How to do Model Selection from Contingency Analysis

[#1]

My domain is Consumer Research.  I have 7 explanatory variables and 1 response variable.  All are categorical.

My objective is to replace the response variable with one or a combination of the explanatory variables.

My approach:

• Perform contingency analyses of each of the explanatory variables with the response.
• From the contingency analysis, select the explanatory variable with the highest R-square (U).  Because the number of levels are different, I don’t think Likelihood Ratio or Pearson chi-square values would be helpful in the model selection.
• From the Measures of Association table, use Lambda and Uncertainty values.  Choose the explanatory variable with the highest values.

Below is a summary describing the variables and results of contingency analysis.

Variable #	# levels	Rsq(U)	LR-chi sq	Pearson chi sq	Lambda Asym (C|R, R|C)	Lambda Sym.	Uncertainty coef (C|R, R|C)	Uncertainty coef (Sym)
A	4	.08	248	268	.08, .13	.1	.08, .08	.08
B	3	.02	76	75	.06, .02	.04	.02, .03	.03
C	10	.04	136	153	.05, .04	.045	.04, .03	.034
D	10	.31	961	1207	.33, .13	.22	.3, .2	.245
E	18	.34	1056	1498	.34, .1	.21	.34, .19	.24
F	40	.345	1084	1590	.34, .05	.17	.35, .15	.21
G	6	.32	1000	1286	.35, .28	.31	.32, .26	.29

The response variable has 6 levels.

Levels in variables, D, E, F, G are ordered by ascending intensity.  It is assumed the low and high boundaries are similar.

Questions:

1.  Is the approach as outlined valid?
2. Can I combine one of the variables from D,E,F,G ( I am inclined to select G) with one or more from A,B,C to get a better model (i.e., better replacement for the response)?  If so, how might one do this and what metrics might be used to select the best model?

[#2 · Accepted solution]

The two-way contingency table analysis is valid in its own right, but it is not sufficient for your purpose. Logistic regression using a linear predictor that combines all the variables will satisfy your need better.

Start here in the JMP on-line documentation to learn what logistic regression is, how to set up your data, how to launch the analysis platform, and the results that are available to answer your questions.

[#3]

Thank you, Mark!
I have used Logistic Regression in the past but only with binary responses (e.g., Stable/Unstable). This instance would be a great learning opportunity. Will get right to it!