Multivariate Models for Normal and Binary Responses in Intervention Studies

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Use of multivariate analysis (e.g., multivariate analysis of variance) is common when normally distributed outcomes are collected in intervention research. However, when mixed responses—a set of normal and binary outcomes—are collected, standard multivariate analyses are no longer suitable. While mixed responses are often obtained in intervention studies and analysis models that can simultaneously include such outcomes are available, we found very limited use of these models in intervention research. To encourage greater use of multivariate analysis for mixed outcomes, this article highlights the benefits and describes important features of models that can incorporate a mix of normal and binary outcomes. Models for intervention research are then fit using Mplus and results interpreted using data from an evaluation of the Early Head Start program, a randomized trial designed to improve child outcomes for an at-risk population. The models illustrated estimate treatment effects for mixed responses in standard and multilevel experimental designs.