A guide for multilevel modeling of dyadic data with binary outcomes using SAS PROC NLMIXED

Abstract

In the social and health sciences, data are often structured hierarchically, with individuals nested within groups. Dyads constitute a special case of hierarchically structured data with variation at both the individual and dyadic level. Analyses of data from dyads pose several challenges due to the interdependence between members within dyads and issues related to small group sizes. Multilevel analytic techniques have been developed and applied to dyadic data in an attempt to resolve these issues. In this article, we describe a set of analyses for modeling individual- and dyad-level influences on binary outcomes using SAS statistical software; and we discuss the benefits and limitations of such an approach. For illustrative purposes, we apply these techniques to estimate individual- and dyad-level predictors of viral hepatitis C infection among heterosexual couples in East Harlem, New York City.

Introduction

Many processes under study in the health sciences, such as treatment delivery, childcare, and disease transmission, involve interpersonal relationships and mutual influence involving two persons (e.g., physician–patient, parent–child, wife–husband). Conventional methods for inferential data analyses, including analysis of variance (ANOVA) and general linear regression, assume that observations obtained from each individual are independent. When such analyses are applied to data obtained from interacting dyads, the assumption of independent observations may be violated, leading to underestimation of standard errors and invalid inferences (i.e., increased Type I error).

To overcome the problem of nonindependence in the case of distinguishable dyad members, such as female–male couples, researchers often conduct separate analysis for each member class. For example, in a study of the effects of spousal support on health indicators, Heffner et al. (2004) performed separate analyses for females and males. Although this approach maintains independence of observations, it can obscure class interactions that may be of theoretical interest. In the example cited, although theory suggested that couple-level effects might moderate health status through interactions with spousal support and other variables, such effects could not be assessed in separate analyses. Several techniques have been developed to circumvent the problem of nonindependence while permitting estimation of dyad-level effects, including interactions (e.g., Kenny, 1996, Gonzalez and Griffin, 1999, Newsom, 2002).

Multilevel linear modeling (MLM) is one such technique developed and applied to dyadic data analysis (Barnett et al., 1993, Raudenbush et al., 1995, Windle and Dumenci, 1997, Kenny and Cook, 1999, Kashy and Kenny, 2000, Hoff, 2005). To make multilevel modeling techniques more accessible to data analysts, Campbell and Kashy (2002) have provided a practical guide for MLM analysis of dyadic data with continuous outcomes using two commercial software programs—SAS PROC MIXED and HLM. Here, we extend the work of these authors by providing a guide for nonlinear multilevel modeling of dyadic data with binary outcomes using NLMIXED and other procedures in SAS.

In Section 2, we briefly introduce multilevel modeling techniques and discuss limitations of this approach to analysis of dyadic data with binary outcomes. We also present model equations for both conditional and unconditional multilevel models and discuss methods for determining the appropriate use of the multilevel approach with dyadic binary response data. Section 3 lists the statistical assumptions of multilevel modeling with binary outcomes. In Section 4, we identify different types of dyadic data and discuss the implications of data properties and structure for multilevel modeling. An illustrative analysis involving risk factors for viral hepatitis C within heterosexual couples is introduced in Section 5. In Section 6, we provide practical guidelines for data preparation, using examples from the couples’ risk study. In Section 7, we describe SAS PROC NLMIXED and provide a step-by-step guide for performing multilevel modeling analysis and interpretation using data from the couples risk study as exemplar. We conclude with a discussion, including limitations of the approach, in Section 8.