Latent Variable Models and Factor Analysis

Bartholomew, David J.; Knott, M.; Moustaki, Irini

doi:10.1002/9781119970583

Cited by 992 publications

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“…There are two main approaches for modelling categorical (binary and ordinal) observed variables with latent variables, namely the full information maximum likelihood approach (FIML) used in item response theory (e.g. Skrondal & Rabe-Hesketh, 2004;Bartholomew et al, 2011) and the limitedinformation approach used in structural equation modelling (SEM) (e.g. Jöreskog, 1990Jöreskog, , 1994Muthén, 1984).…”

Section: Introductionmentioning

confidence: 99%

Pairwise Likelihood Ratio Tests and Model Selection Criteria for Structural Equation Models with Ordinal Variables

Katsikatsou

Moustaki

2016

Psychometrika

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This document is the author's final accepted version of the journal article. There may be differences between this version and the published version. You are advised to consult the publisher's version if you wish to cite from it.Pairwise likelihood ratio tests and model selection criteria for structural equation models with ordinal variablesCorrelated multivariate ordinal data can be analysed with structural equation models. Parameter estimation has been tackled in the literature using limited-information methods including three-stage least squares and pseudo-likelihood estimation methods such as pairwise maximum likelihood estimation. In this paper, two likelihood ratio test statistics and their asymptotic distributions are derived for testing overall goodness-of-fit and nested models respectively under the estimation framework of pairwise maximum likelihood estimation. Simulation results show a satisfactory performance of type I error and power for the proposed test statistics and also suggest that the performance of the proposed test statistics is similar to that of the test statistics derived under the three-stage diagonally weighted and unweighted least squares. Furthermore, the corresponding, under the pairwise framework, model selection criteria, AIC and BIC, show satisfactory results in selecting the right model in our simulation examples. The derivation of the likelihood ratio test statistics and model selection criteria under the pairwise framework together with pairwise estimation provide a flexible framework for fitting and testing structural equation models for ordinal as well as for other types of data. The test statistics derived and the model selection criteria are used on data on 'trust in the police' selected from the 2010 European Social Survey. The proposed test statistics and the model selection criteria have been implemented in the R package lavaan 1 .

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Section: Introductionmentioning

confidence: 99%

Pairwise Likelihood Ratio Tests and Model Selection Criteria for Structural Equation Models with Ordinal Variables

Katsikatsou

Moustaki

2016

Psychometrika

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“…Sometimes background knowledge is useful to provide which observed variable measures which target latent variable (e.g., Y 1 should be a child of X 1 but not of X 2 ). The literature in structural equation models and factor analysis [3,2] provides some examples where observed variables are designed so that latent concepts of interest are measured (up to some measurement error). Background knowledge about other hidden common causes of the observed variables is less clear, though.…”

Section: Illustration: Learning Measurement Error Structurementioning

confidence: 99%

A MCMC Approach for Learning the Structure of Gaussian Acyclic Directed Mixed Graphs

Silva

2013

Statistical Models for Data Analysis

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Graphical models are widely used to encode conditional independence constraints and causal assumptions, the directed acyclic graph (DAG) being one of the most common families of models. However, DAGs are not closed under marginalization: that is, if a distribution is Markov with respect to a DAG, several of its marginals might not be representable with another DAG unless one discards some of the structural independencies. Acyclic directed mixed graphs (ADMGs) generalize DAGs so that closure under marginalization is possible. In a previous work, we showed how to perform Bayesian inference to infer the posterior distribution of the parameters of a given Gaussian ADMG model, where the graph is fixed. In this paper, we extend this procedure to allow for priors over graph structures.Key words: Graphical models, Bayesian inference, sparsity. Acyclic Directed Mixed Graph ModelsDirected acyclic graphs (DAGs) provide a practical language to encode conditional independence constraints (see, e.g., [8]). However, such a family is not closed under marginalization. As an illustration of this concept, consider the following DAG:This model entails several conditional independencies. For instance, it encodes constraints such as Y 2 ⊥ ⊥ Y 4 , as well asDirected graphical models are non-monotonic independence models, in the sense that conditioning on extra variables can destroy and re-create independencies, as the sequence { / 0, {Y 3 }, {Y 3 , X}} has demonstrated.

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“…Latent variable or factor models are a unified tool for the analysis of high-dimensional response data with dependence coming from latent (unobservable) variables/factors so that the number of dependence parameters is O(d) rather than O(d 2 ), where d is the number of observed variables; see for example, Bartholomew et al (2011). For example, a questionnaire or instrument, used in psychometrics to assess abstract concepts, such as the quality of life, conservatism, and general intelligence, may have d ≥ 50 items or questions, but many questions overlap or are correlated by design.…”

Section: Introductionmentioning

confidence: 99%

Factor Copula Models for Item Response Data

Nikoloulopoulos

Joe

2013

Psychometrika

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university of east anglia Harry Joe university of british columbia Factor or conditional independence models based on copulas are proposed for multivariate discrete data such as item responses. The factor copula models have interpretations of latent maxima/minima (in comparison with latent means) and can lead to more probability in the joint upper or lower tail compared with factor models based on the discretized multivariate normal distribution (or multidimensional normal ogive model). Details on maximum likelihood estimation of parameters for the factor copula model are given, as well as analysis of the behavior of the log-likelihood. Our general methodology is illustrated with several item response data sets, and it is shown that there is a substantial improvement on existing models both conceptually and in fit to data.

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Latent Variable Models and Factor Analysis

Abstract: Introduce concepts and develop understanding in readiness for GCSE with clear explanations of all of the up-to-date terminology.

Cited by 992 publications

References 0 publications

Pairwise Likelihood Ratio Tests and Model Selection Criteria for Structural Equation Models with Ordinal Variables

Pairwise Likelihood Ratio Tests and Model Selection Criteria for Structural Equation Models with Ordinal Variables

A MCMC Approach for Learning the Structure of Gaussian Acyclic Directed Mixed Graphs

Factor Copula Models for Item Response Data

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