Measurement and the Study of Change

Abstract

Many constructs developmental scientists study cannot be directly observed. In such cases, scales are created that reflect the construct of interest. Observed behaviors are taken as manifestations of an unobserved common cause. As crucial as measurement is to understanding many psychological phenomenon, it is perhaps even more important when the goal of research is to understand how a construct changes over time. In this article we review several approaches to measurement, note features of latent variable measurement models which are ideally suited to the study of change, describe a hypothetical example, and conclude with a discussion of measurement and development.

ACKNOWLEDGMENT

The authors would like to thank Bill Gardner and Li Cai for helpful comments on earlier drafts of this manuscript. We would also like to express our appreciation to Denis Gerstorf, Nilam Ram, and three anonymous reviewers. The resulting paper is stronger for the input of all seven individuals. Any deficiencies that remain are, of course, our own.

Notes

¹The standard normal assumption for the latent response distribution is not required (Pearson, 1913). However, at the time of this publication all factor analytic software makes this assumption.

²There are several ways this model can be presented. Although Equation 3 does not include a threshold or intercept term, the information from the thresholds contributes to the estimation of the correlations among the latent response distributions (known as polychoric correlations).

³It is unusual to consider constraining thresholds in the factor analytic framework. However, by referring to any of the equations relating IRT parameters to factor analysis parameters (for instance, Equations 5 and 6 in Wirth and Edwards, 2007) it can be shown that there is a direct relationship between constraining severity parameters in IRT and thresholds in factor analysis.

⁴Equating is one example of differing terminology and emphasis between the IRT and factor analysis literatures. Equating is not often discussed in factor analysis, and when it is discussed it is typically presented in the context of scaling and invariance. However, the concepts covered in the IRT literature translate directly to factor analysis.

5http://faculty.psy.ohio-state.edu/edwards.