On the measurement of stability in over-time data

In this article, autoregressive models and growth curve models are compared. Autoregressive models are useful because they allow for random change, permit scores to increase or decrease, and do not require strong assumptions about the level of measurement. Three previously presented designs for estimating stability are described: (a) time-series, (b) simplex, and (c) two-wave, one-factor methods. A two-wave, multiple-factor model also is presented, in which the variables are assumed to be caused by a set of latent variables. The factor structure does not change over time and so the synchronous relationships are temporally invariant. The factors do not cause each other and have the same stability. The parameters of the model are the factor loading structure, each variable's reliability, and the stability of the factors. We apply the model to two data sets. For eight cognitive skill variables measured at four times, the 2-year stability is estimated to be .92 and the 6-year stability is .83. For nine personality variables, the 3-year stability is .68. We speculate that for many variables there are two components: one component that changes very slowly (the trait component) and another that changes very rapidly (the state component); thus each variable is a mixture of trait and state. Circumstantial evidence supporting this view is presented.