Using multidimensional scaling on data from pairs of relatives to explore the dimensionality of categorical...

An accurate specification of the dimensionality and ordering of categorical multifactorial phenotypes (e.g., smoking status, including heavy, moderate, light, and nonsmokers) is an important prerequisite for the genetic analysis of these traits. Typically, phenotypic dimensionality and ordering are determined by comparing the relative fits of alternative parametric threshold models. Here, a method of analysis is described which addresses the same issue of trait dimensionality but does not require parametric assumptions. Specifically, we detail how nonmetric multi-dimensional scaling (MDS), applied to contingency tables which cross-classify the phenotypes or responses of one relative with another, may be used to explore trait dimensionality. Scaling results from deterministic simulation studies indicate that the latent structure of categorical phenotypes can be recovered with nonmetric MDS. Results from stochastic simulations, however, indicate that the accuracy of recovery, as well as the rejection of models of incorrect dimensionality, are strongly dependent upon sample size and the latent liability correlation between relatives. As an application of the method, the dimensionality of a measure of smoking status in 1,656 pairs of monozygotic twins ascertained through the American Association of Retired Persons is considered. The MDS results indicate that the onset of the smoking habit and the quantity smoked in this aging population represent a unidimensional process. The implication this finding has for subsequent genetic analysis is discussed.