2 Models for Multiple Rating Data

A primary source of information about a child's behavior is the description of that behavior by his or her parents. In the study of child and adolescent psychopathology for example, parental reports are fundamental to the widely used assessment system developed by Achenbach and Edelbrock (1981). However, different informants do not generally agree in detail about a given child's behavior (Achenbach et al., 1987; Loeber et al., 1989) and, of course, there are very good reasons why this should be so (Cox and Rutter, 1985). Different informants, such as the child, parents, teachers or peers, have different situational exposure, different degrees of insight, and different perceptions, evaluations and normative standards that may create rater differences of various kinds in reporting problem behaviors. How we analyze parental ratings of children's behavior, and the models we employ in the course of our analyses, will depend on the assumptions we make. In this chapter we discuss the application of three classes of models -- biometric, psychometric, and bias models. First, suppose we took an agnostic view of the relationship between the ratings by different informants by thinking of them as assessing different phenotypes of the child. The phenotypes may be correlated but for unspecified reasons. This view may be appropriate if mothers and fathers reported on behaviors observed in distinct situations, or if they did not share a common understanding of the behavioral descriptions. In such a case it would be appropriate to treat the analysis of mothers' and fathers' ratings as a standard bivariate genetic and environmental analysis where the two variables are the mothers' ratings and fathers' ratings. We shall refer to the class of standard bivariate factor model as biometric models (see Chapter 10 for examples). Second, suppose we made the more restrictive assumption that there is (i) a common phenotype of the children which is assessed both by mothers and by fathers, and (ii) a component of each parent's ratings which results from an assessment of an independent aspect of the child. Mothers' ratings and fathers' ratings would correlate because they are indeed making assessments based on shared observations and have a shared understanding of the behavioral descriptions used in the assessments. In this case, we approach the analysis of parental ratings through a special form of model for bivariate data which we will refer to as psychometric models (see Chapter 10 for examples). Third, we consider a model of rater bias. Bias in this context is considered to be the tendency of an individual rater to overestimate or underestimate scores consistently. This tendency is a deviation from the mean of all possible raters in the rater group; no reference is made here to any external criterion such as a clinician's judgement. Neale and Stevenson (1989) considered the general problem of rater bias and the particular issues of parental biases in ratings of children. They presented a model in which the rating of a child's phenotype is considered to be a function both of the child's phenotype and of the bias introduced by the rater. In this way it is possible, when two parents rate each of their twin children, to conduct a behavior genetic analysis of the variation in the latent phenotype while allowing for variation due to rating biases. If the rater bias model adopted by Neale and Stevenson (1989) provides an adequate account of the ratings of children by their parents, it becomes possible to partition the variance in these parental ratings into their components due to reliable trait variance, due to parental bias , and due to unreliability or error in the particular rating of a particular child. The reliable trait variance can then be decomposed into its components due to genetic influences, shared environments, and individual environments. Since rater bias models represent restricted special cases for the parental ratings of more general biometric and psychometric models of the kind discussed by Heath et al., (1989) and McArdle and Goldsmith (1990) and in Chapter 10 of this volume, it is possible to compare the adequacy of bias models with the alternative bivariate psychometric and biometric models. Further, comparison of the biometric and psychometric models indicates how reasonable it is to assume that two raters are assessing the same phenotype in a child. As we move from the biometric to the psychometric to the bias models, our assumptions become more restrictive but, if appropriate, our analyses become more directly informative psychologically. Here we outline how an analysis of parental ratings using the bias model can be implemented simply using Mx. We discuss the properties of the alternative models and illustrate their application with data from a twin study of child and adolescent behavior problems.