SEM The Musical 9

Our ninth annual SEM The Musical was held on April 30, 2015. We performed some new songs this year, as shown below. We also performed songs from previous SEM Musicals (links: 1, 2, 3, 4, 5, 6, 7, 8).

SEM Musical NINE!
Lyrics by Alan Reifman (retread from previous years)
(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 (NINE!), SEM Musical (HERE!),
SEM Musical (NINE!), SEM Musical (HERE!),
SEM Musical (NINE!), SEM Musical (HERE!),
SEM Musical (NINE!), 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 (NINE!), SEM Musical (HERE!),
SEM Musical (NINE!), SEM Musical (HERE!),
SEM Musical (NINE!), SEM Musical (HERE!),
SEM Musical (NINE!), SEM Musical (HERE!),
Yeah…


Let's Run the S-E-M
Lyrics by Tobi Ruwase
(May be sung to the tune of "Let's Call the Whole Thing Off," George & Ira Gershwin)

We have finally, come to the end,
Of Dr. Alan Reifman’s class,
QM 1 to 4 have taken two years,
From correlation to regression,

Goodness knows, what the end will be,
As we prep, for our exams,
It’s time for us, to go down memory lane... (slight pause)
Some things, that we’ve learnt:

We need constructs and we need items,
We need items, for each of our constructs,
Constructs and items, items and constructs,
Let’s run the SEM,

Open the data, run your bivariates,
Check for loadings, higher than the cut-off,
Correlations! Loadings! Inform your decisions,
Let’s run the SEM,

But oh! If we run the SEM (slow),
There may be a glitch,
And oh! If we get a glitch,
Then AMOS would not run,

So, we’ve got correlations, we proceed to AMOS,
Select the data file, from SPSS,
Click on OK, now we’ve got our data,
Now we run SEM,
Oh! Let’s run the SEM,

We call it, the BAM TOOL!!!
In the AMOS toolbar,
It draws your constructs, and then your items,
Constructs and items, items and constructs,
Let’s run the SEM,

Using your cursor, for two types of arrows,
Uni-directed or two-headed arrows,
Construct to items, Oh, structural paths,
Let’s run the SEM,

But oh! If we run the SEM,
There may be a glitch,
And oh! If we get a glitch,
Then AMOS would not run,

So label your constructs, don’t forget items,
Time to run the AMOS, don’t forget properties,
Means and intercepts, for the missing data,
Now we run SEM,
Oh! Lets’ run the SEM,

We need construct and we need items,
We need items, for each of our constructs,
Constructs and items, items and constructs,
Let’s run the SEM,

Open the data, run your bivariates,
Check for loadings, higher than the cut-off,
Correlations! Loadings! Inform your decisions,
Let’s run the SEM,

But oh! If we run the SEM,
There may be a glitch,
And oh! If we get a glitch,
Then AMOS would not run,

So, we’ve got correlations, we proceed to AMOS,
Click on OK, now we’ve got our data,
Now we run SEM,
Oh! Let’s run the SEM,
Let’s run the SEMMMMMMMMMMMM........

The AMOS Structural Equation Modeling program has a lot of graphical features, which the beginning SEM student must adjust to. Let's do an earlier song ("Once You Work in AMOS") on the topic before our new one.

Click, Hold, and Drag
Lyrics by Alan Reifman, inspired by Tobi Ruwase
(May be sung to the tune of "Jump, Jive, and Wail," Louis Prima, popularized in recent decades by the Brian Setzer Orchestra)

Video of this song being performed.

Tobi, Tobi, drew a big model, on her pad,
Tobi, Tobi, drew a big model, on her pad,
When you learn AMOS,
You gotta make the paths, zig and zag,

Oh, you gotta click and hold, then you drag,
You gotta click and hold, then you drag,
You gotta click and hold, then you drag,
You gotta click and hold, then you drag,
You gotta click and hold, then you drag away...

(Saxophone solo)

All these shapes, with a label, she's got to tag,
All these shapes, with a label, she's got to tag,
With the variable names,
From SPSS, in the bag,

Oh, you gotta click and hold, then you drag,
You gotta click and hold, then you drag,
You gotta click and hold, then you drag,
You gotta click and hold, then you drag,
You gotta click and hold, then you drag away...

