**SEM The Musical 2**.

**[Update: It's now been presented.]**I've written some new songs, as has one of our students (shown below), plus we'll perform some "classics" from last year's musical.

**It Do Run Run**

Lyrics by Alan Reifman

(May be sung to the tune of “Da Doo Run Run,” Spector/Greenwich/Barry)

Got to draw a model that is error-free,

So it will run, run, so it will run,

Got to have constraints where they’re supposed to be,

So it will run, run, so it will run,

Oh, I got a Heywood Case,

Variance, I must replace,

Everything, is back on pace,

It do run, run, run; it do run, run,

Making sure my model is identified,

So it will run, run, so it will run,

Making sure conditions are all satisfied,

So it will run, run, so it will run,

Yeah, it runs so well,

The fit indices are swell,

No problems on which to dwell,

It do run, run, run; it do run, run...

*And now, three songs about enumerating your degrees of freedom and the related issue of model identification.*

**Count ’Em Up**

Lyrics by Alan Reifman

(May be sung to the tune of “Build Me Up Buttercup,” d'Abo/Macaulay, for The Foundations)

You’ve got to count ’em up (count ’em up), degrees of freedom,

So you’ll understand (understand), the model at hand,

And when you compare (you compare), two nested models,

When you add some paths (add some paths), to your arrow graphs,

You’ll know how (you’ll know how), to conduct the delta test,

And decide which model you’ll seize,

So count ’em up (count ’em up), all of your freedom’s degrees,

The measures in your trove, their variances and cov’s,

Are in a half-matrix, they’re your known elements,

From these you subtract, parameters you enact,

The model that you state, and freely estimate,

(Hey, hey, hey!) The df’s, are the difference,

(Hey, hey, hey!) Start out with known elements,

(Hey, hey, hey!) Then deduct,

The free parameters, and now it all makes sense,

You’ve got to count ’em up (count ’em up), degrees of freedom,

So you’ll understand (understand), the model at hand,

And when you compare (you compare), two nested models,

When you add some paths (add some paths), to your arrow graphs,

You’ll know how (you’ll know how), to conduct the delta test,

And decide which model you’ll seize,

So count ’em up (count ’em up), all of your freedom’s degrees…

**D-of-F in SEM**

Lyrics by Shera Jackson

(May be sung to the tune of "Flowers on the Wall," Lew DeWitt for the Statler Brothers)

I keep hearing about counting degrees of freedom for SEM,

Trying to keep it all straight is hard to do,

If I were a statistician, I wouldn’t worry none,

As I’m adding this up, I’m starting to have fun,

Counting degrees of freedom for SEM,

That don’t bother me at all,

Counting up the elements,

And now the parameters,

I’m adding all the knowns and subtracting the unknowns,

Now, don’t tell me I’ve nothing to do,

Last night I made a matrix, found the diagonal,

That’s my variances, and underneath are my co-v’s,

Please, don’t forget the means when using “means and intercepts,”

Square the elements, subtract them, divide by 2, and add them back,

Counting degrees of freedom for SEM,

That don’t bother me at all,

Counting up the elements,

And now the parameters,

I’m adding all the knowns and subtracting the unknowns,

Now, don’t tell me I’ve nothing to do,

Well, let’s count the unknowns, so many, free factor loadings,

Structural Paths, non-directional correlations,

Indicator residual variances, and

Construct residual variances ,and construct variances,

Counting degrees of freedom for SEM,

That don’t bother me at all,

Counting up the elements,

And now the parameters,

I’m adding all the knowns and subtracting the unknowns,

Now, don’t tell me I’ve nothing to do,

Now , counting degrees of freedom for SEM,

That don’t bother me at all,

Counting up the elements,

And now the parameters,

I’m adding all the knowns and subtracting the unknowns,

Now, don’t tell me I’ve nothing to do,

Don’t tell me I’ve nothing to do...

**Over-identified**

Lyrics by Alan Reifman

(May be sung to the tune of “Overjoyed,” Stevie Wonder)

To get your, structural diagram, to run fine,

Elements, and your parameters, must align, oh,

If you ask too much, your model will crash,

Plan it carefully, don’t let your choices be rash,

You cannot, have unknowns that number, more than knowns,

Negative, your degrees of freedom, cannot go, yeah,

You can use constraints, so free paths reduce,

Without more measures, that’s all you can do,

Under-iden-tified will not run,

What have you done?

You’ve posited,

More than known in-for-ma-tion,

To make sure that all is satisfied,

It has to be,

Overall, over-iii-dentified…

If you draw, all the curves and arrows, that you can,

You will have, mandated perfect fit, on your hands, oh,

If you saturate, you can’t judge the fit,

It’s always perfect, that’s automatic,

Just-i-den-ti-fied fit, will be one,

What have you done?

You’ve drawn all paths,

There could be under the sun,

To make sure that all is satisfied,

It has to be,

Overall, over-iii-dentified…

**Chi-Square Rising**

Lyrics by Alan Reifman

(May be sung to the tune of “Bad Moon Rising,” John Fogerty)

I see a chi-square rising,

I see the fit going astray,

You need to add more parameters,

What could be another pathway?

Parsimony’s nice, bad fit could be a price,

There’s a chi-square on the rise,

I see a chi-square rising,

I see there’s more that can be done,

Relations, you need to account for,

Then you can let the model run,

Parsimony’s nice, bad fit could be a price,

There’s a chi-square on the rise…

**Curvy, Swervy, Dual-Connected, Correlation Bi-Directed**

Lyrics by Alan Reifman

(May be sung to the tune of “Itsy-Bitsy, Teeny-Weeny, Yellow Polka-Dot Bikini,” Vance/Pockriss)

They were unsure whether A tends to precede B,

Or whether B occurs prior to A,

What could they do, to depict this in their model?

What symbolic notation could they portray?

It's not too late,

A and B could correlate,

They drew a curvy, swervy, dual-connected, correlation bi-directed,

That goes right in between A and B,

A curvy, swervy, dual-connected, correlation bi-directed,

So no one had to state causality...

**Three Wave**

Lyrics by Alan Reifman

(May be sung to the tune of “Heat Wave,” Holland/Dozier/Holland, popularized by Martha Reeves and the Vandellas)

You’re doing a survey,

Of how people change,

A trio of interviews,

With each person, you’ll arrange,

Autoregressive, and cross-lagged paths,

Equality constraints on the math,

You’ve got a three-wave,

Panel study design (three-wave!),

Not quite causation (three-wave!),

But, precedence of time…

*Example of a three-wave panel model.*