The applicability of 5 conventional guidelines for construct measurement is critically examined: (a) Construct indicators should be internally consistent for valid measures, (b) there are optimal magnitudes of correlations between items, (c) the validity of measures depends on the adequacy with which a specified domain is sampled, (d) within-construct correlations must be greater than between-construct correlations, and (e) linear composites of indicators can replace latent variables. A structural equation perspective is used, showing that without an explicit measurement model relating indicators to latent variables and measurement errors, none of these conventional beliefs hold without qualifications. Moreover, a "causal" indicator model is presented that sometimes better corresponds to the relation of indicators to a construct than does the classical test theory "effect" indicator model.
Factor analysis (Spearman, 1904) and classical test theory (Lord & Novick, 1968;Spearman, 1910) have influenced perspectives on measurement not only in psychology but in most of the social sciences. These traditions have given rise to criteria to select "good" measures and to a number of beliefs about the way valid and reliable indicators' should behave. For instance, Nunnally (1978, p. 102) warned that if correlations among measures are near zero, they measure different things. Some have argued that high correlations are better than low ones (e.g, Horst, 1966, p. 147), whereas others have claimed that moderate correlations are best (Cattell, 1965, p. 88). As the preceding example illustrates, the guidelines to indicator selection are sometimes contradictory. The result is that one can justify keeping or discarding an indicator depending on whose advice is followed. Obviously, this is an undesirable state of affairs that suggests that the conventional beliefs on measurement and indicator selection require clarification.
We contend that these contradictions can largely be traced to two sources. One is that some items do not conform to the classical test theory or factor analysis models that treat indicators as effects of a construct. We present an alternative model in which indicators influence a construct. Second is the failure to present a measurement model that explicitly shows the assumed relation between constructs, measures, and errors of measurement.
We are grateful to Jane Scott-Lennox for her suggestions on several versions of the manuscript and for her help in creating Figures 1 and2. We also thank Lewis Goldberg, Rick Hoyle, Jeff Tanaka, and Raymond Wolfe for their many helpful suggestions on drafts of this article.