Explanatory Models for Relating Growth Processes

For many purposes, longitudinal data are a great advance over cross-sectional data. The opportunities for modelling are enhanced if data for several occasions are obtained for a response, y, and at least one time-varying explanatory variable, x. The article describes, with examples, three modelling approaches when both y and x change over time. The first - a conditional approach - relates x to y in a regression framework. Earlier versions of these models were known as two-wave, two-variable (2W2V) 'causal' models. In the second, unconditional approach, growth or change parameters for x and y are themselves related in a second stage analysis. The third approach is based on structural equations modelling. All three approaches can be implemented in a multilevel framework. The article describes how multilevel models can extend the way we think about the analysis of longitudinal data, and hence how more interesting hypotheses about social processes can be modelled.