ICLUST: A cluster analytic approach to exploratory and confirmatory scale construction

A common problem in the social sciences is to form a set of relatively independent and internally consistent scales from a large pool of items. Frequently, these scales are formed by simply summing the responses to keyed items. The problem, then, is to determine how best to partition the initial set of items into subsets or scales that are highly internally consistent and relatively independent. A common alternative is to factor analyze the interitem correlation matrix and then to select items on the basis of factor loadings. Those items with a high loading on a particular factor are combined into a scale by applying unit weights to the items. This method, although probably the most common scale construction procedure, has several drawbacks: Inter­ item correlations are usually small (average interitem correlations ~.3) and the sample sizes are usually not much larger than the number of items. These problems tend to lead to overfactoring (extracting too many factors), unstable rotations, and generally nonsensical solutions. In fact, because of the problems encountered in factoring items, many experienced factor analysts recommend against such procedures (Cattell, 1973; Comrey, 1961; Nunnally, 1967). However, a sampling of journals in the social sciences suggests that this advice is rarely followed. When the item pool is large (greater than 10-20 items), when the item intercorrelations are small (between 0.0 and .5), or when the sample sizes are small, an alterna­ tive method that is particularly appropriate is cluster analysis. Cluster analysis is a loosely defined set of procedures associated with the partitioning of a set of objects into nonoverlapping groups or clusters (Everitt, 1974; Hartigan, 1975). Although normally used to group objects, occasionally cluster analysis has been applied to the problem of grouping variables and, as such, is similar to procedures of group factor analysis (Loevinger, Gieser, & Dubois, 1953; Revelle, in press; Tryon & Bailey, 1970). A disadvantage for scale construction of many clustering procedures is that they do not include basic psychometric decision rules to evaluate either the quality or the number of clusters to extract. It is possible, though, to combine psychometric principles with clustering procedures. This combination results in a simple but useful approach to scale construction, and, for forming scales from items, may be compared