(Guitar solo)

A model is a model, and an AMOS error, is a nag,
A model is a model, and an AMOS error, is a nag,
You gotta draw things right,
So other statisticians, will not rag,

Let's make sure, her drawing work, doesn't lag,
Let's make sure, her drawing work, doesn't lag,
So that she can get,
Her model to run, without a snag,

Oh, you gotta click and hold, then you drag,
You gotta click and hold, then you drag,
You gotta click and hold, then you drag,
You gotta click and hold, then you drag,
You gotta click and hold, then you drag away...

You gotta click and hold, then you drag,
You gotta click and hold, then you drag,
You gotta click and hold, then you drag,
You gotta click and hold, then you drag,
You gotta click and hold, then you drag away...

Oh, you gotta click and hold, then you drag,
You gotta click and hold, then you drag,
You gotta click and hold, then you drag,
You gotta click and hold, then you drag,
You gotta click and hold, then you drag away...

You gotta click and hold...
You gotta click and hold...
You gotta click and hold...

(Guitar flourish)


Common Model Mistakes
Lyrics by Alan Reifman
(May be sung to the tune of "My Favorite Mistake," Crow/Trott)

Performance videos of this song from SEM The Musical 9 and 10.

Omitting, residual bubbles,
Will surely, get you in trouble,
When AMOS gives your model, a run,

Deleting a, fixed-one loading,
Should trigger a sense, of foreboding,
The error messages, are no fun,

You should know, as you go,
When you're, just beginning,
These are some of, the more subtle errors,

You should know, as you go,
These are, common mistakes,

(Instrumental)

Misnaming, your indicators,
Will bring an, emotional nadir,
You'll have to find out, just where you failed,

Grouping scales, with low correlation,
Your constructs, will bring frustration,
Check Pearson r's, and then you'll sail,

You should know, as you go,
When you're, just beginning,
These are some of, the more subtle errors,

You should know, as you go,
These are common mistakes,
These are common mistakes,

(Bridge)

Well, SEM is, quite technical,
Little things, will send a ripple,
If you get, an error message,
Look at the, above suggestions,
They should help you, find your way,

(Instrumental)

Keep in mind, you will find,
These aren't, the only ones,
That you'll encounter,
Other things, can go wrong,

Keep your concentration, high,
These mistakes, can make you cry,

These are common mistakes,
These are common mistakes,
These are common mistakes...

Fit It
Lyrics by Brandon Logan
(May be sung to the tune of "Whip It," G. Casale/M. Mothersbaugh for Devo)

Performance video.

Check that fit,
Really question it,
Pick out a stat,
Take a look at that,

When a matrix, comes along,
You must fit it,
To prove that, the model’s strong,
You must fit it,
When something’s going wrong,
You must fit it,

Now fit it,
N-F-I,
Get it high,
Com-par...
...i-tive or,
Absolute,
Try to increase it,
The C-F-I,
Go fit it,
Fit it good,

Minimum is not achieved,
You won’t fit it,
Constraints to be released,
So you can fit it,
This must be policed,
For you can fit it,

I say fit it,
Fit it good,
I say fit it,
Fit it good,

(Interlude)

Check that fit,
Really question it,
Pick out a stat,
Take a look at that,

When a matrix comes along,
You must fit it,
To prove that, the model’s strong,
You must fit it,
When something’s going wrong,
You must fit it,

Now fit it,
N-F-I,
Get it high,
Com-par...
...i-tive or,
Absolute,
Try to increase it,
The C-F-I...

Now fit it,
N-F-I,
Get it high,
Com-par...
...i-tive or,
Absolute,
Try to increase it,
The C-F-I
Go fit it,
Oh, fit it good!


We'll now perform some "classics" and, finally, our traditional closing number: Parsi-Mony

SEM The Musical 8

UPDATE: Our eighth annual SEM The Musical was held on April 29, 2014. We had three new songs this year, which are shown below. We also performed some songs from previous SEM Musicals (links: 1, 2, 3, 4, 5, 6, 7).

