Factor analysis is a versatile class of psychometric techniques used by researchers to provide insight into the psychological dimensions (factors) that may account for the relationships among variables in a given dataset. The primary goal of a factor analysis is to determine a more parsimonious set of variables (i.e., fewer than the number of…

Indefinite symmetric matrices that are estimates of positive-definite population matrices occur in a variety of contexts such as correlation matrices computed from pairwise present missing data and multinormal based methods for discretized variables. This note describes a methodology for scaling selected off-diagonal rows and columns of such a…

The presence of suppression (and multicollinearity) in multiple regression analysis complicates interpretation of predictor-criterion relationships. The mathematical conditions that produce suppression in regression analysis have received considerable attention in the methodological literature but until now nothing in the way of an analytic…

This article describes why measurement invariance is a critical issue to quantitative theory building within the field of human resource development. Readers will learn what measurement invariance is and how to test for its presence using techniques that are accessible to applied researchers. Using data from a LibQUAL+[TM] study of user…

This paper developed a Democratic Classroom Survey to measure students' perceived democratic environment of the classroom. Perceived democratic environment is one of the most important variables for understanding classroom activity and indeed any type of group activity, but actually measuring perceptions in an objective manner has been…

The extent to which students feel connected to their school is a powerful predictor of many health, social and academic outcomes. These outcomes are also influenced by other factors including characteristics of the school such as its size, policies and practices, but how do these characteristics modify the relationship between a student and his or…

This paper discusses how a seldom-used statistical procedure, recursive regression (RR), can numerically and graphically illustrate data-driven nonlinear relationships and interaction of variables. This routine falls into the family of exploratory techniques, yet a few interesting features make it a valuable compliment to factor analysis and…

The assumptions of the model for factor analysis do not exclude a class of indeterminate covariances between factors and error variables (Grayson, 2003). The construction of all factors of the model for factor analysis is generalized to incorporate indeterminate factor-error covariances. A necessary and sufficient condition is given for…

A new methodology is proposed for the simultaneous reduction of units, variables, and occasions of a three-mode data set. Units are partitioned into a reduced number of classes, while, simultaneously, components for variables and occasions accounting for the largest common information for the classification are identified. The model is a…

The article uses confirmatory factor analysis (CFA) as a template to explain didactically multilevel structural equation models (ML-SEM) and to demonstrate the equivalence of general mixed-effects models and ML-SEM. An intuitively appealing graphical representation of complex ML-SEMs is introduced that succinctly describes the underlying model and…

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)

The article presents a psychometric description of 11 statements related to use of physical violence. The items were tested in a normal sample (N=1700, age: 15-16) from urban and rural areas in Western Norway. The internal reliability was @a=0.86, and the factor analysis resulted in two factors. Boys had higher mean scores than girls.…

A significant issue existing within the rural economic development literature revolves around the difficulty with sorting out the controversy of the effects of amenity activities on rural economic growth. This problem is due to the different ways amenity attributes are linked to regional economic performance. Numerous researchers utilize principal…

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…

Structural equation modeling (SEM) refers to a family of statistical techniques that explores the relationships among a set of variables. Structural equation modeling provides an extremely versatile method to model very specific hypotheses involving systems of variables, both measured and unmeasured. Researchers can use SEM to study patterns of…