Open AccessLINKING WITH CONTINUOUS EXPONENTIAL FAMILIES: SINGLE‐GROUP DESIGNS
Author(s) -
Haberman Shelby J.
Publication year - 2008
Publication title -
ets research report series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.235
H-Index - 5
ISSN - 2330-8516
DOI - 10.1002/j.2333-8504.2008.tb02147.x
Subject(s) - mathematics , bivariate analysis , univariate , exponential family , marginal distribution , quantile , natural exponential family , exponential distribution , statistics , exponential function , equating , distribution (mathematics) , sample (material) , sample size determination , group (periodic table) , multivariate statistics , mathematical analysis , random variable , rasch model , chemistry , organic chemistry , chromatography
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.