An important component of many Adaptive Instructional Systems (AIS) is a 'Learner Model' intended to track student learning and predict future performance. Predictions from learner models are frequently used in combination with mastery criterion decision rules to make pedagogical decisions. Important aspects of learner models, such as learning…

An important component of many Adaptive Instructional Systems (AIS) is a 'Learner Model' intended to track student learning and predict future performance. Predictions from learner models are frequently used in combination with mastery criterion decision rules to make pedagogical decisions. Important aspects of learner models, such as learning…

De la Torre and Deng suggested a resampling-based approach for person-fit assessment (PFA). The approach involves the use of the [math equation unavailable] statistic, a corrected expected a posteriori estimate of the examinee ability, and the Monte Carlo (MC) resampling method. The Type I error rate of the approach was closer to the nominal level…

This study investigated how population parameters representing heterogeneity of variance, skewness, kurtosis, bimodality, and outlier-proneness, drawn from normal and eleven non-normal distributions, also characterized the ranks corresponding to independent samples of scores. When the parameters of population distributions from which samples were…

Rasch used a Poisson model to analyze errors and speed in reading tests. An important property of the Poisson distribution is that the mean and variance are equal. However, in social science research, it is very common for the variance to be greater than the mean (i.e., the data are overdispersed). This study embeds the Rasch model within an…

Two Monte Carlo simulations were performed to compare methods for estimating and testing hypotheses of quadratic effects in latent variable regression models. The methods considered in the current study were (a) a 2-stage moderated regression approach using latent variable scores, (b) an unconstrained product indicator approach, (c) a latent…

Crawford and Howell (1998) have pointed out that the common practice of z-score inference on cognitive disability is inappropriate if a patient's performance on a task is compared with relatively few typical control individuals. Appropriate univariate and multivariate statistical tests have been proposed for these studies, but these are only valid…

This study compares two confirmatory factor analysis methods on their ability to verify whether correct assignments of items to subtests are supported by the data. The confirmatory common factor (CCF) method is used most often and defines nonzero loadings so that they correspond to the assignment of items to subtests. Another method is the oblique…

Differential item functioning (DIF) analysis is a statistical technique used for ensuring the equity and fairness of educational assessments. This study formulates a new DIF analysis method using the information similarity index (ISI). ISI compares item information functions when data fits the Rasch model. Through simulations and an international…

This study examines how conversing with passengers in a vehicle differs from conversing on a cell phone while driving. We compared how well drivers were able to deal with the demands of driving when conversing on a cell phone, conversing with a passenger, and when driving without any distraction. In the conversation conditions, participants were…

For two random variables, X and Y, let D = X - Y, and let theta[subscript x], theta[subscript y], and theta[subscript d] be the corresponding medians. It is known that the Wilcoxon-Mann-Whitney test and its modern extensions do not test H[subscript o] : theta[subscript x] = theta[subscript y], but rather, they test H[subscript o] : theta[subscript…

Through simulation, the power of the U3 statistic was compared with the power of one of the simplest person-fit statistics, the sum of the number of Guttman errors. In most cases, a weighted version of the latter statistic performed as well as the U3 statistic. (SLD)

Using simulation, the effect that misspecification of elements in the weight matrix has on estimates of basic parameters of the linear logistic test model was studied. Results indicate that, because specifying elements of the weight matrix is a subjective process, it must be done with great care. (SLD)