NDLI: Testing order restrictions in contingency tables

Content Provider	Springer Nature Link
Author	Colombi, R. Forcina, A.
Copyright Year	2015
Abstract	Though several interesting models for contingency tables are defined by a system of inequality constraints on a suitable set of marginal log-linear parameters, the specific features of the corresponding testing problems and the related procedures are not widely well known. After reviewing the most common difficulties which are intrinsic to inequality restricted testing problems, the paper concentrates on the problem of testing a set of equalities against the hypothesis that these are violated in the positive direction and also on testing the corresponding inequalities against the saturated model; we argue that valid procedures should consider these two testing problems simultaneously. By reformulating and adapting procedures appeared in the econometric literature, we propose a likelihood ratio and a multiple comparison procedure which are both based on the joint distribution of two relevant statistics; these statistics are used to divide the sample space into three regions: acceptance of the assumed equality constraints, rejection towards inequalities in the positive direction and rejection towards the unrestricted model. A simulation study indicates that the likelihood ratio based procedure perform substantially better. Our procedures are applied to the analysis of two real data sets to clarify how they work in practice.
Starting Page	73
Ending Page	90
Page Count	18
File Format	PDF
ISSN	00261335
Journal	Metrika
Volume Number	79
Issue Number	1
e-ISSN	1435926X
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2015-04-18
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Stochastic orderings Chi-bar squared distribution Positive association Statistics Statistics for Business/Economics/Mathematical Finance/Insurance Probability Theory and Stochastic Processes Economic Theory/Quantitative Economics/Mathematical Methods
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Statistics, Probability and Uncertainty

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