Simultaneously Modeling Joint and Marginal Distributions of Multivariate Categorical Responses
提出一种同时分析多元分类响应变量联合分布和边际分布的模型拟合方法，改进最大似然算法，适用于纵向数据、民意调查等场景，并用社会调查数据演示。
Abstract We discuss model-fitting methods for analyzing simultaneously the joint and marginal distributions of multivariate categorical responses. The models are members of a broad class of generalized logit and loglinear models. We fit them by improving a maximum likelihood algorithm that uses Lagrange's method of undetermined multipliers and a Newton-Raphson iterative scheme. We also discuss goodness-of-fit tests and adjusted residuals, and give asymptotic distributions of model parameter estimators. For this class of models, inferences are equivalent for Poisson and multinomial sampling assumptions. Simultaneous models for joint and marginal distributions may be useful in a variety of applications, including studies dealing with longitudinal data, multiple indicators in opinion research, cross-over designs, social mobility, and inter-rater agreement. The models are illustrated for one such application, using data from a recent General Social Survey regarding opinions about various types of government spending. Key Words: Adjusted residualsConstrained maximum likelihoodLagrange multiplierMarginal modelsOrdinal dataRepeated measurement