Ivette Noriega, sporting her homemade Daft Punk helmet, and Dr. Reifman perform "Saturated Your Model." You may click on the photo to enlarge it. 

Saturated Your Model (example)
Lyrics by Ivette Noriega and Alan Reifman
(May be sung to the tune of “Get Lucky,” Bangalter/de Homem-Christo/Williams/Rodgers)

Performance videos of this song from SEM The Musical 9 and 10.

In the world, of SEM graphs,
All the paths, have beginnings,
It keeps, statisticians spinning (uh-huh),
AMOS will be helping,

(Look)

You've, gone too far,
You’ve linked all, paths there are,
None you’ve left out,
Einstein’s quote, did you flout?

Fit indices are at 1,
Degrees of freedom are none,
You’ve got to know, what you’ve done,
You’ve saturated your model!

Fit indices are at 1,
Degrees of freedom are none,
You’ve got to know, what you’ve done,
You’ve saturated your model!

You’ve saturated your model,
You’ve saturated your model,
You’ve saturated your model,
You’ve saturated your model,

(Instrumental)

S-E-M, has no limits,
Your theory, is depicted,
What is it, you’re testing?
Parsimony says, leave out paths (uh-huh),

You've, gone too far,
You’ve linked all, paths there are,
None you’ve left out,
Einstein’s quote, did you flout?

Fit indices are at 1,
Degrees of freedom are none,
You’ve got to know, what you’ve done,
You’ve saturated your model!

Fit indices are at 1,
Degrees of freedom are none,
You’ve got to know what you’ve done,
You’ve saturated your model!

You’ve saturated your model,
You’ve saturated your model,
You’ve saturated your model,
You’ve saturated your model,

(Voice-synthesizer in background, shown in red)

Fit indices are at 1, 
Fit indices are at 1, 
Fit indices are at 1, 
Fit indices are at 1 

Fit indices are at 1 (all of them), 
Fit indices are at 1 (it's hard to interpret), 
Fit indices are at 1, 
Fit indices are at 1,

You’ve saturated your model! 
You’ve saturated your model! 
You’ve saturated your model! 
You’ve saturated your model!

You’ve saturated your model! 
You’ve saturated your model! 
You’ve saturated your model! 
You’ve saturated your model!

You've, gone too far,
You’ve linked all, paths there are,
None you’ve left out,
Einstein’s quote, did you flout?

Fit indices are at 1,
Degrees of freedom are none,
You’ve got to know, what you’ve done,
You’ve saturated your model!

Fit indices are at 1,
Degrees of freedom are none,
You’ve got to know, what you’ve done,
You’ve saturated your model!

You’ve saturated your model!
You’ve saturated your model!
You’ve saturated your model!
You’ve saturated your model!

You’ve saturated your model!
You’ve saturated your model!
You’ve saturated your model!
You’ve saturated your model...

***

The "Spice Guys," Nicholas (Hairy Spice) and Alan (Veggie Spice), perform "If You Wanna Join My Construct."

If You Wanna Join My Construct (You've Got to Load with My Friends) 
Lyrics by Nicholas Johnston and Alan Reifman
May be sung to the tune of “Wannabe” (Spice Girls/Rowe/Stannard)

Performance video of this song from SEM The Musical 9 and 10.

Yo, I’ll tell you what to draw, what you really need to draw,
So, tell me what to draw, what I really need to draw,
I’ll tell you what to draw, what you really need to draw,
So, tell me what to draw, what I really need to draw,
I need a circle, need a box, I need a circle, need a box...,
Really, really, really, really, really, need a box, 

If you like my construct, then load significantly,
If you wanna join me, minimize residuality,
Now don't go wasting, iterations,
Get your r's together, we could load just fine,

I’ll tell you what to draw, what you really need to draw,
So, tell me what to draw, what I really need to draw,
I need a circle, need a box, I need a circle, need a box...,
Really, really, really, really, really, need a box,

If you want to join my construct, you gotta load with my friends,
Sharing variation, on that constructs depend,
If you want to join my construct, you have got to show,
High r’s with the other, manifests, you know,

