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.
The now well‐documented explosion in prison populations over the last 30 years has spurred significant attention in the literature. Early research focused primarily on economic explanations. More recently it has focused on political explanations of prison growth. Here we extend research on political explanations of imprisonment by drawing on the literature on state politics and public policy. We argue that the effect of partisan politics on punishment is conditional on how much electoral competition legislators face. We test this hypothesis using annual state level data on imprisonment from 1978 to 1996. Our findings show that the effect of Republican state legislative strength on prison admissions depends on time and the level of competition in state legislative elections. We argue that these findings suggest the need for a more nuanced understanding of the link between partisan U.S. politics and imprisonment.
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