The present study investigates different approaches to adding covariates and the impact in fitting mixture item response theory models. Mixture item response theory models serve as an important methodology for tackling several psychometric issues in test development, including the detection of latent differential item functioning. A Monte Carlo…

The purpose of this report is to review ETS psychometric contributions that focus on test scores. Two major sections review contributions based on assessing test scores' measurement characteristics and other contributions about using test scores as predictors in correlational and regression relationships. An additional section reviews additional…

The Graded Response Model (GRM; Samejima, "Estimation of ability using a response pattern of graded scores," Psychometric Monograph No. 17, Richmond, VA: The Psychometric Society, 1969) can be derived by assuming a linear regression of a continuous variable, Z, on the trait, [theta], to underlie the ordinal item scores (Takane & de Leeuw in…

This dissertation comprises three papers that propose, discuss, and illustrate models to make improved inferences about research questions regarding student achievement in education. Addressing the types of questions common in educational research today requires three different "extensions" to traditional educational assessment: (1)…

There is a degree of instability in any measurement, so that if it is repeated, it is possible that a different result may be obtained. Such instability, generally described as "measurement error", may affect the conclusions drawn from an investigation, and methods exist for allowing it. It is less widely known that different disciplines, and…

The question of least-squares weights versus equal weights has been a subject of great interest to researchers for over 60 years. Several researchers have compared the efficiency of equal weights and that of least-squares weights under different conditions. Recently, S. V. Paunonen and R. C. Gardner stressed that the necessary and sufficient…

The effectiveness of 19 methods of smoothing was investigated as those methods apply to the equipercentile method of test equating. Seven methods involved smoothing the score distribution before the tests were equated (presmoothing). Seven involved smoothing the resultant points after the equating (postsmoothing). Five methods involved combining…

Psychometricians working in factor analysis and econometricians working in regression with measurement error in all variables are both interested in the rank of dispersion matrices under variation of diagonal elements. This paper reviews both fields; points out various small errors; and presents a methodological comparision of factor analysis and…

The results of six major projects are discussed including a comprehensive mathematical and statistical analysis of the problems caused by errors of measurement in linear models for assessing change. In a general matrix representation of the problem, several new analytic results are proved concerning the parameters which affect bias in…