An Empirical Assessment of Saddlepoint Approximations for Testing a Logistic Regression Parameter

Bedrick, Edward J.; Hill, Joe R.

doi:10.2307/2532307

Cited by 19 publications

(9 citation statements)

References 24 publications

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“…Some real examples of other sorts of small data sets are given in Reference [1]. Inference based on large sample results can be highly inaccurate when applied to small samples, particularly when data are imbalanced or nearly separated [2]; saddlepoint and Edgeworth approximations can signiÿcantly improve inference [3,4]. However, if a hyperplane can be found that separates the independent variables for one outcome from those for the alternative outcome, logistic regression procedures will fail to converge, and maximum likelihood estimates (MLEs) for the regression parameters will tend to ±∞.…”

Section: Introductionmentioning

confidence: 99%

A permutation test for inference in logistic regression with small‐ and moderate‐sized data sets

Potter

2004

Statistics in Medicine

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Inference based on large sample results can be highly inaccurate if applied to logistic regression with small data sets. Furthermore, maximum likelihood estimates for the regression parameters will on occasion not exist, and large sample results will be invalid. Exact conditional logistic regression is an alternative that can be used whether or not maximum likelihood estimates exist, but can be overly conservative. This approach also requires grouping the values of continuous variables corresponding to nuisance parameters, and inference can depend on how this is done. A simple permutation test of the hypothesis that a regression parameter is zero can overcome these limitations. The variable of interest is replaced by the residuals from a linear regression of it on all other independent variables. Logistic regressions are then done for permutations of these residuals, and a p-value is computed by comparing the resulting likelihood ratio statistics to the original observed value. Simulations of binary outcome data with two independent variables that have binary or lognormal distributions yield the following results: (a) in small data sets consisting of 20 observations, type I error is well-controlled by the permutation test, but poorly controlled by the asymptotic likelihood ratio test; (b) in large data sets consisting of 1000 observations, performance of the permutation test appears equivalent to that of the asymptotic test; and (c) in small data sets, the p-value for the permutation test is usually similar to the mid-p-value for exact conditional logistic regression.

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Section: Introductionmentioning

confidence: 99%

A permutation test for inference in logistic regression with small‐ and moderate‐sized data sets

Potter

2004

Statistics in Medicine

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“…Although it would be simpler to illustrate the methods for continuous data, we feel that much of the important practical use of these methods, for exponential families, will be for discrete data. Davison (1988) and Bedrick and Hill (1992) consider applications much the same as here.…”

Section: Introductionmentioning

confidence: 99%

Practical Use of Higher Order Asymptotics for Multiparameter Exponential Families

Pierce

Peters

1992

Journal of the Royal Statistical Society Series B: Statistical Methodology

106

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SUMMARY Recently developed asymptotics based on saddlepoint methods provide important practical methods for multiparameter exponential families, especially in generalized linear models. The aim here is to clarify and explore these. Attention is restricted to tests and confidence intervals regarding a single parametric function which can be represented as a natural parameter of a full rank exponential family. Excellent approximations to exact conditional inferences are often available, in terms of simple adjustments to the signed square root of the likelihood ratio statistic. The focus is on distinguishing between two aspects of the adjustments: one reducing effects of nuisance parameter estimation and the other adjusting for little information regarding the parameter of interest. Numerical results are given for some Poisson and multinomial models.

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“…This can also happen when the table is small but contains very large as well as small cell counts. For such problematic tables, there should be additional research on (1) hybrid algorithms that use exact methods for some parts of the computation and approximations for other parts (Baglivo, Olivier and Pagano, 1988), (2) fast ways of simulating the exact distribution (Kreiner, 1987;Mehta, Patel and Senchaudhuri, 1988), and (3) better asymptotic approximations (e.g., Koehler, 1986), including saddlepoint approximations (Davison, 1988;Booth and Butler, 1990;Bedrick and Hill, 1992;Pierce and Peters, 1992).…”

Section: Future Researchmentioning

confidence: 99%

A Survey of Exact Inference for Contingency Tables

Agresti¹

1992

Statist. Sci.

941

650

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JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. Abstract. The past decade has seen substantial research on exact inference for contingency tables, both in terms of developing new analyses and developing efficient algorithms for computations. Coupled with concomitant improvements in computer power, this research has resulted in a greater variety of exact procedures becoming feasible for practical use and a considerable increase in the size of data sets to which the procedures can be applied. For some basic analyses of contingency tables, it is unnecessary to use large-sample approximations to sampling distributions when their adequacy is in doubt. This article surveys the current theoretical and computational developments of exact methods for contingency tables. Primary attention is given to the exact conditional approach, which eliminates nuisance parameters by conditioning on their sufficient statistics. The presentation of various exact inferences is unified by expressing them in terms of parameters and their sufficient statistics in loglinear models. Exact approaches for many inferences are not yet addressed in the literature, particularly for multidimensional contingency tables, and this article also suggests additional research for the next decade that would make exact methods yet more widely applicable. Institute of Mathematical Statistics

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An Empirical Assessment of Saddlepoint Approximations for Testing a Logistic Regression Parameter

Cited by 19 publications

References 24 publications

A permutation test for inference in logistic regression with small‐ and moderate‐sized data sets

A permutation test for inference in logistic regression with small‐ and moderate‐sized data sets

Practical Use of Higher Order Asymptotics for Multiparameter Exponential Families

A Survey of Exact Inference for Contingency Tables

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