What do you think about that, now that you know the deal?
Say you fit my construct, is your manifest for real?
Got a small residual, I'll give you a try,
If the construct won't account for your variance, then I'll say goodbye,

Yo, I’ll tell you what to draw, what you really need to draw,
So, tell me what to draw, what I really need to draw,
I need a circle, need a box, I need a circle, need a box...,
Really, really, really, really, really, need a box,

If you want to join my construct, you gotta load with my friends,
Sharing variation, on that constructs depend,
If you want to join my construct, you have got to show,
High r’s with the other, manifests, you know,

So here's a story, from r to p,
You wanna get with me, you gotta load significantly,
We got CFA tests in place, and coefficients to taste,
You then see, on your screen, which V loads, on the C,
All your V's, you can see, reflect variance, manifestly,
And if you please, you'll see...

Get your constructs drawn, and run your model now,
Get your constructs drawn, and run your model now,

If you want to join my construct, you gotta load with my friends,
Sharing variation, on that constructs depend,
If you want to join my construct, you have got to show,
High r’s with the other, manifests, you know,

If you want to join my construct...
You gotta, you gotta, you gotta, you gotta, you gotta, load, load, load, load....

Get your constructs drawn and run your model now,
Get your constructs drawn and run your model now (uh, uh, uh, uh...).
Get your constructs drawn and run your model now,
Get your constructs drawn zigazig-ah,

If you want to join my construct...


Non-Exchangeable 
Lyrics by Alan Reifman
May be sung to the tune of “Unforgettable” (Irving Gordon; popularized by Nat King Cole) 

Non-exchangeable,
Some dyads’ fate,
They’re arrange-able,
By role, or trait,

Such as hetero, spouses or steadies,
Teacher-student pairs, boss and employees,
(Slow) These are studied,
From a distinguishable, view,

But, exchangeable,
Are some, you see,
It’s not absolute,
Who’s A, and B,

Friends, or twins, or old college roommates,
Same-sex spouses, or pairs who go on dates,
More complex stats,
Will be needed, for you...

[Interlude -- Instrumental and vocal improvisation]

Non-exchangeable,
Some dyads’ fate,
They’re arrange-able,
By role, or trait,

Other pairs are, interchangeable,
Their data are, re-arrangeable,
So their, APIM models,
Are harder, to do...

Thanks to Satabdi and Rebecca for the photos!

SEM The Musical 7

SEM The Musical 7 is now complete. New songs for this year are listed below, along with photos from some of the performances. Thanks to Hannah Korkow, Andrea Parker, Nancy Trevino Schafer, and Paulina Velez for the pictures. Links to the songs from our previous musicals are as follows: 1, 2, 3, 4, 5, 6.

The Road to S-E-M
Lyrics by Alan Reifman
May be sung to the tune of “Shambala” (Daniel Moore, popularized by Three Dog Night)

Factor analysis, and how to correlate,
On the road to S-E-M,
Need to know regression, and draw paths so straight,
On the road to S-E-M,

Ooh-ooh-hoo, ooh-ooh-ooh, yeah...
Run your S-E-M,
Ooh-ooh-hoo, ooh-ooh-ooh, yeah...
Run your S-E-M,

You’ll draw little boxes, and these larger hoops,
On the road to S-E-M,
You’ll run panel models, and multiple groups,
On the road to S-E-M,

Ooh-ooh-hoo, ooh-ooh-ooh, yeah...
Run your S-E-M,
Ooh-ooh-hoo, ooh-ooh-ooh, yeah...
Run your S-E-M,

What... is your NFI,
Once you’ve run, your S-E-M?
What... is your TLI,
Once you’ve run, your S-E-M?

(Brief guitar solo)

The measurement model, that’s a CFA,
On the road to S-E-M,
There’s the structural part, paths that flow one way,
On the road to S-E-M,

Ooh-ooh-hoo, ooh-ooh-ooh, yeah...
Run your S-E-M,
Ooh-ooh-hoo, ooh-ooh-ooh, yeah...
Run your S-E-M,

What... is, Hoelter’s CN,
Once you’ve run, your S-E-M?
What... is your CFI,
Once you’ve run, your S-E-M?

