Confirmatory factor analysis is some of the most widely used statistical techniques in the social sciences. Frequently, variables (i.e., items) stemming from questionnaires are analyzed. Two ...competing approaches for estimating confirmatory factor analysis can be distinguished. First, ordinal variables could be treated as in the case of continuous variables using Pearson correlations, and maximum likelihood estimation method would be applied. Second, an ordinal factor analysis based on polychoric correlations can be fitted. In the majority of the psychometric literature, there is a preference for the ordinal factor analysis based on polychoric correlations because the continuous treatment of variables results in biased factor loadings and biased factor correlations. This article argues that it is not legitimate to speak about bias when comparing the two competing factor analytic approaches because it depends on how true model parameters are defined. This decision can be made individually by a researcher. It is shown in simulation studies and analytical derivations that treating variables ordinally using polychoric correlations instead of continuous using Pearson correlations can also lead to biased estimates of factor loadings and factor correlations. Consequently, it should only be stated that different model parameters are defined in a continuous and an ordinal treatment, and one approach should not generally be preferred over the other.
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Three distinctive methods of assessing measurement equivalence of ordinal items, namely, confirmatory factor analysis, differential item functioning using item response theory, and latent class ...factor analysis, make different modeling assumptions and adopt different procedures. Simulation data are used to compare the performance of these three approaches in detecting the sources of measurement inequivalence. For this purpose, the authors simulated Likert-type data using two nonlinear models, one with categorical and one with continuous latent variables. Inequivalence was set up in the slope parameters (loadings) as well as in the item intercept parameters in a form resembling agreement and extreme response styles. Results indicate that the item response theory and latent class factor models can relatively accurately detect and locate inequivalence in the intercept and slope parameters both at the scale and the item levels. Confirmatory factor analysis performs well when inequivalence is located in the slope parameters but wrongfully indicates inequivalence in the slope parameters when inequivalence is located in the intercept parameters. Influences of sample size, number of inequivalent items in a scale, and model fit criteria on the performance of the three methods are also analyzed.
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Differential item functioning (DIF) occurs when an item on a test, questionnaire, or interview has different measurement properties for one group of people versus another. One way to test items with ...ordinal response scales for DIF is likelihood ratio (LR) testing using item response theory (IRT), or IRT-LR-DIF. Despite the various advantages of IRT-LR-DIF, one disadvantage is that the latent variable is usually assumed to be normally distributed. If this normality assumption is violated, nonparametric alternatives such as the Mantel test, generalized Mantel—Haenszel (GMH) test, and poly-SIBTEST may be preferable. Simulations were carried out to compare IRT-LR-DIF to poly-SIBTEST and the GMH and Mantel tests when the latent density is nonnormal for both groups but presumed normal for IRT-LR-DIF. Results indicated that latent nonnormality detrimentally affected all three procedures, but IRT-LR-DIF was surprisingly more robust to latent nonnormality than all of the nonparametric approaches.
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El incremento de estudios exploratorios y confirmatorios en psicometría debido al avance tecnológico obliga a revisar su metodología. Generalmente estos estudios utilizan el coeficiente de ...correlación r de Pearson, diseñado para variables continuas y extendido posteriormente a las categóricas (dicotómicas o politómicas). Los paquetes estadísticos actuales permiten aplicar procedimientos robustos ideados específicamente para variables categóricas, entre los que se destacan las correlaciones tetracóricas y policóricas, cuya relevancia metodológica radica en que la mayoría de las escalas psicométricas se compone de reactivos dicotómicos y politómicos (principalmente formatos Likert). El presente trabajo expone en primer lugar particularidades vinculadas al uso de estos estadísticos, softwares que facilitan su ejecución, problemas asociados a su aplicación y posibles soluciones a los mismos. En segundo término se ejemplifican ambas metodologías tanto en análisis factorial exploratorio como confirmatorio.
Item bias is a major threat to measurement validity. Methods for detecting differential item functioning (DIF) are now commonly used to identify potentially biased items. DIF detection methods for ...dichotomous items are well developed, but those for ordinal items are less well developed. In this article, the authors compare four methods for detecting DIF in ordinal items: the Mantel, generalized Mantel-Haenszel (GMH), logistic discriminant function analysis (LDFA), and unconstrained cumulative logits ordinal logistic regression (UCLOLR). Factors varied include type of DIF, group ability differences, studied item discrimination, skewness in ability distributions, and sample size ratio. All procedures had good Type I error control as well as high power for detecting uniform DIF. However, the Mantel could not detect nonuniform DIF, and the LDFA also performed poorly in detecting nonuniform DIF, particularly when item discrimination was high. The UCLOLR and GMH performed extremely well under conditions simulated in this study. Implications for research and practice are discussed.
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A full-information maximum likelihood method for fitting a multidimensional latent variable model to a set of ordinal observed variables is discussed. This method is an implementation of a general ...class of models for ordinal variables, and for regression models with one ordinal dependent variable and all explanatory variables observed. Estimation of the model, scoring of persons on the latent dimensions, and the goodness-of-fit of the model are also discussed. The method is applied to an example dataset concerning attitudes toward technology.
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Three distinctive methods of assessing measurement equivalence of ordinal items, namely, confirmatory factor analysis, differential item functioning using item response theory, and latent class ...factor analysis, make different modeling assumptions and adopt different procedures. Simulation data are used to compare the performance of these three approaches in detecting the sources of measurement inequivalence. For this purpose, the authors simulated Likert-type data using two nonlinear models, one with categorical and one with continuous latent variables. Inequivalence was set up in the slope parameters (loadings) as well as in the item intercept parameters in a form resembling agreement and extreme response styles. Results indicate that the item response theory and latent class factor models can relatively accurately detect and locate inequivalence in the intercept and slope parameters both at the scale and the item levels. Confirmatory factor analysis performs well when inequivalence is located in the slope parameters but wrongfully indicates inequivalence in the slope parameters when inequivalence is located in the intercept parameters. Influences of sample size, number of inequivalent items in a scale, and model fit criteria on the performance of the three methods are also analyzed.
The purpose of this study is to develop and evaluate two diagnostic classification models (DCMs) for scoring ordinal item data. We first applied the proposed models to an operational dataset and ...compared their performance to an epitome of current polytomous DCMs in which the ordered data structure is ignored. Findings suggest that the much more parsimonious models that we proposed performed similarly to the current polytomous DCMs and offered useful item-level information in addition to option-level information. We then performed a small simulation study using the applied study condition and demonstrated that the proposed models can provide unbiased parameter estimates and correctly classify individuals. In practice, the proposed models can accommodate much smaller sample sizes than current polytomous DCMs and thus prove useful in many small-scale testing scenarios.
Online consumer product ratings data are increasing rapidly. While most of the current graphical displays mainly represent the average ratings, Ho and Quinn proposed an easily interpretable graphical ...display based on an ordinal item response theory (IRT) model, which successfully accounts for systematic interrater differences. Conventionally, the discrimination parameters in IRT models are constrained to be positive, particularly in the modeling of scored data from educational tests. In this article, we use real-world ratings data to demonstrate that such a constraint can have a great impact on the parameter estimation. This impact on estimation was explained through rater behavior. We also discuss correlation among raters and assess the prediction accuracy for both the constrained and the unconstrained models. The results show that the unconstrained model performs better when a larger fraction of rater pairs exhibit negative correlations in ratings.
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