Welcome!

Here are links to our lecture notes on the different course topics...

Intro: The Pyramid of Success

Correlation, Least-Squares Principle, and Multiple Regression

Path Analysis

Exploratory Factor Analysis (herehere, and here)

Confirmatory Factor Analysis (herehere, and here)...

...and Associated Basic Concepts (degrees of freedom [here and here]; model fitreporting fit)

ONYX Program

Writing Up SEM/CFA Results

Full Structural Models (herehere, and here); also see the following article for discussion of what a "model" represents:

Rodgers, J. L. (2010). The epistemology of mathematical and statistical modelling. A quiet revolution. American Psychologist, 65, 1-12. 

Video clip of legendary physicist Richard Feynman discussing conclusions one can draw from tests of theoretical models.

Comparative Model Testing and Nestedness

Beyond the Basics of SEM (contains all our topics for roughly the second half of the course)

Diagram for Assignment 2

Refresher Diagram on SEM Terminology

SEM The Musical: 1234567, 8, 9, 10

Graphic arts programs

Reminder of Terminology in an SEM

To the beginning SEM practitioner, terms such as "parameter," "factor loading," and "directional path" may be confusing. Here's a drawing on the whiteboard (with some touch-ups in PowerPoint) to help clarify proper usage. Thanks to the students who photographed the board!


Introduction to ONYX

ONYX is a free SEM package developed in Germany. We will use it for Assignment 1 in our Spring 2017 class, a CFA on the Hendrick and Hendrick love styles. Here are some tips I have come up with for using ONYX, given its differences from other SEM programs:

1. Everything is done through right-clicking to bring up menus.

2. You can use a plain-text (tab-delimited) ".dat" file saved from an SPSS data file. The ONYX user manual lists available options for designating missing data. Once you've drawn your model, you can use "Load Data" to connect to the .dat file, yielding what's called a "Data Panel."

3. Use the "Create Variable" option to generate either latent or observed variables.

4. You should name latent variables (in ALL CAPITALS) via the right-clicking. However, but you’ll have to drag in the measured variables from the "Data Panel" to the variables' respective boxes in the model. By hovering over the measured-variable boxes, you can verify that the data have been linked.

5. By right-clicking on top of a variable, you can use the "Add Path" tool (the default is to draw unidirectional "causal" paths, whereas holding down the Shift key while using "Add Path" yields dual-headed correlational arrows).

6. All unstandardized factor loadings start out fixed at 1; you should free all of them (i.e., letting them take on freely estimated values). To identify the model (i.e., make sure you're not estimating more quantities than you have information for), construct variances should be fixed to 1.*

7. The default settings yield an unstandardized solution, whereas usually we're interested in a standardized one. You can obtain a standardized solution by right-clicking on each indicator’s box and selecting “z-score Transform.”

8. Covariances (correlations between factors) are also fixed and should be freed.

9. Unlike other programs, where you submit a run, ONYX is constantly running in the background and responds to changes you make in model specifications. Right-clicking and selecting “Show Estimate Summary” will show current results.

---
*Fixing (or constraining) variables, underidentification, and degrees of freedom are discussed here. I have edited the linked document to distinguish between suggestions for when the AMOS program is used, vs. ONYX.

SEM The Musical 10


The tenth annual SEM The Musical was held on Thursday, May 5. We performed a few new songs this year, as shown below. We also performed songs from previous SEM Musicals. Three older songs we performed this year are available on YouTube (thanks to SH for filming). These songs are "Common Model Mistakes" (originally from SEM The Musical 9), "Saturated Your Model" and "If You Wanna Join My Construct (You've Gotta Load with My Friends)," the latter two from SEM The Musical 8. To see the lyrics from these (and other) older songs, just click on the year number of the musical: 123456789.