And, chi-square to df,
Once you’ve run, your S-E-M?
And, RM-SEA,
Once you’ve run, your S-E-M?

Ooh-ooh-hoo, ooh-ooh-ooh, yeah...
Run your S-E-M,
Ooh-ooh-hoo, ooh-ooh-ooh, yeah...
On the road to S-E-M,

Ooh-ooh-hoo, ooh-ooh-ooh, yeah...
On... the... road...
Ooh-ooh-hoo, ooh-ooh-ooh, yeah...
On the road to S-E-M...

(More guitar)

His right hand a blur, Dr. Reifman shows off some of his air-guitar technique.

---

Why Don’t You Run a Set of Nested Models?
Lyrics by Alan Reifman
(May be sung to the tune of [I Don’t Know Why You Don’t Take Me] Downtown; Laird/McAnally/Hemby; popularized by Lady Antebellum)

Well, I was trying to get a model going,
Staring at AMOS, bright on my screen,
I tried to think, but not really knowing,
Had a few pathways,
But really now, what does it mean?

Knew a scale, which could be a mediator,
Could draw paths, right through X-Y-Z,
Inside my mind, I became a debater,
Should I model cause-to-effect, directly?
But then... a low voice, said to me:

“Why don’t you run, a set of nested models?
Why don’t you run, a test, to check and see,
If the new paths, lower the chi-square?
I mean, significant-ly?”

“It is a very simple, calculation,
Subtract the smaller, from the larger chi-square,
Then you compare results, to a table,
And that’s how you, test nested models, if you dare,
Oh-oh-oh, if you dare...”

I want to keep my, number of paths low,
To follow notions, of parsimony,
Einstein said to keep, scientific theories,
As simple as they, can possibly be,
But no simpler!

And here... comes that voice...

“Why don’t you run, a set of nested models?
Why don’t you run, a test, to check and see,
If the new paths, lower the chi-square?
I mean, significant-ly?”

“It is a very simple, calculation,
Subtract the smaller, from the larger chi-square,
Then you compare results, to a table,
And that’s how you, test nested models, if you dare...”

(Guitar solos)

“Why don’t you run, a set of nested models?
Why don’t you run, a test, to check and see,
If the new paths, lower the chi-square?
I mean, significant-ly?”

“It is a very simple, calculation,
Subtract the smaller, from the larger chi-square,
Then you compare results, to a table,
And that’s how you, test nested models, if you dare,
Oh-oh-oh, if you dare...”

“Yeah, why don’t you run a set of nested models?”

OK, I’ll run a set of nested models...
(Music fades out)

Now I get it...

 Violeta Kadieva, the first student ever to write two songs for a single musical (see next two songs).

Trouble When I Ran You
Lyrics by Violeta Kadieva
(May be sung to the tune of “I Knew You Were Trouble,” Swift/Martin/Shellback)

I discovered how, to draw AMOS models,
And I was having fun, getting it to run,
It dawned on me, it dawned on me, it dawned on me…. (ee-ee-ee-ee-ee)

I had to run a, new measurement model,
I used AMOS, to fit hypothesized paths,
And draw the diagram, draw the diagram, draw the diagrammmm (ee-ee-ee-ee-ee)

And I raaannnn the modeelll, with all the vaaaariables,
And I also included, the factor indicators there,

And I knew you were trouble when I ran you,
So shame on me that,
I did not draw, another alternative model,
To check if it, could be a better fit,

And I knew you were trouble when I ran you,
So shame on me that,
I did not draw another, alternative model,
Noooow I am so wondering about it, 

Runs? No! Trouble, trouble, trouble,
Runs? No! Trouble, trouble, trouble,

So what can I do? Let’s run another one,
Explore another one, by adding other paths,
And check if it's a better one, it's a better one, and improves the model (ee-ee-ee-ee-ee)

I checked the chi squares, with and without new paths,
So, the model changed degrees, the delta of the change is,
We'll just have to see, we'll just have to see, we'll just have to see (ee-ee-ee-ee-ee),

The chi squaaaare table, showwwwed signiiiificant improvement,
And I realized having more paths, improves the model signiiificantly,

