We propose a new limited-information goodness of fit test statistic C[subscript 2] for ordinal IRT models. The construction of the new statistic lies formally between the M[subscript 2] statistic of Maydeu-Olivares and Joe (2006), which utilizes first and second order marginal probabilities, and the M*[subscript 2] statistic of Cai and Hansen…

Good quality data is paramount for applied economic research. If the data are distorted, corresponding conclusions may be incorrect. We demonstrate how Benford's law, the distribution that first digits of numbers in certain data sets should follow, can be used to test for data abnormalities. We conduct an analysis of nine commonly used data sets…

Examination of the stochastics of moderated multiple regression (MMR) reveals that MMR is an appropriate technique when predictors are fixed variables and the distribution of errors is normal but is not appropriate when predictors are random variables and the joint distribution of criterion and predictor variables is multivariate normal. (SLD)

The normalized mean is developed and discussed as a descriptive measure of central location. The advantages of the normalized mean over the arithmetic mean, median, and trimmed mean are discussed. (Author)

A Monte Carlo experiment was conducted to investigate the performance of bootstrap methods in normal theory maximum likelihood factor analysis when the distributional assumption was satisfied or unsatisfied. Problems arising with the use of bootstrap methods are highlighted. (SLD)

Methods of testing relatively complete (distributional) models of internal psychological processes are described. It is shown that there is a sufficient condition for additive models to imply this property of the likelihood ratio. Also discussed are the examination of hazard rate functions of component processes and change in cumulative…

The derivation of the variance of similarity judgments is made from the 3-D process in nonlinear psychophysics. The idea of separability of dimensions in metric space theories of similarity is replaced by one parameter that represents the degree of a form of interdimensional cross-sampling. (SLD)

The precision of the group-based item-response theory (IRT) model applied to school ability estimation is described, assuming use of Bayesian estimation with precision represented by the standard deviation of the posterior distribution. Similarities with and differences between the school-based model and the individual-level IRT are explored. (SLD)

A useful method is proposed for identifying a variable as inconsistent in factor analysis. The procedure, based on the likelihood principle, is illustrated. Statistical properties such as the effect of misspecified hypotheses, the problem of multiple comparisons, and robustness to violation of distributional assumptions are investigated. (SLD)

Global economic transformations have never been as dramatic as in the twentieth century. Most countries have experienced radical changes in the standards of income per capita, technology, fertility, mortality, income inequality and the extent of democracy in the course of the past century. It is the goal of many disciplines--economics, history,…

DIMTEST is a statistical test procedure for assessing essential unidimensionality of binary test item responses. The test statistic T used for testing the null hypothesis of essential unidimensionality is a nonparametric statistic. That is, there is no particular parametric distribution assumed for the underlying ability distribution or for the…