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On the Sampling Interpretation of Confidence Intervals and Hypothesis Tests in the Context of Conditional Maximum Likelihood Estimation

Published online by Cambridge University Press:  01 January 2025

E. Maris
E. Maris*
Affiliation:
Department of Mathematical Psychology, Nijmegen Institute for Cognition and Information (NICI) National Institute for Educational Measurement (CITO)
*
Requests for reprints should be sent to Eric Maris, Department of Mathematical Psychology (NICI), Catholic University of Nijmegen, P.O. Box 9104, 6500 HE Nijmegen, THE NETHERLANDS.
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Abstract

In the context of conditional maximum likelihood (CML) estimation, confidence intervals can be interpreted in three different ways, depending on the sampling distribution under which these confidence intervals contain the true parameter value with a certain probability. These sampling distributions are (a) the distribution of the data given the incidental parameters, (b) the marginal distribution of the data (i.e., with the incidental parameters integrated out), and (c) the conditional distribution of the data given the sufficient statistics for the incidental parameters. Results on the asymptotic distribution of CML estimates under sampling scheme (c) can be used to construct asymptotic confidence intervals using only the CML estimates. This is not possible for the results on the asymptotic distribution under sampling schemes (a) and (b). However, it is shown that the conditional asymptotic confidence intervals are also valid under the other two sampling schemes.

Keywords

CML estimationconfidence intervalsconditional inference
Type
Original Paper
Information
Psychometrika , Volume 63 , Issue 1 , March 1998 , pp. 65 - 71
Copyright
Copyright © 1998 The Psychometric Society

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Footnotes

I am indebted to Theo Eggen, Norman Verhelst and one of Psychometrika's reviewers for their helpful comments.

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