A Dyadic IRT Model

Psychometrika - We propose a dyadic Item Response Theory (dIRT) model for measuring interactions of pairs of individuals when the responses to items represent the actions (or behaviors,...     

Multilevel and Latent Variable Modeling with Composite Links and Exploded Likelihoods

Composite links and exploded likelihoods are powerful yet simple tools for specifying a wide range of latent variable models. Applications considered include survival or duration models, models for rankings, small area estimation with census information, models for ordinal responses, item response models with guessing, randomized response models, unfolding models, latent class models with random effects, multilevel latent class models, models with log-normal latent variables, and zero-inflated Poisson models with random effects. Some of the ideas are illustrated by estimating an unfolding model for attitudes to female work participation. We wish to thank The Research Council of Norway for a grant supporting our collaboration.     

Improved Regression Calibration

The likelihood for generalized linear models with covariate measurement error cannot in general be expressed in closed form, which makes maximum likelihood estimation taxing. A popular alternative is regression calibration which is computationally efficient at the cost of inconsistent estimation. We propose an improved regression calibration approach, a general pseudo maximum likelihood estimation method based on a conveniently decomposed form of the likelihood. It is both consistent and computationally efficient, and produces point estimates and estimated standard errors which are practically identical to those obtained by maximum likelihood. Simulations suggest that improved regression calibration, which is easy to implement in standard software, works well in a range of situations.     

The Role of Conditional Likelihoods in Latent Variable Modeling

Psychometrika - In psychometrics, the canonical use of conditional likelihoods is for the Rasch model in measurement. Whilst not disputing the utility of conditional likelihoods in measurement, we...     

Regression among factor scores

Structural equation models with latent variables are sometimes estimated using an intuitive three-step approach, here denoted factor score regression. Consider a structural equation model composed of an explanatory latent variable and a response latent variable related by a structural parameter of scientific interest. In this simple example estimation of the structural parameter proceeds as follows: First, common factor models areseparately estimated for each latent variable. Second, factor scores areseparately assigned to each latent variable, based on the estimates. Third, ordinary linear regression analysis is performed among the factor scores producing an estimate for the structural parameter. We investigate the asymptotic and finite sample performance of different factor score regression methods for structural equation models with latent variables. It is demonstrated that the conventional approach to factor score regression performs very badly. Revised factor score regression, using Regression factor scores for the explanatory latent variables and Bartlett scores for the response latent variables, produces consistent estimators for all parameters.     

IMPS 2008 PLANNED SESSIONS

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IMPS 2008 PLANNED SESSIONS     

Validation of the NEO Personality Inventory and the five-factor model. Can findings from exploratory and confirmatory factor analysis be reconciled?

The aims of the study were (i) to analyse a Norwegian version of the NEO Personality Inventory (NEO-PI), using both exploratory factor analysis (EFA) and confirmatory factor analysis (CFA); (ii) to compare the results of the two factor analytic strategies, both within the present study and across different studies; and (iii) to discuss possible causes of discrepant findings (across factor-analytic methods and across samples). The sample comprised 961 subjects representative of the non-institutionalized Norwegian adult population. Using an EFA strategy, very high coefficients of factor comparability (r=0.93–0.99) across sexes were found. None of the five main domains turned out to be as homogeneous as suggested by the original five-factor model, but most of the deviations from the assumed simple structure were comparable to results from recent American studies. However, none of the revised EFA-based models were supported using CFA methods. Moreover, a large number of modifications were necessary to obtain a model with acceptable fit. It is argued that these discrepant findings can be accounted for, at least in part, by (i) consequences of different model acceptance criteria in the EFA and CFA tradition, (ii) the inherent logical–semantical structure of the NEO-PI, and (iii) consequences of selection effects (factorial invariance problem). © 1997 by John Wiley & Sons, Ltd.     

Generalized multilevel structural equation modeling

A unifying framework for generalized multilevel structural equation modeling is introduced. The models in the framework, called generalized linear latent and mixed models (GLLAMM), combine features of generalized linear mixed models (GLMM) and structural equation models (SEM) and consist of a response model and a structural model for the latent variables. The response model generalizes GLMMs to incorporate factor structures in addition to random intercepts and coefficients. As in GLMMs, the data can have an arbitrary number of levels and can be highly unbalanced with different numbers of lower-level units in the higher-level units and missing data. A wide range of response processes can be modeled including ordered and unordered categorical responses, counts, and responses of mixed types. The structural model is similar to the structural part of a SEM except that it may include latent and observed variables varying at different levels. For example, unit-level latent variables (factors or random coefficients) can be regressed on cluster-level latent variables. Special cases of this framework are explored and data from the British Social Attitudes Survey are used for illustration. Maximum likelihood estimation and empirical Bayes latent score prediction within the GLLAMM framework can be performed using adaptive quadrature in gllamm, a freely available program running in Stata.gllamm can be downloaded from http://www.gllamm.org. The paper was written while Sophia Rabe-Hesketh was employed at and Anders Skrondal was visiting the Department of Biostatistics and Computing, Institute of Psychiatry, King's College London.