areas: methods: poem 

ARContribution by A. Baleno

searching the parameter space

1. Introduction

Long before you went heteroskedastic,
do you remember when models were plastic?

Your friends most often had troubles with stat.
But as a modeler type you knew it was phat.

This poem therefore will now cover four chapters
from marketing science to analysis of factors. 

2. Marketing Science

Asymmetric and fuzziest set,
linear, quadratic, cubic, quartet.

Scalars, vectors, numbers in rows
waiting in line for Little's Flows.

Pricing changes in models stochastic,
monopoly markets where demand's inelastic.

Snowballs and strata in sampling frames.
Nash equilibria in the theory of games.

Forecasting incidence of trial and repeat.
When you go make your choice, better make it discrete.

But who here among us would choose a dense probit
that amounts to exactly one half of a Tobit?

Where classmates who sit in the same latent classes
recite the same answers after multiple passes?

Iterate, update, climb for the pass.
Predict TV sales from Sopranos to Bass.

Market share, week+1, hierarchical Bayes.
We'll see who switches, we'll see who pays

using parameters that we can estimate
from a casually chosen Markov state.

Parameters free in a finite mixture.
Degrees of freedom by constant fixture.

3. Experimental Research

Assigning subjects by addition or subtraction,
with main effect and interaction,

there is no telling what you can find
through the lense of a factorial design.

Missing variables randomized away.
"Cause and effect," the data say.

4. Matrix Algebra

Extraction, rotation, plotting the scree.
Eigenvalues greater than unity.

Degrees of freedom, matrix ranks.
Lambda stolen without even thanks!

Wasn't that eigen supposed to be zero
instead of playing the brute force hero?

5. Estimation

Various forms of longitudinal data
have autocorrelation that biases beta.

Better to be consistent, efficient and good
with density explicit and max likelihood.

But if you should pick up the wrong distribution
you'll surprise the reviewers with a late substitution.

6. Covariance Models

Neither scatterplot, pie chart, leaf or stem
can capture a factor from SEM

with errors in models badly specified
and errors in variables where the measurement lied.

Minus two times the ratio's log.
Matrices swallowed a la Joreskog.

Measurement models that don't technically fit.
The logic of Chi Square?  Forget about it.

7. Future Directions

Its actually possible for an infinite sum
to add to a number a bit more than one

but a bit doesn't reach to the height of an elf.
Its what; more than half? Its only itself.

So first we decide on our own causal path.
Its hard to figure.  You do the math.