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  • 1.
    Bryant, Fred B.
    et al.
    Loyola Univ, Dept Psychol, 1032 W Sheridan Rd, Chicago, IL 60660 USA..
    Jöreskog, Karl Gustav
    Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.
    Confirmatory Factor Analysis of Ordinal Data Using Full-Information Adaptive Quadrature2016In: Australian & New Zealand journal of statistics (Print), ISSN 1369-1473, E-ISSN 1467-842X, Vol. 58, no 2, 173-196 p.Article in journal (Refereed)
    Abstract [en]

    We conducted confirmatory factor analysis (CFA) of responses (N=803) to a self-reported measure of optimism, using full-information estimation via adaptive quadrature (AQ), an alternative estimation method for ordinal data. We evaluated AQ results in terms of the number of iterations required to achieve convergence, model fit, parameter estimates, standard errors (SE), and statistical significance, across four link-functions (logit, probit, log-log, complimentary log-log) using 3-10 and 20 quadrature points. We compared AQ results with those obtained using maximum likelihood, robust maximum likelihood, and robust diagonally weighted least-squares estimation. Compared to the other two link-functions, logit and probit not only produced fit statistics, parameters estimates, SEs, and levels of significance that varied less across numbers of quadrature points, but also fitted the data better and provided larger completely standardised loadings than did maximum likelihood and diagonally weighted least-squares. Our findings demonstrate the viability of using full-information AQ to estimate CFA models with real-world ordinal data.

  • 2.
    Katsikatsou, Myrsini
    et al.
    Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.
    Moustaki, Irini
    Yang-Wallentin, Fan
    Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.
    Jöreskog, Karl G.
    Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.
    Pairwise Likelihood Estimation for factor analysis models with ordinal data2011Report (Other academic)
    Abstract [en]

    Pairwise maximum likelihood (PML) estimation is developed for factor analysis models with ordinal data fitted both in an exploratory and confirmatory set-up, and its performance is studied and compared with full information maximum likelihood (FIML) and a three-stage limited information estimation method. More specifically, estimates and standard errors ob- tained from PML are compared with those obtained from FIML and those from robust un- weighted least squares (3S-RULS). All three methods provide very close estimates and stan- dard errors. However, the PML estimates and standard errors are on average slightly closer to FIML than the 3S-RULS are. The advantage of PML over FIML is mainly computational. The computational complexity of FIML increases with the number of factors or observed variables depending on the model formulation, while that of PML is affected by neither of them. Contrary to 3S-RULS, in PML, all model parameters are simultaneously estimated and therefore the final estimates reflect all the sampling variability. In the 3S-RULS method the standard errors of the parameter estimates in stage three do not incorporate the variability of the estimates obtained in step one. Furthermore, PML does not require the estimation of a weight matrix for computing correct standard errors. The performance of PML estimates and their estimated asymptotic standard errors are investigated through a simulation study where the effect of different models and sample sizes are studied. The bias and mean squared error of PML estimators and their standard errors are found to be small in all experimental conditions and decreasing with the sample size. 

  • 3.
    Katsikatsou, Myrsini
    et al.
    Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.
    Moustaki, Irini
    London School of Economics, Department of Statistics.
    Yang-Wallentin, Fan
    Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.
    Jöreskog, Karl G.
    Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.
    Pairwise likelihood estimation for factor analysis models with ordinal data2012In: Computational Statistics & Data Analysis, ISSN 0167-9473, Vol. 56, no 12, 4243-4258 p.Article in journal (Refereed)
    Abstract [en]

    A pairwise maximum likelihood (PML) estimation method is developed for factor analysis models with ordinal data and fitted both in an exploratory and confirmatory set-up. The performance of the method is studied via simulations and comparisons with full information maximum likelihood (FIML) and three-stage limited information estimation methods, namely the robust unweighted least squares (3S-RULS) and robust diagonally weighted least squares (3S-RDWLS). The advantage of PML over FIML is mainly computational. Unlike PML estimation, the computational complexity of FIML estimation increases either with the number of factors or with the number of observed variables depending on the model formulation. Contrary to 3S-RULS and 3S-RDWLS estimation, PML estimates of all model parameters are obtained simultaneously and the PML method does not require the estimation of a weight matrix for the computation of correct standard errors. The simulation study on the performance of PML estimates and estimated asymptotic standard errors investigates the effect of different model and sample sizes. The bias and mean squared error of PML estimates and their standard errors are found to be small in all experimental conditions and decreasing with increasing sample size. Moreover, the PML estimates and their standard errors are found to be very close to those of FIML.

  • 4.
    Yang-Wallentin, Fan
    et al.
    Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.
    Jöreskog, Karl
    Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.
    Luo, Hao
    Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.
    Confirmatory Factor Analysis of Ordinal Variables With Misspecified Models2010In: Structural Equation Modeling, ISSN 1070-5511, E-ISSN 1532-8007, Vol. 17, no 3, 392-423 p.Article in journal (Refereed)
    Abstract [en]

    Ordinal variables are common in many empirical investigations in the social and behavioral sciences. Researchers often apply the maximum likelihood method to fit structural equation models to ordinal data. This assumes that the observed measures have normal distributions, which is not the case when the variables are ordinal. A better approach is to use polychoric correlations and fit the models using methods such as unweighted least squares (ULS), maximum likelihood (ML), weighted least squares (WLS), or diagonally weighted least squares (DWLS). In this simulation evaluation we study the behavior of these methods in combination with polychoric correlations when the models are misspecified. We also study the effect of model size and number of categories on the parameter estimates, their standard errors, and the common chi-square measures of fit when the models are both correct and misspecified. When used routinely, these methods give consistent parameter estimates but ULS, ML, and DWLS give incorrect standard errors. Correct standard errors can be obtained for these methods by robustification using an estimate of the asymptotic covariance matrix W of the polychoric correlations. When used in this way the methods are here called RULS, RML, and RDWLS.

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