Pairwise maximum likelihood (PML) estimation method is developed for factor analysis models with ordinal data and tted both in an exploratory and conrmatory set-up. The performance of the method is studied via simulations
Summary When missing data are produced by a non‐ignorable non‐response mechanism, analysis of the observed data should include a model for the probabilities of responding. We propose such models for non‐response in survey questions which are treated as measures of latent constructs and analysed by using latent variable models. The non‐response models that we describe include additional latent variables (latent response propensities) which determine the response probabilities. We argue that this model should be specified as flexibly as possible, and we propose models where the response propensity is a categorical variable (a latent response class). This can be combined with any latent variable model for the survey items, and an association between the latent variables measured by the items and the latent response propensities then implies a model with non‐ignorable non‐response. We consider in particular such models for the analysis of data from cross‐national surveys, where the non‐response model may also vary across the countries. The models are applied to data on welfare attitudes in 29 countries in the European Social Survey.
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 .
In survey interviews, "Don't know" (DK) responses are commonly treated as missing data. One way to reduce the rate of such responses is to probe initial DK answers with a follow-up question designed to encourage respondents to give substantive, non-DK responses. However, such probing can also reduce data quality by introducing additional or differential measurement error. We propose a latent variable model for analyzing the effects of probing on responses to survey questions. The model makes it possible to separate measurement effects of probing from true differences between respondents who do and do not require probing. We analyze new data from an experiment which compared responses to two multi-item batteries of questions with and without probing. In this study, probing reduced the rate of DK responses by around a half. However, it also had substantial measurement effects, in that probed answers were often weaker measures of constructs of interest than were unprobed answers. These effects were larger for questions on attitudes than for pseudo-knowledge questions on perceptions of external facts. The results provide evidence against the use of probing of "Don't know" responses, at least for the kinds of items and respondents considered in this study.
Methods for the treatment of item non‐response in attitudinal scales and in large‐scale assessments under the pairwise likelihood (PL) estimation framework and under a missing at random (MAR) mechanism are proposed. Under a full information likelihood estimation framework and MAR, ignorability of the missing data mechanism does not lead to biased estimates. However, this is not the case for pseudo‐likelihood approaches such as the PL. We develop and study the performance of three strategies for incorporating missing values into confirmatory factor analysis under the PL framework, the complete‐pairs (CP), the available‐cases (AC) and the doubly robust (DR) approaches. The CP and AC require only a model for the observed data and standard errors are easy to compute. Doubly‐robust versions of the PL estimation require a predictive model for the missing responses given the observed ones and are computationally more demanding than the AC and CP. A simulation study is used to compare the proposed methods. The proposed methods are employed to analyze the UK data on numeracy and literacy collected as part of the OECD Survey of Adult Skills.
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