Accession Number:

ADA231850

Title:

Essential Independence and Likelihood-Based Ability Estimation for Polytomous Items

Descriptive Note:

Technical rept. 1987-1990

Corporate Author:

ILLINOIS UNIV AT URBANA DEPT OF STATISTICS

Personal Author(s):

Report Date:

1991-01-07

Pagination or Media Count:

48.0

Abstract:

A definition of essential independence is proposed for sequences of polytomous items. For items satisfying the reasonable assumption that the expected amount of credit awarded increases with examinee ability, we develop a theory of essential unidimensionality which closely parallels that of Stout. Essentially unidimensional item sequences can be shown to have a unique up to change-of-scale dominant underlying trait, which can be consistently estimated by a monotone transformation of the sum of the item scores. In more general polytomous-response latent trait models with or without ordered responses, an M-estimator based upon maximum likelihood may be shown to be consistent for theta under essentially unidimensional violations of local independence and a variety of monotonicityidentifiability conditions. A rigorous proof of this fact is given, and the standard error of the estimator is explored. These results suggest that ability estimation methods that rely on the summation form of the log likelihood under local independence should generally be robust under essential independence, but standard errors may vary greatly from what is usually expected, depending on the degree of departure from local independence. An index of departure from local independence is also proposed.

Subject Categories:

  • Statistics and Probability

Distribution Statement:

APPROVED FOR PUBLIC RELEASE