When comparing digits of different physical sizes, numerical and physical size interact. For example, in a numerical comparison task, people are faster to compare two digits when their numerical size (the relevant dimension) and physical size (the irrelevant dimension) are congruent than when they are incongruent. Two main accounts have been put…

The present paper determines whether community college transfer students have higher baccalaureate rates when they enroll in four-year colleges and departments that have larger shares of transfer students. Transfers attending non-technical campuses with larger shares of transfers have higher eight-year baccalaureate rates, but within-campus…

Because of response disturbances such as guessing, cheating, or carelessness, item response models often can only approximate the "true" individual response probabilities. As a consequence, maximum-likelihood estimates of ability will be biased. Typically, the nature and extent to which response disturbances are present is unknown, and, therefore,…

Ramsay-curve item response theory (RC-IRT) is a nonparametric procedure that estimates the latent trait using splines, and no distributional assumption about the latent trait is required. For item parameters of the two-parameter logistic (2-PL), three-parameter logistic (3-PL), and polytomous IRT models, RC-IRT can provide more accurate estimates…

We discuss the need for devoting time in differential equations courses to modelling and the completion of the modelling process with efforts to estimate the parameters in the models using data. We estimate the parameters present in several differential equation models of chemical reactions of order n, where n = 0, 1, 2, and apply more general…

The goal of the dissertation is to determine aspects of the structure of the human language faculty, a cognitive system, specifically focusing on human syntactic systems, (unique in the animal kingdom) which enable us to creatively produce an unlimited number of grammatical sentences (like the one you just read, probably never before written or…

A plane algebraic curve, the complete set of solutions to a polynomial equation: f(x, y) = 0, can in many cases be drawn using parametric equations: x = x(t), y = y(t). Using algebra, attempting to parametrize by means of rational functions of t, one discovers quickly that it is not the degree of f but the "relative degree," that describes how…

Topics commonly taught in a general chemistry course can be used to calculate the quantity of carbon dioxide emitted into the atmosphere by various human activities. Each calculation begins with the balanced chemical equation for the reaction that produces the CO[subscript 2] gas. Stoichiometry, thermochemistry, the ideal gas law, and dimensional…

Our understanding of carbonium ions as intermediates in chemical reaction mechanisms derives from the early work of Julius Stieglitz and the more famous Hans Meerwein, the latter studying the racemization of isobornyl chloride when treated with Lewis acids. This review analyzes how key mechanistic concepts for this reaction evolved and gives the…

Survey items with multiple response categories and multiple-choice test questions are ubiquitous in psychological and educational research. We illustrate the use of log-multiplicative association (LMA) models that are extensions of the well-known multinomial logistic regression model for multiple dependent outcome variables to reanalyze a set of…

A continuous representation of a hybrid method with three "off-step" points is developed via interpolation and collocation procedures, and used to obtain initial value methods (IVMs) for solving initial value problems. The IVMs are assembled into a single block matrix equation which is convergent and A-stable. We note that accuracy is improved by…

The aim of this study was to provide evidence for knowledge of the syntax governing the verbal form of large numbers in preschoolers long before they are able to count up to these numbers. We reasoned that if such knowledge exists, it should facilitate the maintenance in short-term memory of lists of lexical primitives that constitute a number…

Structural equation mixture models (SEMMs) are latent class models that permit the estimation of a structural equation model within each class. Fitting SEMMs is illustrated using data from 1 wave of the Notre Dame Longitudinal Study of Aging. Based on the model used in the illustration, SEMM parameter estimation and correct class assignment are…

Identifying price sensitive consumers is an important problem in marketing. We develop a Bayesian multi-level factor analytic model of the covariation among household-level price sensitivities across product categories that are substitutes. Based on a multivariate probit model of category incidence, this framework also allows the researcher to…

The authors describe an activity they have created in which students can visualize a theoretical neural network whose states evolve according to a well-known simple law. This activity provided an uncomplicated approach to a paradigm commonly represented through complex mathematical formulation. From their observations, students learned many basic…