Chapter 7: Multilevel Logistic and Ordinal Models

So far, the models covered in this book have assumed a normal or approximately normal distribution for the outcome of interest, and thus for the errors across the multiple levels of the model. However, many response variables of interest in education and the social sciences do not fit the normal distribution framework; most often, these non-normal outcomes involve dependent variables with discrete or limited response categories. Common statistical approaches for analyzing these kinds of data are drawn from a class of linear models where the outcomes follow a distribution from the exponential family (McCullagh & Nelder, 1989). These models are referred to as generalized linear models (GLMs) and can be applied to binary outcomes, count data, and ordinal or categorical data. In fact, models for normally distributed outcomes—often referred to as general linear models—are simply a special case of the generalized linear model where the normal distribution is used to describe the distribution of model errors. In the generalized case, binary outcomes typically are analyzed using the logistic distribution; count data by the Poisson or negative binomial distribution; and ordinal/categorical data by the cumulative logistic or multinomial logistic models. This chapter presents logistic models for two types of categorical responses: (a) binary response variables and (b) ordinal response variables.