Summary
Contents
Subject index
Quantitative Psychology is arguably one of the oldest disciplines within the field of psychology and nearly all psychologists are exposed to quantitative psychology in some form. While textbooks in statistics, research methods, and psychological measurement exist, none offer a unified treatment of quantitative psychology. The SAGE Handbook of Quantitative Methods in Psychology does just that. Each chapter covers a methodological topic with equal attention paid to established theory and the challenges facing methodologists as they address new research questions using that particular methodology. The reader will come away from each chapter with a greater understanding of the methodology being addressed as well as an understanding of the directions for future developments within that methodological area.
Drawing on a global scholarship the Handbook is divided into seven parts:
Part I: Measurement Theory: Begins with a chapter on classical test theory, followed by the common factor analysis model as a model for psychological measurement. The models for continuous latent variables in item response theory are covered next, followed by a chapter on discrete latent variable models as represented in latent class analysis.
Part II: Structural equation models: Addresses topics in general structural equation modeling, modeling mean structures, multiple-group models, nonlinear structural equation models, mixture models, and multilevel structural equation models.
Part III: Longitudinal models: Covers the analysis of longitudinal data via mixed modeling, repeated measures ANOVA, growth modeling, time series analysis, and event history analysis.
Part IV: Data analysis: Includes chapters on regression models, categorical data analysis, multilevel or hierarchical models, resampling methods, robust data analysis, meta-analysis, Bayesian data analysis, and cluster analysis.
Part V: Design and inference: Addresses issues in the inference of causal relations from experimental and non-experimental research, along with the design of true experiments and quasi-experiments, and the problem of missing data due to various influences such as attrition or non-compliance.
Part VI: Scaling methods: Covers metric and non-metric scaling methods as developed in multidimensional scaling, followed by consideration of the scaling of discrete measures as found in dual scaling and correspondence analysis. Models for preference data such as those found in random utility theory are covered next.
Part VII: Specialized methods: Covers specific topics including the analysis of social network data, the analysis of neuro-imaging data, and functional data analysis.
This volume is an excellent reference and resource for advanced students, academics, and professionals studying or using quantitative psychological methods in their research.
Factor Analysis
Factor Analysis
Introduction
Researchers in psychology routinely observe that variables of interest are intercorrelated in sample data. Correlations among measured variables (MVs) may be due to a number of phenomena, including direct causation, indirect causation, or joint dependence on other variables. Although it may be relatively straightforward to explain a simple correlation between two variables, accounting for an array of correlations among a substantial number of variables is much more difficult. Given a set of p MVs, the observed intercorrelations among them comprise a complex set of information, and the investigator seeks to understand and account for this information in a simple and meaningful way. Factor analysis models and methods provide a framework for addressing this problem.
The fundamental premise of factor analysis is that there exist latent variables (LVs) that influence the MVs. An LV, or a factor in factor analysis, is a hypothetical construct that is not directly measured. LVs are a central principle in psychology where researchers are routinely interested in constructs such as depression, intelligence, personality traits, etc. According to factor analytic theory, LVs influence MVs, meaning that the level of an individual on an LV influences that individual's response or measurement on MVs that are indicators of that LV. By way of these influences, the LVs account for variation and covariation of the MVs. For example, individuals vary with respect to their level on the LV mathematical ability. That LV influences performance on tests such as arithmetic skills and algebra skills. Observed variation among individuals on these tests is due, in part, to variation on the underlying LV, and observed covariation on these tests is due, in part, to the fact that both are influenced by the same LV. In empirical research when an investigator observes correlations among p MVs, factor analytic theory would postulate that those correlations could be explained by a smaller set of LVs that influence the MVs. Starting from the observed correlations among the MVs, the objective in factor analysis is to determine the number and nature of the LVs, or factors, and their pattern of influence on the MVs. As will be seen below, this objective is approached by first specifying a formal model and then implementing methods for fitting that model to observed data.
Historical Origins
The seeds of factor analysis were sewn in a classic paper by Charles Spearman (1904) on the nature of intelligence. Spearman believed that performance on any mental test was determined by two factors, general intelligence (g), and a specific ability factor associated with each test that was unique to that test and distinct from g. According to Spearman, the latent variable g influenced all mental tests and accounted for all intercorrelations among tests. To test his theory Spearman conducted a series of studies in which he obtained measures from samples of people on various tests of cognitive and perceptual abilities and skills. He then sought to show that the resulting intercorrelations (after various corrections and adjustments) could be accounted for precisely by his theory. He was able to obtain numerical estimates of the influence of g on each test and argued that his results firmly supported his theory. Although Spearman did not present a formal factor-analytic model and did not explain how he estimated effects of g on observed tests, he did establish key elements of factor analytic theory and methods. These include the ideas that LVs influence MVs and thereby explain variation and covariation, that one can obtain numerical estimates of those influences, and that one can consider issues such as the number of factors and the degree to which the factors account for the observed data.
...
- Loading...
Get a 30 day FREE TRIAL
-
Watch videos from a variety of sources bringing classroom topics to life
-
Read modern, diverse business cases
-
Explore hundreds of books and reference titles
Sage Recommends
We found other relevant content for you on other Sage platforms.
Have you created a personal profile? Login or create a profile so that you can save clips, playlists and searches