Approximate likelihood inference in generalized linear latent variable models based on the dimension-wise quadrature

We propose a new method to perform approximate likelihood inference in latent variable models. Our approach provides an approximation of the integrals involved in the likelihood function through a reduction of their dimension that makes the computation feasible in situations in which classical and adaptive quadrature based methods are not applicable. We derive new theoretical results on the accuracy of the obtained estimators. We show that the proposed approximation outperforms several existing methods in simulations, and it can be successfully applied in presence of multidimensional longitudinal data when standard techniques are not applicable or feasible

A general multivariate latent growth model with applications in student careers Data warehouses

The evaluation of the formative process in the University system has been assuming an ever increasing importance in the European countries. Within this context the analysis of student performance and capabilities plays a fundamental role. In this work we propose a multivariate latent growth model for studying the performances of a cohort of students of the University of Bologna. The model proposed is innovative since it is composed by: (1) multivariate growth models that allow to capture the different dynamics of student performance indicators over time and (2) a factor model that allows to measure the general latent student capability. The flexibility of the model proposed allows its applications in several fields such as socio-economic settings in which personal behaviours are studied by using panel data.Comment: 20 page

A note on goodness of fit test in latent variable models with categorical variables

Assessing the goodness-of-fit of latent variable models for categorical data becomes a problem in presence of sparse data since the classical goodness-of-fit statistics are badly approximated by the chi square distribution. A good solution to this problem is represented by statistical tests based on the residuals associated to marginal distributions of the manifest variables (Cagnone and Mignani, 2007; Maydeu-Olivares and Joe, 2005; Reiser, 1996). The quadratic form associated to the test involves the use of a generalized inverse of the covariance matrix of the sample proportions. In this article we prove that the rank of the Moore-Penrose generalized inverse is univocally determined and hence it can be used appropriately

Appunti sulla metodologia Lisrel: aspetti teorici e applicativi

Introduzione, specificazione, stima dei modelli a equazioni strutturali con una applicazione ad una analisi di Customer satisfactio

The role of posterior densities in latent variable models for ordinal data

In latent variable models, problems related to the integration of the likelihood function arise since analytical solutions do not exist. Laplace and Adaptive Gauss-Hermite (AGH) approximations have been discussed as good approximating methods. Their performance relies on the assump- tion of normality of the posterior density of the latent variables, but, in small samples, this is not necessarily assured. Here, we analyze how the shape of the posterior densities varies as function of the model parame- ters, and we investigate its influence on the performance of AGH and of the Laplace approximation

A multilevel latent variable model for multidimensional and longitudinal data

Collection of short papers presented at the Cladag meetin

Dynamic latent variable models for the analysis of cognitive abilities in the elderly population

Cognitive functioning is a key indicator of overall individual health. Identifying factors related to cognitive status, especially in later life, is of major importance. We concentrate on the analysis of the temporal evolution of cognitive abilities in the elderly population. We propose to model the individual cognitive functioning as a multidimensional latent process that accounts also for the effects of individual-specific characteristics (gender, age, and years of education). The proposed model is specified within the generalized linear latent variable framework, and its efficient estimation is obtained using a recent approximation technique, called dimensionwise quadrature. It provides a fast and streamlined approximate inference for complex models, with better or no degradation in accuracy compared with standard techniques. The methodology is applied to the cognitive assessment data from the Health and Retirement Study combined with the Asset and Health Dynamic study in the years between 2006 and 2010. We evaluate the temporal relationship between two dimensions of cognitive functioning, that is, episodic memory and general mental status. We find a substantial influence of the former on the evolution of the latter, as well as evidence of severe consequences on both cognitive abilities among less-educated and older individuals

Approximate inference in latent variable models based on dimension-wise quadrature

Approximate methods are considered for likelihood inference to longitudinal and multidimensional data within the context of health science studies.The complexity of these data necessitates the use of sophisticated statistical models that can pose significant challenges for model fitting in termsof computational speed, memory storage, and accuracy of the estimates. Our methodology is motivated by a study that examines the temporal evolution of the mental status of the US elderly population between 2006 and 2010. We propose modeling the individual mental status as a latentprocess also accounting for the effects of individual specific characteristics, such as gender, age, and years of educational attainment. We describethe specification of such a model within the generalized linear latent variable framework, and its efficient estimation using a recent technique,called dimension-wise quadrature. The latter allows a fast and streamlined analytical approximate inference for complex models, with better orno degradation in accuracy compared with the standard techniques, such as Laplace approximation and adaptive quadrature. The model and themethod are applied in the analysis of cognitive assessment data from the health and retirement study combined with the asset and health dynamicstudy