# The Box-Cox Transformation and Non-Iterative Estimation Methods For Ordinal Log-Linear Models

Eric J. Beh, Thomas B Farver

Research output: Contribution to journalArticle

### Abstract

Recently Beh and Farver investigated and evaluated three non-iterative procedures for estimating the linear-by-linear parameter of an ordinal log-linear model. The study demonstrated that these non-iterative techniques provide estimates that are, for most types of contingency tables, statistically indistinguishable from estimates from Newton's unidimensional algorithm. Here we show how two of these techniques are related using the Box-Cox transformation. We also show that by using this transformation, accurate non-iterative estimates are achievable even when a contingency table contains sampling zeros.

Original language English (US) 475-484 10 Australian and New Zealand Journal of Statistics 54 4 https://doi.org/10.1111/anzs.12007 Published - Dec 2012

### Fingerprint

Box-Cox Transformation
Log-linear Models
Contingency Table
Estimate
Zero
Log-linear models
Box-Cox transformation
Contingency table

### Keywords

• Box-Cox transformation
• Linear-by-linear association
• Newton's unidimensional method
• Ordinal log-linear model

### ASJC Scopus subject areas

• Statistics and Probability
• Statistics, Probability and Uncertainty

### Cite this

In: Australian and New Zealand Journal of Statistics, Vol. 54, No. 4, 12.2012, p. 475-484.

Research output: Contribution to journalArticle

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