Consistent Estimation of Low-Dimensional Latent Structure in High-Dimensional Data
11
Citation
14
Reference
10
Related Paper
Citation Trend
Abstract:
We consider the problem of extracting a low-dimensional, linear latent variable structure from high-dimensional random variables. Specifically, we show that under mild conditions and when this structure manifests itself as a linear space that spans the conditional means, it is possible to consistently recover the structure using only information up to the second moments of these random variables. This finding, specialized to one-parameter exponential families whose variance function is quadratic in their means, allows for the derivation of an explicit estimator of such latent structure. This approach serves as a latent variable model estimator and as a tool for dimension reduction for a high-dimensional matrix of data composed of many related variables. Our theoretical results are verified by simulation studies and an application to genomic data.propcnsreg combines information from several observed variables into a single latent variable and estimates the effect of this latent variable on the depedent variable. These observed variables are so-called causal indicators (Bollen and Lennox, Psychological Bulletin 1991), that is, they influence the latent variable. It forms an alternative to factor analysis, which assumes that the latent variable influences the observed variables.
Variables
Causal model
Local independence
Cite
Citations (0)
propcnsreg combines information from several observed variables into a single latent variable and estimates the effect of this latent variable on the depedent variable. These observed variables are so-called causal indicators (Bollen and Lennox, Psychological Bulletin 1991), that is, they influence the latent variable. It forms an alternative to factor analysis, which assumes that the latent variable influences the observed variables.
Variables
Causal model
Local independence
Cite
Citations (1)
A model is proposed for identifying latent predictor score patterns associated with a latent outcome variable. The model employs 2 new devices: (a) a path coefficient vector of contrast coefficients to describe a configural pattern in a structural model, and (b) a new type of latent variable with values that quantify the match of the person's latent predictor variable profile pattern to a theoretical pattern associated with the factor. The model is illustrated using data on perceptions and evaluations of political candidates during a debate. Findings suggest a pattern of scores on the perceptual variables associated with perceived debate success for female observers but not for male observers.
Association (psychology)
Local independence
Cite
Citations (8)
In clinical research, interest sometimes lies in analysing variables which are not measured directly. Instead, information about these ‘latent variables’ can be inferred from surrogates or other imperfect indicators, using latent variable models. Common examples of ‘hypothetical’ latent variables in clinical research include quality of life (QoL), anxiety and depression. Another type of latent variable is a variable used as a device for dimension reduction, for example, a principal component. The aim of this thesis is to explore and develop latent variable methods for the statistical analysis of clinical data, with an emphasis on including latent variables in time-to-event models.
Local independence
Cite
Citations (0)
Human-computer interaction research increasingly involves investigating psychological phenomena as latent variables. In this chapter, we discuss basic latent variable models using a path model approach. In addition, we given some examples of conducting a latent variable model analysis using the lavaan package in the R statistical programming language.
Local independence
Cite
Citations (633)
We develop a
Cite
Citations (0)
Until recently, latent variable models such as the factor analysis model for metric responses, the two-parameter logistic model for binary responses, the multinomial model for nominal responses considered only main effects of latent variables without allowing for interaction or polynomial latent variable effects. However, nonlinear relationships among the latent variables might be necessary in real applications. Methods for fitting models with nonlinear latent terms have been developed mainly under the structural equation modelling approach. In this paper, we consider a general latent variable model framework for mixed responses (metric and categorical) that allows inclusion of both nonlinear latent and covariate effects. The model parameters are estimated using full Maximum Likelihood based on a hybrid integration-maximization algorithm. Finally, a new method for obtaining factor scores based on Multiple Imputation is proposed here for the model with nonlinear terms.
Categorical variable
Factor Analysis
Local independence
Multinomial distribution
Cite
Citations (0)
Local independence
Cite
Citations (4)
Latent growth modeling
Local independence
Cite
Citations (0)
Until recently, latent variable models such as the factor analysis model for metric responses, the two-parameter logistic model for binary responses, the multinomial model for nominal responses considered only main effects of latent variables without allowing for interaction or polynomial latent variable effects. However, nonlinear relationships among the latent variables might be necessary in real applications. Methods for fitting models with nonlinear latent terms have been developed mainly under the structural equation modelling approach. In this paper, we consider a general latent variable model framework for mixed responses (metric and categorical) that allows inclusion of both nonlinear latent and covariate effects. The model parameters are estimated using full Maximum Likelihood based on a hybrid integration-maximization algorithm. Finally, a new method for obtaining factor scores based on Multiple Imputation is proposed here for the model with nonlinear terms.
Categorical variable
Local independence
Factor Analysis
Multinomial distribution
Cite
Citations (0)