Article

Psychometrika

, Volume 63, Issue 1, pp 65-71

On the sampling interpretation of confidence intervals and hypothesis tests in the context of conditional maximum likelihood estimation

  • E. MarisAffiliated withDepartment of Mathematical Psychology (NICI), Catholic University of NijmegenNational Institute for Educational Measurement (CITO)

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Abstract

In the context ofconditional 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 theincidental 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 theconditional asymptotic confidence intervals are also valid under the other two sampling schemes.

Key words

CML estimation confidence intervals conditional inference