Cox (1972) proposed a discrete-time survival model that is somewhat analogous to the proportional hazards model for continuous time. Efron (1988) showed that this model can be estimated using ordinary logistic regression software, and Singer and Willett (1993) provided a detailed illustration of a particularly flexible form of the model that…

Three methods of estimating test score distributions that may improve on using the observed frequencies (OBFs) as estimates of a population test score distribution are considered: the kernel method (KM); the polynomial method (PM); and the four-parameter beta binomial method (FPBBM). The assumption each method makes about the smoothness of the…

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…

The current status of item response theory (IRT) is discussed. Several IRT methods exist for assessing whether an item is biased. Focus is on methods proposed by L. M. Rudner (1975), F. M. Lord (1977), D. Thissen et al. (1988) and R. L. Linn and D. Harnisch (1981). Rudner suggested a measure of the area lying between the two item characteristic…

Two modification formulas are presented for the test information function in order to provide better measures of local accuracies of the estimation of "theta" when maximum likelihood estimation is used to provide the estimate of ability "theta." A minimum bound of any estimator, biased or unbiased, is considered; and Formula 1…

Three strategies for augmenting the interpretation of significance test results are illustrated. Determining the most suitable indices to use in evaluating empirical results is a matter of considerable debate among researchers. Researchers increasingly recognize that significance tests are very limited in their potential to inform the…

A variety of locally dependent models are introduced having individual difference parameters that may be interpreted as reflecting effective learning abilities. One version is a univariate extension of the Rasch model with a Markov property: the probability that a given individual will pass an item depends on previous items only through the…

Work on item response theory was extended to two areas not extensively researched previously, including models for: (1) test items that require more than one ability for a correct response (MIRT); and (2) interaction between modules of instruction that have a hierarchical relationship (HST). In order to develop the MIRT and HST models, the author…

Methods for examining the viability of assumptions underlying generalized linear models are considered. By appealing to the likelihood, a natural generalization of the raw residual plot for normal theory models is derived and is applied to investigating potential misspecification of the linear predictor. A smooth version of the plot is also…

Standard procedures for estimating item parameters in Item Response Theory models make no use of auxiliary information about test items, such as their format or content, or the skills they require for solution. This paper describes a framework for exploiting this information, thereby enhancing the precision and stability of item parameter…

The analysis of fit of data to a measurement model for graded responses is described. The model is an extension of Rasch's dichotomous model to formats which provide more than two levels of response to items. The model contains one parameter for each person and one parameter for each "step" in an item. A dichotomously-scored item…

Problems and procedures in assessing and obtaining fit of data to the Rasch model are treated and assumptions embodied in the Rasch model are made explicit. It is concluded that statistical tests are needed which are sensitive to deviations so that more than one item parameter would be needed for each item, and more than one person parameter would…

In an experiment manipulating artificial data in a factorial design, model misspecification and varying levels of error in measurement and in model structure are shown to have significant effects on LISREL parameter estimates in a modified peer influence model. (Author/LMO)

A solution to the problem of specification error due to excluded variables in statistical models of treatment effects in nonrandomized (nonequivalent) control group designs is presented. It involves longitudinal observation with at least two pretests. A maximum likelihood estimation program such as LISREL may provide reasonable estimates of…

California Assessment Program's application of matrix sampling and item response curve theory to the scaling and reporting of state assessment data is described. It is designed to express educational outcomes in an efficient and interpretable form that is both immediately informative and suited to analysis over extended periods of time.…