This paper presents an application of the Kalman filter in signal processing in instrumentation systems when the conditions of the environment generate a large amount of interference for the acquisition of signals from measurement systems. The unwanted interferences make important use of the instrumentation system resources and do not represent…

Stan is a new Bayesian statistical software program that implements the powerful and efficient Hamiltonian Monte Carlo (HMC) algorithm. To date there is not a source that systematically provides Stan code for various item response theory (IRT) models. This article provides Stan code for three representative IRT models, including the…

Instead of reserving the study of probability and statistics for special fourth-year high school courses, the Common Core State Standards for Mathematics (CCSSM) takes a "statistics for all" approach. The standards recommend that students in grades 6-8 learn to summarize and describe data distributions, understand probability, draw…

The residuals obtained from fitting a structural equation model are crucial ingredients in obtaining chi-square goodness-of-fit statistics for the model. The authors present a didactic discussion of the residuals, obtaining a geometrical interpretation by recognizing the residuals as the result of oblique projections. This sheds light on the…

A challenging problem in some developing countries such as Nigeria is inadequate training of students in effective problem solving using the core concepts of their disciplines. Related to this is a disconnection between their learning and socio-economic development agenda of a country. These problems are more vivid in statistical education which…

Generalized bilinear models are presented for the statistical analysis of two-way arrays. These models combine bilinear models and generalized linear modeling, and yield a family that includes many useful models. A three-step procedure is presented for analyzing data sets by generalized bilinear models. (SLD)

Multilevel models have come to play an increasingly important role in many areas of social science research. However, in contrast to other modeling strategies, there is currently no widely used approach for graphically diagramming multilevel models. Ideally, such diagrams would serve two functions: to provide a formal structure for deriving the…

This study analytically examined the multiple comparison procedures for testing a combined set of planned and post hoc comparisons. To establish a practical guideline, the following issues were investigated: (1) when the generalized sequentially rejective Bonferroni method (GSRB) is and is not applicable; (2) the required alpha levels for the GSRB…

This note shows that the formula suggested by N. D. Bryant and S. Gokhale (1972) for correcting indirectly restricted correlations when no information is available on the third (directly restricted) variable is accurate only in one special instance. A more general correction formula is illustrated. (SLD)

Conditional observed score (COS) and latent trait (LT) definitions of differential item functioning (DIF) are explored to determine when they are equivalent. COS methods rely solely on observed measurements, and LT methods model the response to an item as a function of an unobserved hypothetical latent ability or trait. For the case of dichotomous…

A general model is developed for the analysis of multivariate multilevel data structures. Special cases of this model include: repeated measures designs; multiple matrix samples; multilevel latent variable models; multiple time series and variance and covariance component models. (Author)

An extended marginal homogeneity model is introduced for the analysis of square contingency tables with the same ordinal row and column classifications. The model hypothesizes that the ratio in each column of table delta will exhibit an exponential function of the column. (SLD)

A method is proposed for comparison of distinct partitions of the same set of n objects through a simple cross-product index defined between corresponding entries from two proximity matrices providing particular a priori codings of the within-class and between-class relationships for the partitions. (SLD)

A truncated version of the Cauchy distribution is introduced. Unlike the Cauchy distribution, this possesses finite moments of all orders and could therefore be a better model for certain practical situations. One such situation in finance is discussed. Explicit expressions for the moments of the truncated distribution are also derived.

An integrated overview is provided of selected multiple comparison methods, with an emphasis on the sequentially rejective Bonferroni (SRB) test and its modifications. Multiple comparisons of means is a frequently used, and yet confusing, method in educational and psychological research. Seven multiple comparison methods are reviewed: (1) the…