SEM Musical TEN!
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 (TEN!), SEM Musical (HERE!),
SEM Musical (TEN!), SEM Musical (HERE!),
SEM Musical (TEN!), SEM Musical (HERE!),
SEM Musical (TEN!), 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 (TEN!), SEM Musical (HERE!),
SEM Musical (TEN!), SEM Musical (HERE!),
SEM Musical (TEN!), SEM Musical (HERE!),
SEM Musical (TEN!), SEM Musical (HERE!),
Yeah...


The Part That’s Error-Free 
Lyrics by Alan Reifman
(May be sung to the tune of “Biggest Part of Me,” David Pack for Ambrosia)

Boxes, they hold the manifestations,
Bubbles, are error locations,
Constructs, house the shared variation,
They're the part, that’s error-free,

Loadings, show measures, are correlated,
That makes, indicators validated,
Errors, in the bubbles, they are gated,
So constructs, are error-free,

Well...
You remove error,
And the paths, become more true*,
This is such, a key thing,
Latent constructs, do for you,

So draw it now,
Tell measurement error, to shoo.
You can estimate, the paths,
Without error, troubling you,

Sometimes, you have just, total-scale measures,
Of those, certain constructs, that you treasure,
Alpha, gives a way to block displeasure,
Controls, unreliability,

Parcels, a technique, that can’t be plainer,
Items, placed into, random containers,
These sets, can then serve, as indicators,
Constructs now, are error-free,

Well-l-l-l-l...
You remove error,
And the paths, become more true,
This is such, a key thing,
Latent constructs, do for you,

So draw it now,
Tell the measurement error, to shoo,
You can estimate, the paths,
Without error, troubling you,

(Instrumentals)

It’s an SEM hallmark,
Going back to CFA,
It’s a major advantage, of using LV’s,

Not all techniques, give you this,
Measurement error, doesn’t go away,
So use latent constructs, to be error-free,
Be error-free,
Be error-free...

*Stephenson, M. T., & Holbert, R. L. (2003). A Monte Carlo simulation of observable versus latent variable structural equation modeling techniques. Communication Research, 30, 332-354.

See also previous lecture modules here and here.


Those Kinds of Paths (Are Autoregressive)
Lyrics by Alan Reifman
(May be sung to the tune of “Because the Night,” Springsteen/Smith)

Panel models, longitudinally,
Follow the same people, over time,
Each major construct, we include repeatedly,
It gets us the time-ordering, of causality,

So, come on now, no hand-calculated math,
In cross-lagged models, we run paths,
From Construct A at one time, to B at the next,
We also have paths, from the same construct,
Time 1 to Time 2, and Time 2 to Time 3,

Those kinds of paths, are auto-regressive,
Those kinds of paths, test stability,
Those kinds of paths, are auto-regressive,
Those kinds of paths, test stability,

Autoregressive paths, play a crucial role,
They control for earlier levels, of a later DV,
So when a cross-lagged path, is significant,
It shows association, beyond stability,

So, come on now, no hand-calculated math,
In cross-lagged models, we run paths,
From Construct A at one time, to B at the next,
We also have paths, from the same construct,
Time 1 to Time 2, and Time 2 to Time 3,

Those kinds of paths, are auto-regressive,
Those kinds of paths, test stability,
Those kinds of paths, are auto-regressive,
Those kinds of paths, test stability,

(Guitar solo)

These kinds, of paths,
Predict, to later versions, of themselves,
Without them, analyses would lack rigor,
So include them...

Time 1 to Time 2, Time 2 to Time 3,
Time 1 to Time 2, Time 2 to Time 3,
Time 1 to Time 2, Time 2 to Time 3,

Those kinds of paths, are auto-regressive,
Those kinds of paths, test stability,
Those kinds of paths, are auto-regressive,
Those kinds of paths, test stability,

Those kinds of paths, are auto-regressive,
Those kinds of paths, test stability,
Those kinds of paths, are auto-regressive,
Those kinds of paths, test stability,

Those kinds of paths, are auto-regressive,
Those kinds of paths, test stability,
Those kinds of paths, are auto-regressive,
Those kinds of paths, test stability,

Those kinds of paths, are auto-regressive,
Those kinds of paths, test stability,
Those kinds of paths, are auto-regressive,
Those kinds of paths, test stability...


