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      A General Linear Framework for Modeling Continuous Responses With Error in Persons and Items

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          Abstract

          This study develops a general linear model intended for personality and attitude items with (approximately) continuous responses that is based on a double source of measurement error: items and persons. Two restricted sub-models are then obtained from the general model by placing restrictions on the item and person parameters. And it follows that the standard unidimensional factor-analytic model is one of these sub-models. Procedures for (a) calibrating the items, (b) obtaining individual estimates of location and fluctuation, (c) assessing model-data fit, and (d) assessing measurement precision are discussed for all the models considered, and illustrated with two empirical examples in the personality domain.

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          Most cited references33

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          Item factor analysis: Current approaches and future directions.

          R. Wirth, Michael C. Edwards (2007)
          The rationale underlying factor analysis applies to continuous and categorical variables alike; however, the models and estimation methods for continuous (i.e., interval or ratio scale) data are not appropriate for item-level data that are categorical in nature. The authors provide a targeted review and synthesis of the item factor analysis (IFA) estimation literature for ordered-categorical data (e.g., Likert-type response scales) with specific attention paid to the problems of estimating models with many items and many factors. Popular IFA models and estimation methods found in the structural equation modeling and item response theory literatures are presented. Following this presentation, recent developments in the estimation of IFA parameters (e.g., Markov chain Monte Carlo) are discussed. The authors conclude with considerations for future research on IFA, simulated examples, and advice for applied researchers. (c) 2007 APA, all rights reserved.
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            On The Robustness Of Factor Analysis Against Crude Classification Of The Observations.

            U Olsson (1979)
            The paper is concerned with the consequences for maximum likelihood factor analysis which may follow if the observed variables are ordinal with only a few scale steps, which are assigned integer values. It is hypothesized that the observed variables are obtained through a classification of some true variables, which are multivariate normal and for which a factor model holds. Using simple formulas for the relations between true correlations and correlations based on the classified variables, we demonstrate numerically the relationships between true factor models and results obtained from classified data. This is done for several choices of thresholds, true factor loadings and numbers of variables, assuming a one-factor model. The results indicate that classification may lead to a substantial lack of fit of the model, i.e. an erroneous indication that more factors are needed. This is especially true if the variables are skewed in opposite direction and have high true loadings, but does not depend much on the number of scale steps. The classification also attenuates the loading estimates, and this effect is increased with a decreasing number of scale steps and increasing variation in skewness among the variables.
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              How to score questionnaires

              A.A.J. Hendriks, W.K.B. Hofstee, J.M.F.Ten Berge (1998)
              Article 0 comments Cited 36 times – based on 0 reviews     Review now
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                Author and article information

                Journal
                Journal ID (publisher-id): med
                Title: Methodology
                Subtitle: European Journal of Research Methods for the Behavioral and Social Sciences
                Publisher: Hogrefe Publishing
                ISSN (Print): 1614-1881
                ISSN (Electronic): 1614-2241
                Publication date (Print): July 2012
                Publication date (Electronic): 2013
                Volume: 9
                Issue: 4
                Pages: 150-161
                Affiliations
                [ 1 ] Research Centre for Behavioral Assessment, Universidad Rovira i Virgili, Tarragona, Spain
                Author notes
                Pere Joan Ferrando, Department de Psicología, Universitat Rovira i Virgili, Carretera Valls s/n, 43007 Tarragona, Spain +34 977 558-175, +34 977 558-088, perejoan.ferrando@ 123456urv.cat
                Article
                Apa ID: med_9_4_150
                DOI: 10.1027/1614-2241/a000060
                SO-VID: 00dc32e7-0a0b-4bfe-8193-157802cd3de1
                Copyright statement: Copyright @ 2012
                History
                Date: October 26, 2011
                Date accepted : April 6, 2012
                Categories
                Subject: Original Article

                ScienceOpen disciplines: Psychology,Applications,General social science,Methodology,Clinical Psychology & Psychiatry
                Keywords: personality and attitude measurement,person fluctuation,factor analysis,item response theory
                Data availability:
                ScienceOpen disciplines: Psychology, Applications, General social science, Methodology, Clinical Psychology & Psychiatry
                Keywords: personality and attitude measurement, person fluctuation, factor analysis, item response theory

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