Browne, Michael W., Journal of the American Statistical Association
To progress, a scientific discipline must develop methodology for obtaining measurements of relevant constructs and to extract meaning from the measurements it does have. This is not a straightforward matter in psychology. Typically, constructs of interest are not clearly defined and cannot be measured directly. In addition, the measurements that are available are subject to substantial measurement error. Consequently, the measurement process often consists of repeated attempts to measure the same construct in different ways. When the relationship between several constructs is under investigation, each of the constructs is measured repeatedly, resulting in a substantial number of measurements. Thus the statistical methodology developed for the analysis of psychological measurements is typically multivariate.
Because constructs are not clearly defined, the investigator is often not sure exactly what is being measured. This has led to the concept of a latent or hidden variable that is not measured directly. Inferences about the latent variable are deduced from interrelationships between manifest, or observed, variables.
In a broad sense, psychometrics may be regarded as the discipline concerned with the quantification and analysis of human differences. This involves both the construction of procedures for measuring psychological constructs and the analysis of data consisting of the measurements made. In this sense, both the construction of a psychological attitude scale and the analysis of the data resulting from its application may be regarded as part of psychometrics. In a narrower sense, psychometrics is often regarded as the development of mathematical or statistical methodology for the analysis of measurement data in psychology. This methodology is primarily multivariate, and latent variables feature strongly. It is this aspect of psychometrics that I consider here.
Although many of the techniques that currently constitute psychometrics date far earlier, psychometrics emerged as a formal discipline with the formation of the Psychometric Society in 1935, with L. L. Thurstone as its first president. Thurstone had played a leadership role at the University of Chicago in providing methodology for analyzing measurements of psychological constructs, and students of his featured strongly among the founding members of the society (Horst and Stalnaker 1986). From the beginning, the Psychometric Society has had an international membership, and the proportion of members outside the United States has grown steadily over the years.
The Psychometric Society produced a journal, Psychometrika, whose stated aim was the "development of psychology as a quantitative rational science." Subsequently, Psychometrika has been joined by other journals with some overlap of subject matter: Educational and Psychological Measurement, Journal of Educational Measurement, Journal of Educational and Behavioral Statistics (formerly Journal of Educational Statistics), Applied Psychological Measurement, Journal of Classification, Psychological Methods (formerly the Quantitative Methods in Psychology section of Psychological Bulletin) and Journal of Mathematical Psychology. In addition, two journals with similar content to Psychometrika have been founded overseas: British Journal of Mathematical and Statistical Psychology (formerly British Journal of Statistical Psychology) and Behaviormetrika, a Japanese journal published in the English language.
It is conventional to classify psychometrics into three major areas: mental test theory, factor analysis and associated methods, and multidimensional scaling. I consider each of these separately, and examine some significant work.
MENTAL TEST THEORY
Mental test theory is concerned with methodology developed for the analysis of mental tests. Two general approaches currently in use for the analysis of tests consisting of dichotomous items are classical test theory and item response theory. …