Latent variable model

About: Latent variable model is a research topic. Over the lifetime, 3589 publications have been published within this topic receiving 235061 citations.

Multilevel structural equation modeling

Abstract: In conventional structural equation models, all latent variables and indicators vary between units (typically subjects) and are assumed to be independent across units. The latter assumption is violated in multilevel settings where units are nested in clusters, leading to within-cluster dependence. Different approaches to extending structural equation models for such multilevel settings are examined. The most common approach is to formulate separate within-cluster and between-cluster models. An advantage of this set-up is that it allows software for conventional structural equation models to be ‘tricked’ into estimating the model. However, the standard implementation of this approach does not permit cross-level paths from latent or observed variables at a higher level to latent or observed variables at a lower level, and does not allow for indicators varying at higher levels. A multilevel regression (or path) model formulation is therefore suggested in which some of the response variables and some of the explanatory variables at the different levels are latent and measured by multiple indicators. The Generalized Linear Latent and Mixed Modeling (GLLAMM) framework allows such models to be specified by simply letting the usual structural part of the model include latent and observed variables varying at different levels. Models of this kind are applied to the U.S. sample of the Program for International Student Assessment (PISA) 2000 to investigate the relationship between the school-level latent variable ‘teacher excellence’ and the student-level latent variable ‘reading ability’, each measured by multiple ordinal indicators.

Modeling Sentences in the Latent Space

Abstract: Sentence Similarity is the process of computing a similarity score between two sentences Previous sentence similarity work finds that latent semantics approaches to the problem do not perform well due to insufficient information in single sentences In this paper, we show that by carefully handling words that are not in the sentences (missing words), we can train a reliable latent variable model on sentences In the process, we propose a new evaluation framework for sentence similarity: Concept Definition Retrieval The new framework allows for large scale tuning and testing of Sentence Similarity models Experiments on the new task and previous data sets show significant improvement of our model over baselines and other traditional latent variable models Our results indicate comparable and even better performance than current state of the art systems addressing the problem of sentence similarity

Bayesian Gaussian Copula Factor Models for Mixed Data

Abstract: Gaussian factor models have proven widely useful for parsimoniously characterizing dependence in multivariate data. There is rich literature on their extension to mixed categorical and continuous variables, using latent Gaussian variables or through generalized latent trait models accommodating measurements in the exponential family. However, when generalizing to non-Gaussian measured variables, the latent variables typically influence both the dependence structure and the form of the marginal distributions, complicating interpretation and introducing artifacts. To address this problem, we propose a novel class of Bayesian Gaussian copula factor models that decouple the latent factors from the marginal distributions. A semiparametric specification for the marginals based on the extended rank likelihood yields straightforward implementation and substantial computational gains. We provide new theoretical and empirical justifications for using this likelihood in Bayesian inference. We propose new default pri...