Item response theory (IRT) and related latent variable models represent modern psychometric theory, the successor to classical test theory in psychological assessment. Although IRT has become prevalent in the measurement of ability and achievement, its contributions to clinical domains have been less extensive. Applications of IRT to clinical…

We present scaling outcomes for mathematics assessments used in the fall to screen students at risk of failing to learn the knowledge and skills described in the National Council of Teachers of Mathematics (NCTM) Focal Point Standards. At each grade level, the assessment consisted of a 48-item test with three 16-item sub-test sets aligned to the…

Person-fit research in the context of paper-and-pencil tests is reviewed, and some specific problems regarding person fit in the context of computerized adaptive testing (CAT) are discussed. Some new methods are proposed to investigate person fit in a CAT environment. These statistics are based on Statistical Process Control (SPC) theory. A…

There has been considerable research regarding the extent to which psychometric sound assessments sometimes yield individual score estimates that are inconsistent with the response patterns of the individual. It has been suggested that individual response patterns may differ from expectations for a number of reasons, including subject motivation,…

Theoretical null distributions of several fit statistic have been derived for paper-and-pencil tests. Examined whether these distributions also hold for computerized adaptive tests through simulation. Rates for two statistics studied were found to be similar in most cases. (SLD)

The purpose of this study is to determine an efficient way to reduce the bias in estimates of the Rasch model parameters due to aberrant response patterns. First, the benefits of using one- or two-sided goodness-of-fit tests of patterns with the model are discussed. Then, the consequences of removing non-fitting patterns from Rasch model data are…

Derivations of several item selection algorithms for use in fitting test items to target information functions (IFs) are described. These algorithms, which use an average growth approximation of target IFs, were tested by generating six test forms and were found to provide reliable fit. (SLD)

The use of indices and statistics based on nonlinear factor analysis (NLFA) has become increasingly popular as a means of assessing the dimensionality of an item response matrix. Although the indices and statistics currently available to the practitioner have been shown to be useful and accurate in many testing situations, few studies have…

A study involving 1,000 simulated examinees compared the partial credit and graded response models in computerized adaptive testing (CAT). The graded response model fit the data well and provided slightly more accurate ability estimates than those of the partial credit model. Benefits of polytomous model-based CATs are discussed. (SLD)

A 1992 study by R. Gershon found discrepancies when comparing the theoretical Rasch item characteristic curve with the average empirical curve for 1,304 vocabulary items administered to 7,711 students. When person-item mismatches were deleted (for any person-item interaction where the ability of the person was much higher or much lower than the…

The quality of fit between the data and the measurement model is fundamental to any discussion of results. Fit has been the subject of inquiry since as early as the 1920s. Most early explorations concentrated on assessing global fit or subset fits on fixed length, traditional paper and pencil tests given as a single unit. The detection of aberrant…

The robustness of a partial credit (PC) model-based computerized adaptive test's (CAT's) ability estimation to items that did not fit the PC model was investigated. A CAT program was written based on the PC model. The program used maximum likelihood estimation of ability. Item selection was on the basis of information. The simulation terminated…

Six papers on applications of item response theory are presented. Applications involved include item bias, criterion-referenced measurement problems, test score equating, computerized ability testing, information processing approaches, unidimensional binary responses, multidimensional and polychotomous responses, and estimation and goodness of…

Advantages and disadvantages of standard Rasch analysis computer programs are discussed. The unconditional maximum likelihood algorithm allows all observations to participate equally in determining the measures and calibrations to be obtained quickly from a data set. On the advantage side, standard Rasch programs can be used immediately, are…

This study attempts to estimate Structure of Learning Outcome (SOLO) levels in mathematics using the Partial Credit and Rating Scale models. A 30-item test comprising 10 testlets of 3 items each was designed and administered to 674 lower secondary school students. The items were arranged in a hierarchical manner, each testing SOLO levels in this…