Constructs (Don’t be Afraid of Changing!)
Lyrics by Diane Wittie
(May be sung to the tune of “Landslide,” Stevie Nicks)

Gathered the data, and they abound,
I cleaned them up, then I went to town,
And I saw some variables, that looked interesting,
And now my sleep, would be sound,

Oh, yes I can begin, naming latent constructs,
But will those, constructs make any sense?
Will they adequately represent,
What I envision?
Can I implement, my central concepts?

Uh-hum, I do think so,

Well, don’t be, afraid of changing,
’Cause your constructs, need to make sense,
Think through, your decisions,
You may need, revisions,
Don't do anything, you'll rue,

(Brief guitar)

So, don’t be, afraid of changing,
’Cause your constructs, need to make sense,
Think through, your decisions,
You may need, revisions,
Don't do anything, you'll rue,
To your theory, be true,

So, analyze your data, see what you've found,
Your model, may earn great renown!
If you see factor loadings, at plus or minus .4,
Well maybe, high points you will score,
If you see structural paths, that are significant,
Yes, high points, you will score!

Mediational Models

As we saw in the journal-assignment presentations, many SEM-based studies examine mediation between variables. To mediate is to go in the middle, like a negotiation mediator comes between the labor union and management.

In statistical analysis, we often start out with a relationship between two variables. Using an example from one of my grad-school mentors, Patricia Gurin, cigarette smoking and lung cancer are positively associated.

Cigarette Smoking ==> Lung Cancer

Why does this relationship exist? A more fine-grained understanding would be that smoking leads to lung tissue damage, and tissue damage leads to cancer. Tissue damage would thus be considered the mediator or mechanism.

Cigarette Smoking ==> Tissue Damage ==> Lung Cancer

Reuben Baron and David Kenny published an article in 1986 on mediation that has been cited over 58,000 times! Kenny summarizes the process in a nutshell here. In the following figure, I apply Baron and Kenny's "old school" method to Gurin's example. Note that one would run the model twice.



(Illustration of Baron and Kenny's, 1986, logic. Example from Patricia Gurin, University of Michigan, circa 2002-2003, link)

The above diagram presents the scenario of full mediation (i.e., the initially significant direct path from antecedent to outcome becomes nonsignificant). One can then say that the mediator accounts fully for the antecedent-outcome relationship. If the initial direct path from antecedent to outcome remains significant after addition of the two mediational paths, but the initial direct path is reduced in magnitude, one can claim partial mediation (see Huselid and Cooper, 1994, "Gender roles as mediators of sex differences in expressions of pathology").

As Kenny writes on his website, "More contemporary analyses focus on the indirect effect." The leading names associated with contemporary mediational analysis are Andrew Hayes and Kristopher Preacher, who indeed emphasize indirect effects. The indirect effect can be calculated by multiplying the standardized paths from antecedent to mediator, and from mediator to outcome (think back to our unit on path-analysis tracing rules).


The indirect effect is .15 in the above example. If each of the two segments of the indirect effect (A to M, and M to O) is each statisically significant (i.e., different from zero), we would be confident that the indirect effect also is significant. As Hayes (2009, "Beyond Baron and Kenny: Statistical mediation analysis in the new millennium") notes, however, "it is possible for an indirect effect to be detectably different from zero even though one of its constituent paths is not." What is called for is a significance test of the indirect effect of .15 (or whatever value one has).

The problem is that there is no existing theoretical distribution such as the z, t, F, or chi-square distribution to judge the statistical significance of an indirect effect (i.e., whether or not one's obtained indirect effect falls in the upper or lower 2.5% of the distribution for a two-tailed p < .05 significance level). Therefore, researchers use a "synthetic" statistical distribution for testing the significance of indirect effects, known as a "bootstrap" distribution. Kenny discusses this on his website and it is also illustrated in slide 6 of this slideshow.

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: 1234567, 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: 1234567).

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!