We describe mathematical and statistical models for factor invariance. We demonstrate that factor invariance is a condition of measurement invariance. In any study of change (as over age) measurement invariance is necessary for valid inference and interpretation. Two important forms of factorial invariance are distinguished: "configural" and "metric". Tests for factorial invariance and the range of tests from strong to weak are illustrated with multiple group factor and structural equation modeling analyses (with programs such as LISREL, COSAN, and RAM). The tests are for models of the organization and age changes of intellectual abilities. The models are derived from current theory of fluid (Gf) and crystallized (Gc) abilities. The models are made manifest with measurements of the WAIS-R in the standardization sample. Although this is a methodological paper, the key issues and major principles and conclusions are presented in basic English, devoid of technical details and obscure notation. Conceptual principles of multivariate methods of data analysis are presented in terms of substantive issues of importance for the science of the psychology of aging.

A practical and theoretical guide to measurement invariance in aging research

A rating scale was designed to measure dysfunctional discipline practices in parents of young children. Three stable factors of dysfunctional discipline style were identified: (a) Laxness, (b) Overreactivity, and (c) Verbosity. The Parenting Scale exhibited adequate internal consistency and test–retest reliability. Mothers of clinic children reported more dysfunctional parenting than did mothers of nonclinic children. Parenting Scale scores were related to maternal ratings of child behavior and marital discord. Most important, Parenting Scale scores correlated significantly with observational measures of dysfunctional discipline and child misbehavior.

The Parenting Scale: A measure of dysfunctional parenting in discipline situations.

The purpose of this chapter is to provide an overview of exploratory analysis to guide users in selecting appropriate procedures. While it will occasionally be necessary to present some new material to aid in selection of appropriate techniques, no new techniques are presented here. The emphasis will be on the selections to be made and how the results may differ depending on those selections. The result, hopefully, is a guide to the selection and interpretation of appropriate exploratory factor analyses for the researcher familiar with basic factor-analytic procedures and terminology.

Exploratory Factor Analysis

Acceptance of chronic pain entails that an individual reduce unsuccessful attempts to avoid or control pain and focus instead on participation in valued activities and the pursuit of personally relevant goals. Recent research suggests that pain-related acceptance leads to enhanced emotional and physical functioning in chronic pain patients above and beyond the influence of depression, pain intensity, and coping. In these studies, acceptance was measured using the Chronic Pain Acceptance Questionnaire (CPAQ). Preliminary analyses of the CPAQ have supported its psychometric properties. The present study sought to further refine the CPAQ by examining its factor structure and evaluating the relations of these factors to other indices of pain-related distress and disability. Although a previously demonstrated factor structure of the CPAQ was generally supported, only factors assessing (a) the degree to which one engaged in life activities regardless of the pain and (b) willingness to experience pain had adequate reliability and validity and were significantly related to the other measures of patient functioning. A revised version of the CPAQ is suggested.

Acceptance of chronic pain: component analysis and a revised assessment method

Although schemas play a central role in cognitive conceptualizations of personality disorders, research devoted to the assessment of schemas has been scarce. This article describes the preliminary validation of a measure of schemas relevant to personality disorders. The Schema Questionnaire (SQ) was developed using five independent samples (N=1,564). In study 1, factor analyses using a student sample revealed 13 primary schemas. A hierarchical factor analysis revealed three higher-order factors. In study 2, factor analyses using a patient sample revealed 15 primary schemas. The patient and student samples produced similar sets of primary factors which also closely matched the rationally developed schemas and their hypothesized hierarchical relationships (Young, 1991). The primary subscales were found to possess adequate test-retest reliability and internal consistency. In study 3, the SQ was found to possess convergent and discriminant validity with respect to measures of psychological distress, self-esteem, cognitive vulnerability for depression, and personality disorder symptoms.

Karel R. Balcar

Papers

Factor Matching Procedures: an Improvement of the s Index; with Tables