We propose a unifying framework for multilevel modeling of polytomous data and rankings, accommodating dependence induced by factor and/or random coefficient structures at different levels. The framework subsumes a wide range of models proposed in disparate methodological literatures. Partial and tied rankings, alternative specific explanatory variables and alternative sets varying across units are handled. The problem of identification is addressed. We develop an estimation and prediction methodology for the model framework which is implemented in the generally available gllamm software. The methodology is applied to party choice and rankings from the 1987–1992 panel of the British Election Study. Three levels are considered: elections, voters and constituencies.

Composite links and exploded likelihoods are powerful yet simple tools for specifying a wide range of latent variable models. Applications considered include survival or duration models, models for rankings, small area estimation with census information, models for ordinal responses, item response models with guessing, randomized response models, unfolding models, latent class models with random effects, multilevel latent class models, models with log-normal latent variables, and zero-inflated Poisson models with random effects. Some of the ideas are illustrated by estimating an unfolding model for attitudes to female work participation.

A unifying framework for generalized multilevel structural equation modeling is introduced. The models in the framework, called generalized linear latent and mixed models (GLLAMM), combine features of generalized linear mixed models (GLMM) and structural equation models (SEM) and consist of a response model and a structural model for the latent variables. The response model generalizes GLMMs to incorporate factor structures in addition to random intercepts and coefficients. As in GLMMs, the data can have an arbitrary number of levels and can be highly unbalanced with different numbers of lower-level units in the higher-level units and missing data. A wide range of response processes can be modeled including ordered and unordered categorical responses, counts, and responses of mixed types. The structural model is similar to the structural part of a SEM except that it may include latent and observed variables varying at different levels. For example, unit-level latent variables (factors or random coefficients) can be regressed on cluster-level latent variables. Special cases of this framework are explored and data from the British Social Attitudes Survey are used for illustration. Maximum likelihood estimation and empirical Bayes latent score prediction within the GLLAMM framework can be performed using adaptive quadrature in gllamm, a freely available program running in Stata.