Students in an upper-level physical chemistry course utilized an open-sourced statistical software package to construct models fitted to experimental pressure-volume data. In the first part of the experiment, students familiarize themselves with model fitting. In the second part of the experiment, students determine which truncated version of the…

The present guide provides a practical guide to conducting latent profile analysis (LPA) in the Mplus software system. This guide is intended for researchers familiar with some latent variable modeling but not LPA specifically. A general procedure for conducting LPA is provided in six steps: (a) data inspection, (b) iterative evaluation of models,…

About 45 R packages to analyze data using item response theory (IRT) have been developed over the last decade. This article introduces these 45 R packages with their descriptions and features. It also describes possible advanced IRT models using R packages, as well as dichotomous and polytomous IRT models, and R packages that contain applications…

In this digital ITEMS module, Dr. Jue Wang and Dr. George Engelhard Jr. describe the Rasch measurement framework for the construction and evaluation of new measures and scales. From a theoretical perspective, they discuss the historical and philosophical perspectives on measurement with a focus on Rasch's concept of specific objectivity and…

The recent popularity of models that capture the dynamic coevolution of both network structure and behavior has driven the need for summary indices to assess the adequacy of these models to reproduce dynamic properties of scientific or practical importance. Whereas there are several existing indices for assessing the ability of the model to…

This paper proposes a new methodology for checking conformance of the software architectural design of Learning Management System (LMS) to Learning Technology System Architecture (LTSA). In our approach, the architectural designing of LMS follows the formal modeling style of Acme. An ontology is built to represent the LTSA rules and the software…

Drawing valid inferences from item response theory (IRT) models is contingent upon a good fit of the data to the model. Violations of model-data fit have numerous consequences, limiting the usefulness and applicability of the model. This instructional module provides an overview of methods used for evaluating the fit of IRT models. Upon completing…

This paper illustrates an approach for architectural design of a Learning Management System (LMS), which is verifiable against the Learning Technology System Architecture (LTSA) conformance rules. We introduce a new method for software architectural design that extends the Unified Modeling Language (UML) component diagram with the formal…

In order to progress as a field, school psychology research must be informed by effective measurement techniques. One approach to address the need for careful measurement is Rasch analysis. This technique can (a) facilitate the development of instruments that provide useful data, (b) provide data that can be used confidently for both descriptive…

The method of least-squares (LS) has a built-in procedure for estimating the standard errors (SEs) of the adjustable parameters in the fit model: They are the square roots of the diagonal elements of the covariance matrix. This means that one can use least-squares to obtain numerical values of propagated errors by defining the target quantities as…

A promising "underlying bivariate normal" approach was proposed by Jöreskog and Moustaki for use in the factor analysis of ordinal data. This was a limited information approach that involved the maximization of a composite likelihood function. Its advantage over full-information maximum likelihood was that very much less computation was…

Cognitive diagnostic models (CDM) have been around for more than a decade but their application is far from widespread for mainly two reasons: (1) CDMs are novel, as compared to traditional IRT models. Consequently, many researchers lack familiarity with them and their properties, and (2) Software programs doing CDMs have been expensive and not…

We highlight critical conceptual and statistical issues and how to resolve them in conducting Satorra-Bentler (SB) scaled difference chi-square tests. Concerning the original (Satorra & Bentler, 2001) and new (Satorra & Bentler, 2010) scaled difference tests, a fundamental difference exists in how to compute properly a model's scaling correction…

Newer statistical procedures are typically introduced to help address the limitations of those already in practice or to deal with emerging research needs. Quantile regression (QR) is introduced in this paper as a relatively new methodology, which is intended to overcome some of the limitations of least squares mean regression (LMR). QR is more…

This article discusses the ResidPlots-2, a computer software that provides a powerful tool for IRT graphical residual analyses. ResidPlots-2 consists of two components: a component for computing residual statistics and another component for communicating with users and for plotting the residual graphs. The features of the ResidPlots-2 software are…