Goodness-of-Fit Tests for Log-Linear Models in Sparse Contingency Tables

Koehler, Kenneth J.

doi:10.1080/01621459.1986.10478294

Cited by 104 publications

(49 citation statements)

References 16 publications

(13 reference statements)

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“…This problem has been discussed by many authors. Our results are similar to those given in Larntz (1978) for the equiprobability case and of Koehler (1986) for the independent case. Development of more accurate approximate distributions is necessary for the test statistics for complete symmetry.…”

Section: Tests For H(cs)supporting

confidence: 80%

Validity and Applicability of Several Tests for Comparing Marginal Distributions of a Square Table with Ordered Categories

Uesaka¹

1991

Behaviormetrika

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There exist several methods of testing homogeneity of two marginal distributions of a square contingency table with ordinal categories.In the present paper, some notes on the properties of the test are made and validity and powers are examined by Monte Carlo simula tion. A modification of the Koch-Reinfurt test is proposed for achieving better small-sample approximation to the null distribution.Furthermore a cumulative chi-square test is proposed, which is expected to have fairly high power for broad alternatives of location and/or scale shift.Simulation studies indicate that in small or moderate samples, more accurate approxima tion distributions are worth developing for some of the tests examined. It is also shown that the power of tests is highly dependent on the latent distributional model and the skewness of the marginal probabilities.

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Section: Tests For H(cs)supporting

confidence: 80%

Validity and Applicability of Several Tests for Comparing Marginal Distributions of a Square Table with Ordered Categories

Uesaka¹

1991

Behaviormetrika

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“…Some work on sparse tables (Koehler, 1986) suggests that the Pearson test is preferable to the likelihood ratio test in such circumstances. Nevertheless, our empirical work has suggested that neither of these criteria, nor other standard approaches such as Akaike's Information Criterion, are very successful in deciding whether the disclosure risk measures will be well estimated and we shall not consider them further here.…”

Section: Rationalementioning

confidence: 99%

Assessing Identification Risk in Survey Microdata Using Log-Linear Models

Skinner

Shlomo

2008

Journal of the American Statistical Association

118

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ABSTRACT. This article considers the assessment of the risk of identification of respondents in survey microdata, in the context of applications at the United Kingdom (UK) Office for National Statistics (ONS). The threat comes from the matching of categorical 'key' variables between microdata records and external data sources and from the use of log-linear models to facilitate matching. While the potential use of such statistical models is well-established in the literature, little consideration has been given to model specification nor to the sensitivity of risk assessment to this specification. In numerical work not reported here, we have found that standard techniques for selecting log-linear models, such as chi-squared goodness of fit tests, provide little guidance regarding the accuracy of risk estimation for the very sparse tables generated by 1 the accuracy of risk estimates. We find that, within a class of 'reasonable' models, risk estimates tend to decrease as the complexity of the model increases. We develop criteria which detect 'underfitting' (associated with overestimation of the risk). The criteria may also reveal 'overfitting' (associated with underestimation) although not so clearly, so we suggest employing a forward model selection approach. Our criteria turn out to be related to established methods of testing for overdispersion in Poisson log-linear models. We show how our approach may be used for both file-level and record-level measures of risk. We evaluate the proposed procedures using samples drawn from the 2001 UK Census where the true risks can be determined and show that a forward selection approach leads to good risk estimates. There are several 'good' models between which our approach provides little discrimination. The risk estimates are found to be stable across these models, implying a form of robustness. We also apply our approach to a large survey dataset. There is no indication that increasing the sample size necessarily leads to the selection of a more complex model. The risk estimates for this application display more variation but suggest a suitable upper bound.

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“…See also [19]. Extensive simulation experiments have been undertaken to learn in practice what 'large enough' means, see [5,20,21].…”

Section: Literature Reviewmentioning

confidence: 99%

The Information Geometry of Sparse Goodness-of-Fit Testing

Marriott

Sabolová

Bever

et al. 2016

Entropy

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This paper takes an information-geometric approach to the challenging issue of goodness-of-fit testing in the high dimensional, low sample size context where-potentially-boundary effects dominate. The main contributions of this paper are threefold: first, we present and prove two new theorems on the behaviour of commonly used test statistics in this context; second, we investigate-in the novel environment of the extended multinomial model-the links between information geometry-based divergences and standard goodness-of-fit statistics, allowing us to formalise relationships which have been missing in the literature; finally, we use simulation studies to validate and illustrate our theoretical results and to explore currently open research questions about the way that discretisation effects can dominate sampling distributions near the boundary. Novelly accommodating these discretisation effects contrasts sharply with the essentially continuous approach of skewness and other corrections flowing from standard higher-order asymptotic analysis.

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Goodness-of-Fit Tests for Log-Linear Models in Sparse Contingency Tables

Cited by 104 publications

References 16 publications

Validity and Applicability of Several Tests for Comparing Marginal Distributions of a Square Table with Ordered Categories

Validity and Applicability of Several Tests for Comparing Marginal Distributions of a Square Table with Ordered Categories

Assessing Identification Risk in Survey Microdata Using Log-Linear Models

The Information Geometry of Sparse Goodness-of-Fit Testing

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