): Here's an illustration of the terminology you should use, regarding measurement and structural portions of the model, and factor loadings vs. structural paths. (Thanks to Satabdi for the photo.)

Creating Subscales: Exact Factor Scores vs. Unit Weighting

Here's a graphic display I created to illustrate the difference between using exact factor scores to make subscales vs. unit weighting. I also found a good online article by DiStefano et al. and a thorough PowerPoint show by Wuensch on the subject. You can click on the graphics below to enlarge them (note that there are TWO slides to click on, one on top of the other).

SEM The Musical 3

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…..