IRIS Università degli Studi di Bolognahttps://cris.unibo.itIl sistema di repository digitale IRIS acquisisce, archivia, indicizza, conserva e rende accessibili prodotti digitali della ricerca.Sun, 29 Nov 2020 01:29:45 GMT2020-11-29T01:29:45Z10481The Latent Variable-Autoregressive Latent Trajectory Model: A General Framework for Longitudinal Data Analysishttp://hdl.handle.net/11585/644809.1Titolo: The Latent Variable-Autoregressive Latent Trajectory Model: A General Framework for Longitudinal Data Analysis
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/11585/644809.12018-01-01T00:00:00ZAsymptotic properties of adaptive maximum likelihood estimators in latent variable modelshttp://hdl.handle.net/11585/141870Titolo: Asymptotic properties of adaptive maximum likelihood estimators in latent variable models
Abstract: Latent variable models have been widely applied in different fields of research in which the con- structs of interest are not directly observable, so that one or more latent variables are required to reduce the complexity of the data. In these cases, problems related to the integration of the likelihood function of the model arise since analytical solutions do not exist. In the recent litera- ture, a numerical technique that has been extensively applied to estimate latent variable models is the adaptive Gauss-Hermite quadrature. It provides a good approximation of the integral, and it is more feasible than classical numerical techniques in presence of many latent variables and/or random effects. In this paper, we formally investigate the properties of maximum likeli- hood estimators based on adaptive quadratures used to perform inference in generalized linear latent variable models.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/11585/1418702014-01-01T00:00:00ZStudent mobility and academic achievement: a temporal analysis for Bologna Universityhttp://hdl.handle.net/11585/46036Titolo: Student mobility and academic achievement: a temporal analysis for Bologna University
Mon, 01 Jan 2007 00:00:00 GMThttp://hdl.handle.net/11585/460362007-01-01T00:00:00ZThe role of posterior densities in latent variable models for ordinal datahttp://hdl.handle.net/11585/141871Titolo: The role of posterior densities in latent variable models for ordinal data
Abstract: 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.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/11585/1418712014-01-01T00:00:00ZEstimation of generalized linear latent variable models via fully exponential Laplace approximationhttp://hdl.handle.net/11585/117008Titolo: Estimation of generalized linear latent variable models via fully exponential Laplace approximation
Abstract: Latent variable models represent a useful tool in different fields of research in which the constructs of interest are not directly observable. In such models, problems related to the integration of the likelihood function can arise since analytical solutions do not exist. Numerical approximations, like the widely used Gauss Hermite (GH) quadrature, are generally applied to solve these problems. However, GH becomes unfeasible as the number of latent vari- ables increases. Thus, alternative solutions have to be found. In this paper, we propose an extended version of the Laplace method for approximating the integrals, known as fully exponential Laplace approximation. It is com- putational feasible also in presence of many latent variables, and it is more accurate than the classical Laplace approximation. The method is developed within the Generalized Linear Latent Variable Models (GLLVM) framework.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/11585/1170082012-01-01T00:00:00ZMultivariate latent growth models for mixed data with covariate effectshttp://hdl.handle.net/11585/104080Titolo: Multivariate latent growth models for mixed data with covariate effects
Abstract: The paper presents an extension of a new class of multivariate latent growth models (Bianconcini and Cagnone, 2012) to allow for covariate effects on manifest, latent variables and random effects. The new class of models combines: (i) multivariate latent curves that describe the temporal behavior of the responses, and (ii) a factor model that specifies the relationship between manifest and latent variables. Based on the Generalized Linear and Latent Variable Model framework (Bartholomew and Knott, 1999), the response variables are assumed to follow different distributions of the exponential family, with item-specific linear predictors depending on both latent variables and measurement errors. A full maximum likelihood method is used to estimate all the model parameters simultaneously. Data coming from the Data WareHouse of the University of Bologna are used to illustrate the methodology.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/11585/1040802012-01-01T00:00:00ZApproximate likelihood inference in latent variable models for categorical data.http://hdl.handle.net/11585/116332Titolo: Approximate likelihood inference in latent variable models for categorical data.
Abstract: Latent variable models represent a useful tool for the analysis of complex data characterized by the fact that the constructs of interest are not directly observable. One problem related to these models is that the integrals involved in the maximization of the likelihood function cannot be solved analytically. In this paper we propose a new approach for approximating integrals in latent variable models for binary data. Based on a fundamental theorem by Xu and Rahman (2004a), it consists of reducing the dimen- sionality of the integrals involved in the computations.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/11585/1163322012-01-01T00:00:00ZA Dimension Reduction Method for Approximating Integrals in Latent Variable Models for Binary Datahttp://hdl.handle.net/11585/122029Titolo: A Dimension Reduction Method for Approximating Integrals in Latent Variable Models for Binary Data
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/11585/1220292012-01-01T00:00:00ZA reproducing kernel perspective of smoothing spline estimatorshttp://hdl.handle.net/11585/123168Titolo: A reproducing kernel perspective of smoothing spline estimators
Abstract: Spline functions have a long history as smoothers of noisy time series data, and several equivalent kernel representations have been proposed in terms of the Green's function solving the related boundary value problem. In this study we make use of the reproducing kernel property of the Green's function to obtain an hierarchy of time-invariant spline kernels of different order. The reproducing kernels give a good representation of smoothing splines for medium and long length filters, with a better performance of the asymmetric weights in terms of signal passing, noise suppression and revisions. Empirical comparisons of time-invariant filters are made with the classical non linear ones. The former are shown to loose part of their optimal properties when we fixed the length of the filter according to the noise to signal ratio as done in nonparametric seasonal adjustment procedures.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/11585/1231682008-01-01T00:00:00ZLikelihood Inference in Latent Variable Models for ordinal data based on different approximation methodshttp://hdl.handle.net/11585/111114Titolo: Likelihood Inference in Latent Variable Models for ordinal data based on different approximation methods
Abstract: Latent variable models for ordinal data represent a useful tool in different fields of research in which the constructs of interest are not directly observable so that one or more latent variables are required to reduce the complexity of the data. In these cases problems related to the integration of the likelihood function of the model can arise since analytical solutions do not exist. One of the most used classical numerical approximat on is the Gauss Hermite (GH) quadrature. With this approximation the accuracy of estimates is strictly related to the number of quadrature points as well as to the sample
size. In presence of many latent variables, the GH cannot be applied since it requires several quadrature points per dimension in order to obtain quite accurate estimates, and, hence, the computational effort
becomes not feasible.We propose alternative solutions in order to overcome the main drawbacks of this approach
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/11585/1111142011-01-01T00:00:00Z