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CONFIDENCE INTERVALS FOR TEST INFORMATION AND RELATIVE EFFICIENCY
Author(s) -
Oosterloo Sebie
Publication year - 1984
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/j.1467-9574.1984.tb01101.x
Subject(s) - pointwise , mathematics , rasch model , statistics , confidence interval , item response theory , function (biology) , test (biology) , efficiency , score test , likelihood ratio test , econometrics , psychometrics , mathematical analysis , paleontology , evolutionary biology , estimator , biology
In latent theory the measurement properties of a mental test can be expressed in the test information function. The relative merits of two tests for the same latent trait can be described by the relative efficiency function, i.e. the ratio of the test information functions. It is argued that these functions have to be estimated if the values of the item difficulties are unknown. Using conditional maximum likelihood estimation as indicated by Andersen (1973), pointwise asymptotic distributions of the test information and relative efficiency function are derived for the case of dichotomously scored Rasch homogeneous items. Formulas for confidence intervals are derived from the asymptotic distributions. An application to a mathematics test is given and extensions to other latent trait models are discussed.