Conditional Inference in Small Sample Scenarios Using a Resampling Approach

Clemens Draxler and Andreas Kurz
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Clemens Draxler: Institute of Psychology, UMIT—Private University for Health Sciences Medical Informatics and Technology GmbH, 6060 Hall in Tirol, Austria
Andreas Kurz: Institute of Psychology, UMIT—Private University for Health Sciences Medical Informatics and Technology GmbH, 6060 Hall in Tirol, Austria

Stats, 2021, vol. 4, issue 4, 1-13

Abstract: This paper discusses a non-parametric resampling technique in the context of multidimensional or multiparameter hypothesis testing of assumptions of the Rasch model. It is based on conditional distributions and it is suggested in small sample size scenarios as an alternative to the application of asymptotic or large sample theory. The exact sampling distribution of various well-known chi-square test statistics like Wald, likelihood ratio, score, and gradient tests as well as others can be arbitrarily well approximated in this way. A procedure to compute the power function of the tests is also presented. A number of examples of scenarios are discussed in which the power function of the test does not converge to 1 with an increasing deviation of the true values of the parameters of interest from the values specified in the hypothesis to be tested. Finally, an attempt to modify the critical region of the tests is made aiming at improving the power and an R package is provided.

Keywords: conditional distribution; non-parametric resampling; multiparameter hypothesis testing; psychometrics; Rasch model (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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