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Linking With Continuous Exponential Families: Single-Group Designs

Author(s):
Haberman, Shelby J.
Publication Year:
2008
Report Number:
RR-08-61
Source:
ETS Research Report
Document Type:
Report
Page Count:
14
Subject/Key Words:
Information Theory, Score Linking, Continuous Exponential Families

Abstract

Continuous exponential families are applied to linking forms via a single-group design. In this application, a distribution from the continuous bivariate exponential family is used that has selected moments that match those of the bivariate distribution of scores on the forms to be linked. The selected continuous bivariate distribution then yields continuous univariate marginal distributions for the two forms. These marginal distributions then provide distribution functions and quantile functions that may be employed in equating. Normal approximations are obtained for the sample distributions of the conversion functions.

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