I knew you were trouble when I ran you,
So shame on me that,
I did not draw another alternative model,
To check if it could be a better fit,

And I knew you were trouble when I ran you,
So shame on me that,
I did not draw any equivalent models,
Now I am so wondering about it,

Runs? No! Trouble, trouble, trouble,
Runs? No! Trouble, trouble, trouble,

So when the model, is improved significantly,
By costing us only, a few degrees of freedom,
And lowering the chi square significantly,
We have to accept the alternative model as a better model to use,
Yes exactlyyy…

(Lengthy sound-effects riff)

I knew you were trouble when I ran you,
So shame on me that,
I did not draw another alternative model,
To check if it could be a better fit,

I knew you were trouble when I ran you,
So shame on me that,
I did not draw any equivalent models either,
Now I am so wondering about it,

Runs? No! Trouble, trouble, trouble,
Runs? No! Trouble, trouble, trouble,

I knew you were trouble when I ran you,
Trouble, trouble, trouble,

I knew you were trouble when I ran you,
Trouble, trouble, trouble...

A Terrifying Model

Lyrics by Violeta Kadieva (performance accompanied by Esperanza Bregendahl, right)

(May be sung to the tune of "Terrified," DioGuardi/Reeves, popularized by Katharine McPhee)

You, AMOS stats,

Are the greatest... find,

In the world, of software,

You're the  S-E-M package...

Did not make it, with my loadings, to the standard,

Of the point-4 magnitude...

I ran it again, with a new notion,

Each iteration, sends my heart, like a shooting star,

I'm looking at, the weak connections,

But I think that, I might not be too far...

And I-I-I-I-I...

And I-I-I-I-I... I'm terrified…

For the first time, and hopefully the last time,

In S-E-M life (ummm-mmm)

This, could be good,

I'm ready to update, my diagram,

And nothing's worse,

Than not seeking..., a novel path,

And this could be, all that I need,

Maybe if I try...

My revised model, is now in motion,

Each iteration, seems likes it getting near,

I'm looking at, much stronger loadings,

Looking at the fit, I now cheer!

And I-I-I-I-I... ,

And I-I-I-I-I... I'm still terrified,

For the first time and hopefully the last time

In S-E-M… life,

I only, just looked, at the Root Mean Square*,

And the Root Mean Square's, below oh-5,

So don't you doubt, what I've been running,

To point-9, the fit indices are close,

As a modeler, I feel alive...

I checked it again, looked at the fit measures,

Each iteration, is giving a small chi-square,

And its ratio, to degrees of freedom's, not even 3,

And I-I-I-I-I... I did it,

And I am not terrified anymore,

For the first time and hopefully the last time,

In S-E-M… life…life…life,

S-E-M life...

[*Root Mean Square Error of Approximation, more commonly known as the RMSEA.]

 

The next song, "Nice Nice Beta," was performed by Lisa Merchant (left, with brass knuckles spelling out "AMOS"), Kaitlin Leckie (with the Beta necklace), and I-Shan Yang (not pictured)

Nice Nice Beta 
Lyrics by Kaitlin Leckie,
(May be sung to the tune of  "Ice Ice Baby," Vanilla Ice/Earthquake/M. Smooth; based on earlier song "Under Pressure," Queen [Deacon/May/Mercury/Taylor] and Bowie)

Yo SEM let’s run it

(Hook) Nice nice Beta
Nice nice Beta
All right stop.

Correlate and regress them, SEM is back with a brand new edition,
Something grabs a hold of me tightly, could be a residual influence slightly,
Will it be significant? I don't know,
Minimum achieved? Fo sho'!
To the output, I must get a handle, Maximum Likelihood estimate? Full.
Husband and wife, data distinguished,
Exchangeable? Plan is extinguished,
Who checks Betas? Should be everybody,
Anything less than .20, is a felony,
Means and intercepts, with missing, estimate,
Better hit the minimum, the model won’t wait,
If there was an error, yo I’ll will solve it,
Check out the model, while AMOS resolves it

