Principal Component Analysis (PCA) is a powerful statistical technique for reducing the complexity of data and making patterns and relationships within the data more easily understandable. By using PCA, students can learn to identify the most important features of a data set, visualize relationships between variables, and make informed decisions…

There has been increasing interest in applying integrative data analysis (IDA) to analyze data across multiple studies to increase sample size and statistical power. Measures of a construct are frequently not consistent across studies. This article provides a tutorial on the complex decisions that occur when conducting harmonization of measures…

Data collected from surveys can result in hundreds of variables and thousands of respondents. This implies that time and energy must be devoted to (a) carefully entering the data into a database, (b) running preliminary analyses to identify any problems (e.g., missing data, potential outliers), (c) checking the reliability and validity of the…

"R" (R Development Core Team, 2011) is a very powerful tool to analyze data, that is gaining in popularity due to its costs (its free) and flexibility (its open-source). This article gives a general introduction to using "R" (i.e., loading the program, using functions, importing data). Then, using data from Canivez, Konold,…

Bi-factor analysis is a form of confirmatory factor analysis originally introduced by Holzinger and Swineford ("Psychometrika" 47:41-54, 1937). The bi-factor model has a general factor, a number of group factors, and an explicit bi-factor structure. Jennrich and Bentler ("Psychometrika" 76:537-549, 2011) introduced an exploratory form of bi-factor…

There are both conceptual and practical challenges in dealing with data from mixed methods research studies. There is a need for discussion about various integrative strategies for mixed methods data analyses. This article illustrates integrative analytic strategies for a mixed methods study focusing on improving urban schools facing challenging…

Structural equation modeling (SEM) can be adapted in a relatively straightforward fashion to analyze data from interchangeable dyads (i.e., dyads in which the 2 members cannot be differentiated). The authors describe a general strategy for SEM model estimation, comparison, and fit assessment that can be used with either dyad-level or pairwise…

Some mathematical aspects of minimum trace factor analysis (MTFA) are discussed. The uniqueness of an optimal point of MTFA is proved, and necessary and sufficient conditions for any particular point to be optimal are given. The connection between MTFA and classical minimum rank factor analysis is discussed. (Author/JKS)

The Organisation for Economic Cooperation and Development's (OECD's) Programme for International Student Assessment (PISA) surveys, which take place every three years, have been designed to collect information about 15-year-old students in participating countries. PISA examines how well students are prepared to meet the challenges of the future,…

Multi-indicator growth models were formulated as special three-level hierarchical generalized linear models to analyze growth of a trait latent variable measured by ordinal items. Items are nested within a time-point, and time-points are nested within subject. These models are special because they include factor analytic structure. This model can…

Structural equation models merge multiple regression, path analysis, and factor analysis techniques into a single data analytic framework. Measurement models are developed to define latent variables, and structural equations are then established among the latent variables. Explains the development of these models. (KS)

This article suggests the use of structural equation modeling in special education research, to analyze multivariate data from both nonexperimental and experimental research. It combines a structural model linking latent variables and a measurement model linking observed variables with latent variables. (Author/DB)

Multilevel linear models (MLMs) provide a powerful framework for analyzing data collected at nested or non-nested levels, such as students within classrooms. The current article draws on recent analytical and software advances to demonstrate that a broad class of MLMs may be estimated as structural equation models (SEMs). Moreover, within the SEM…

Provides background theory and an experiment relating to chemometrics. Describes the phenomenon where solutions are dichromatic or dichromic. Discusses the difficulty students have in describing such solutions that appear to be several different colors at the same time. (TW)

The conceptual framework for the instructionally sensitive assessment that guided the analyses of data from the Second International Mathematics Study (SIMS) are described. The intellectual rationale for the project effort and the current draft version of the guiding conception of "instructionally sensitive psychometrics" are discussed,…