A classic topic in the fields of psychometrics and measurement has been the impact of the number of scale categories on test score reliability. This study builds on previous research by further articulating the relationship between item response theory (IRT) and classical test theory (CTT). Equations are presented for comparing the reliability and…

FACTOR 9.2 was developed for three reasons. First, exploratory factor analysis (FA) is still an active field of research although most recent developments have not been incorporated into available programs. Second, there is now renewed interest in semiconfirmatory (SC) solutions as suitable approaches to the complex structures are commonly found…

This article focuses on four-parameter logistic (4PL) model as an extension of the usual three-parameter logistic (3PL) model with an upper asymptote possibly different from 1. For a given item with fixed item parameters, Lord derived the value of the latent ability level that maximizes the item information function under the 3PL model. The…

Models of modern test theory imply statistical independence among responses, generally referred to as "local independence." One violation of local independence occurs when the response to one item governs the response to a subsequent item. Expanding on a formulation of this kind of violation as a process in the dichotomous Rasch model,…

The software program DIMTEST can be used to assess the unidimensionality of item scores. The software allows the user to specify a guessing parameter. Using simulated data, the effects of guessing parameter specification for use with the ATFIND procedure for empirically deriving the Assessment Subtest (AT; that is, a subtest composed of items that…

Although Rasch models have been shown to be a sound methodological approach to develop and validate measures of psychological constructs for more than 50 years, they remain underutilized in psychology and other social sciences. Until recently, one reason for this underutilization was the lack of syntactically simple procedures to fit Rasch and…

The violation of the assumption of local independence when applying item response theory (IRT) models has been shown to have a negative impact on all estimates obtained from the given model. Numerous indices and statistics have been proposed to aid analysts in the detection of local dependence (LD). A Monte Carlo study was conducted to evaluate…

Optimal test-design methods are applied to rule-based item generation. Three different cases of automated test design are presented: (a) test assembly from a pool of pregenerated, calibrated items; (b) test generation on the fly from a pool of calibrated item families; and (c) test generation on the fly directly from calibrated features defining…

To address the lack of attention to construct shift in item response theory (IRT) vertical scaling, a multigroup, bifactor model was proposed to model the common dimension for all grades and the grade-specific dimensions. Bifactor model estimation accuracy was evaluated through a simulation study with manipulated factors of percentage of common…

Within the framework of item response theory (IRT), there are two recent lines of work on the estimation of classification accuracy (CA) rate. One approach estimates CA when decisions are made based on total sum scores, the other based on latent trait estimates. The former is referred to as the Lee approach, and the latter, the Rudner approach,…

There has been growing use of ideal point models to develop scales measuring important psychological constructs. For meaningful comparisons across groups, it is important to identify items on such scales that exhibit differential item functioning (DIF). In this study, the authors examined several methods for assessing DIF on polytomous items…

Test developers often need to create unidimensional scales from multidimensional data. For item analysis, "marginal trace lines" capture the relation with the general dimension while accounting for nuisance dimensions and may prove to be a useful technique for creating short-form tests. This article describes the computations needed to obtain…

Vertical scaling is necessary to facilitate comparison of scores from test forms of different difficulty levels. It is widely used to enable the tracking of student growth in academic performance over time. Most previous studies on vertical scaling methods assume relatively long tests and large samples. Little is known about their performance when…

The PROC NLMIXED procedure in Statistical Analysis System can be used to estimate parameters of item response theory (IRT) models. The data for this procedure are set up in a particular format called the "long format." The long format takes a substantial amount of time to execute the program. This article describes a format called the "wide…

Most methods for fitting cognitive diagnosis models to educational test data and assigning examinees to proficiency classes require the Q-matrix that associates each item in a test with the cognitive skills (attributes) needed to answer it correctly. In most cases, the Q-matrix is not known but is constructed from the (fallible) judgments of…