Univariate Analysis

Abstract

In this chapter we take the univariate model for twin data, as described in Chapter 5, and apply it to twin data. We hope that this will enable the readers to apply the models to their own data, and deepen their understanding of both the scope and the limitations of the method. The first example concerns body mass index (BMI), a widely used measure of obesity, and Section 8.2 describes how we obtained and summarized these data. In Section 8.3 we develop and apply a model of additive genetic (A), dominance genetic (D), common environment (C), and random environment (E) effects, even though D and C are confounded when our data have been obtained from pairs of twins reared together. In Section 8.4 we start to fit this model to authentic data, using LISREL 7 in a path coefficients approach. To illustrate the univariate model fitted with variance components, we describe the use of LISREL 8 (in β-test version at the time of writing) in Section 8.5. This second treatment may be skipped without loss of continuity. The results of initial model-fitting to BMI data appear in Section 8.6 and two extensions to the model, the use of means and of unmatched twins, are described before drawing general conclusions about the BMI analyses in Section 8.9. The second example describes the collection and analysis of major depressive disorder in a sample of adult female twins (Section 8.10.1). This application serves to contrast the data summary and analysis required for an ordinal variable against those appropriate for a continuous variable. In most twin studies there is considerable heterogeneity of age between pairs. As we show in Section 8.11, such heterogeneity can give rise to inflated estimates of the effects of the shared environment. We, therefore, provide a method of incorporating age into the structural equation model to separate its effects from other shared environmental influences.