This paper utilized the Rasch model and Joint Maximum Likelihood Estimation to study different scoring options for omitted and not-reached items. Three scoring treatments were studied. The first method treated omitted and not-reached items as "ignorable/blank". The second treatment, scored omits as incorrect with "0" and left not-reached as blank…

Regression discontinuity (RD) analysis is a rigorous nonexperimental approach that can be used to estimate program impacts in situations in which candidates are selected for treatment based on whether their value for a numeric rating exceeds a designated threshold or cut-point. Over the last two decades, the regression discontinuity approach has…

In this article, we present a Bayesian spatial factor analysis model. We extend previous work on confirmatory factor analysis by including geographically distributed latent variables and accounting for heterogeneity and spatial autocorrelation. The simulation study shows excellent recovery of the model parameters and demonstrates the consequences…

Among the traditional measures of student quality, class rank is widely described by admissions officers as the fuzziest. That is why some colleges no longer use it in their evaluations of applicants, while many others do not consider it very important. The measure once had greater appeal. For one thing, it had the whiff of fairness. Seeing how an…

There are two primary interpretations of the mean: as a leveler of data (Uccellini 1996, pp. 113-114) and as a balance point of a data set. Typically, both interpretations of the mean are ignored in elementary school and middle school curricula. They are replaced with a rote emphasis on calculation using the standard algorithm. When students are…

This article introduces procedures for the computation and asymptotic statistical inference for classification consistency and accuracy indices specifically designed for cognitive diagnostic assessments. The new classification indices can be used as important indicators of the reliability and validity of classification results produced by…

Previous assessments of the reliability of test scores for testlet-composed tests have indicated that item-based estimation methods overestimate reliability. This study was designed to address issues related to the extent to which item-based estimation methods overestimate the reliability of test scores composed of testlets and to compare several…

Latent class regression models relate covariates and latent constructs such as psychiatric disorders. Though full maximum likelihood estimation is available, estimation is often in three steps: (i) a latent class model is fitted without covariates; (ii) latent class scores are predicted; and (iii) the scores are regressed on covariates. We propose…

We investigated whether specific input helps 3-1/2-year-olds discover that the last word in a count represents its cardinal value (i.e., the cardinal word principle). In Study 1, we contrasted four training approaches. The only approach to yield significant improvement was to label a set's cardinality and then immediately count it. This training…

Dynamic factor models (DFMs) have typically been applied to multivariate time series data collected from a single unit of study, such as a single individual or dyad. The goal of DFMs application is to capture dynamics of multivariate systems. When multiple units are available, however, DFMs are not suited to capture variations in dynamics across…

This paper provides a conceptual, empirical, and practical guide for estimating ordinal reliability coefficients for ordinal item response data (also referred to as Likert, Likert-type, ordered categorical, or rating scale item responses). Conventionally, reliability coefficients, such as Cronbach's alpha, are calculated using a Pearson…

In this paper, we used simulations to compare the performance of classical and Bayesian estimations in logistic regression models using small samples. In the performed simulations, conditions were varied, including the type of relationship between independent and dependent variable values (i.e., unrelated and related values), the type of variable…

Computational models are powerful tools--too powerful, according to some. We argue that the idea that models can "do anything" is wrong, and we describe how their failures have been informative. We present new work showing surprising diversity in the effects of feedback on children's task-switching, such that some children perseverate despite this…

Fraction of missing information [lambda][subscript j] is a useful measure of the impact of missing data on the quality of estimation of a particular parameter. This measure can be computed for all parameters in the model, and it communicates the relative loss of efficiency in the estimation of a particular parameter due to missing data. It has…

Mathematical ability is a major contributory factor to the success of a student in any science course. This paper aims to determine the source of the difficulty that students often find when performing calculations in chemistry. Through the design and analysis of a set of chemistry questions and analogous mathematics questions, set in a Standard…