The Annals of Statistics

The Order-Restricted RC Model for Ordered Contingency Tables: Estimation and Testing for Fit

Ya'acov Ritov and Zvi Gilula

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Abstract

The RC model has been proposed as a model for ordered contingency tables. It involves parametric scores that are assigned to the rows and columns of the table so that these scores reflect the ordinality of the row and column categories. Efficient estimation of these parameters subject to order constraints remained an open problem mainly due to severe difficulties in computing these estimates and difficulties in deriving an appropriate asymptotic goodness-of-fit test. A nonstandard yet very simple algorithm is derived which produces the desired order-restricted maximum likelihood estimates with probability converging to 1. Testing the order-restricted RC model for fit is also discussed.

Article information

Source
Ann. Statist., Volume 19, Number 4 (1991), 2090-2101.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176348387

Digital Object Identifier
doi:10.1214/aos/1176348387

Mathematical Reviews number (MathSciNet)
MR1135165

Zentralblatt MATH identifier
0745.62058

JSTOR
links.jstor.org

Subjects
Primary: 62H17: Contingency tables
Secondary: 62H20: Measures of association (correlation, canonical correlation, etc.)

Keywords
Collapsed tables maximum likelihood order restriction parameetric scores

Citation

Ritov, Ya'acov; Gilula, Zvi. The Order-Restricted RC Model for Ordered Contingency Tables: Estimation and Testing for Fit. Ann. Statist. 19 (1991), no. 4, 2090--2101. doi:10.1214/aos/1176348387. https://projecteuclid.org/euclid.aos/1176348387


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