(Hook) Nice nice Beta,
Nice nice Beta,
.20 is a nice nice Beta,
.20 is a nice nice Beta,

Now that the arrows are jumping, the constructs kicked in,
The indicators are pumping, stats to the point,
 To the point of no faking, cooking up models, like a pound of bacon,
Burning them if you ain’t thorough and nimble,
I go crazy when I see a Greek symbol,
And a dataset with the groups all stacked,
I’m on a roll and it’s time to see impact,
AMOS version 21-point-0,
With estimates on, so missings won’t blow,
Means on standby, waiting just to say hi,
Did you stop? No I just standardized,
Kept on pursuing the solution, find it relates but no causal attribution,
Effects immense, yo so I determined it’s Actor Partner Interdependence,
Results so hot they’re creatin’ haters,
Research hovers on single-level data,
Jealous ‘cause my model’s lookin’ fine,
TLI with nine-five; CFI with point-nine,
How’s that for goodness of fit?
The haters acting ill, because the model’s such a hit*,

Factor loadings, rang out like a bell,
Check my indicators-all I see is swell,
Following the constructs real fast,
Judged by the indicators-shows that they’ll last,
Factor to factor the model’s packed,
I’m trying to determine if the model lacks,
Effects on the actors and partners you see,
Daring dyadic data analyses,
If there was an error, yo I’ll solve it,
Check out the model, while AMOS resolves it

Nice Nice Beta,
.20 is a nice nice Beta (repeat)

*[One could substitute "hot sh--," but we're a family-oriented group!]

Fit & Fine
Lyrics by Andrea Parker, Anuradha Sastry, and Paulina Velez
(May be sung to the tune of “Suit & Tie,” Timberlake/Mosley/Carter/Harmon/Fauntleroy/Stubbs/Wilson/Still; performed by Justin Timberlake, featuring Jay Z)

Checking on the CFI, TLI, NFI,
Checking on the CFI, TLI, NFI,
Can I show you a few things?
A few things, a few things, how the model fits,

Checking on the CFI, TLI, NFI,
Checking on the CFI, TLI, NFI,
Let me show you a few things, Let me show you a few things,
Are you ready Reifman?

[Verse 1]
I can't wait, till I get to run my model in AMOS,
Got a large data set, just like a census,
I cleaned up the data and I just have to run them,
Hope it fits fine, cause it's all mine,
Hey baby, I have three latent constructs,
If the loadings are above 0.4,
We might learn something,
Hoping that the minimum is achieved when we run it,
Fits so fine, tonight,

[Hook]
And as long as I've got my CFI,
I'mma move on to the NFI,
And they are both above 0.9,
This might be a good fit,
TLI is also high,
RMSEA as low as Kenny likes,
Fit is tested in AMOS, tonight,

Let me show you a few things,
Let me show you a few things,
Show you a few things about fit,
While we’re running a model,
This is a good fit,
Show you a few things about fit,
Hey,

[Verse 2]
Stop, let me get a good look at Hoelter’s,
Ohhh so neat, now I know why Berndt likes it,
Ohhh chi-square is big and might make it rubbish,
But that's alright, cause the rest are fine,
Ohhh go on and celebrate with a party,
I guess friends are mad, cause they wish they had it,
Uuuu my model, the fittest, yeah you're a classic,
And you're all mine tonight,

[Hook]
And as long as I've got my CFI,
I'mma move on to the NFI,
And they are both above 0.9,
 This might be a good fit,
TLI is also high,
RMSEA as low as Kenny likes,
Fit is tested in AMOS tonight,
Let me show you a few things,
Let me show you a few things,
Show you a few things about fit,
While we’re running a model,
This is a good fit,
Show you a few things about fit...

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 April 17, 2018)

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.

NEW! Video of Todd Little speaking at Texas Tech about parceling (February 2, 2018). Dr. Little discusses strategic parceling approaches, as opposed to random parceling. Follow this link to the video (limited to TTU); listed under Daniel Bontempo, organizer of IMMAP series.

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. (2014). Manifest variable path analysis: Potentially serious and misleading consequences due to uncorrected measurement error. Psychological Methods, 19, 300-315. (LINK)

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

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!