Ordinal Measures in Multiple Indicator Models: A Simulation Study of Categorization Error

Johnson, David R.; Creech, James C.

doi:10.2307/2095231

Cited by 399 publications

(231 citation statements)

References 11 publications

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“…Johnson and Creech (1983) have noted that variability in parameter estimates is quite small with five or more response categories in the model. In practice, empirical researchers have suggested using MLR in ordinal CFA or CFA-based models (e.g., multiple-indicator multiple-cause models, or measurement invariance) when the number of response categories for each item was equal to or greater than five (e.g., Raykov, 2012;Rigdon, 1998, and the references therein).…”

Section: Present Studymentioning

confidence: 99%

Confirmatory factor analysis with ordinal data: Comparing robust maximum likelihood and diagonally weighted least squares

2015

Behav Res

1,968

1,162

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In confirmatory factor analysis (CFA), the use of maximum likelihood (ML) assumes that the observed indicators follow a continuous and multivariate normal distribution, which is not appropriate for ordinal observed variables. Robust ML (MLR) has been introduced into CFA models when this normality assumption is slightly or moderately violated. Diagonally weighted least squares (WLSMV), on the other hand, is specifically designed for ordinal data. Although WLSMV makes no distributional assumptions about the observed variables, a normal latent distribution underlying each observed categorical variable is instead assumed. A Monte Carlo simulation was carried out to compare the effects of different configurations of latent response distributions, numbers of categories, and sample sizes on model parameter estimates, standard errors, and chi-square test statistics in a correlated two-factor model. The results showed that WLSM V was less biased and more accurate than MLR in estimating the factor loadings across nearly every condition. However, WLSMV yielded moderate overestimation of the interfactor correlations when the sample size was small or/and when the latent distributions were moderately nonnormal. With respect to standard error estimates of the factor loadings and the interfactor correlations, MLR outperformed WLSMV when the latent distributions were nonnormal with a small sample size of N = 200. Finally, the proposed model tended to be over-rejected by chi-square test statistics under both MLR and WLSMV in the condition of small sample size N = 200.

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Section: Present Studymentioning

confidence: 99%

Confirmatory factor analysis with ordinal data: Comparing robust maximum likelihood and diagonally weighted least squares

2015

Behav Res

1,968

1,162

View full text Add to dashboard Cite

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“…A este respecto, Jöreskog y Sörbom (1996a) proponen, como alternativa al uso de correlaciones de Pearson, recurrir a correlaciones policóricas. Estas permiten superar los problemas que conllevan su uso, ya analizados por Johnson y Creech (1983) y O'Brien (1985 y tratados posteriormente en diferentes estudios (e.g., Coenders y Saris, 1995;Holgado et al, 2010).…”

Section: Introductionunclassified

Análisis factorial confirmatorio. Recomendaciones sobre mínimos cuadrados no ponderados en función del error Tipo I de Ji-Cuadrado y RMSEA

et al. 2015

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Resumen En Psicología, para obtener evidencias sobre validez de constructo mediante Análisis Factorial Confirmatorio es habitual trabajar con variables ordinales que presentan asimetría. En este estudio de simulación se analiza el comportamiento del método de Mínimos Cuadrados no Ponderados (ULS) en escalas tipo Likert con base en los índices χ2 de razón de verosimilitud (C2) y RMSEA. Para ello, se han manipulado cuatro factores experimentales: el número de factores o dimensiones (2, 3, 4, 5, 6), número de puntos de respuesta (3, 4, 5, 6), grado de asimetría de la distribución de respuestas (simétrica, asimétrica moderada y severa) y tamaño muestral (100, 150, 250, 450, 650, 850) de los modelos simulados. Según los principales resultados, el índice C2 muestra siempre un error Tipo I mayor que RMSEA, con independencia de los factores experimentales analizados. Finalmente, se discuten diferentes alternativas de acción y se presentan futuras líneas de investigación. AbstractIn order to obtain evidences about construct validity through Confirmatory Factor Analysis in Social Sciences, working with skewed ordinal variables has been usual. In this simulation study the performance of Unweighted Least Squares (ULS) method in Likert scales according to Likelihood Ratio Test (C2) and RMSEA indices is analysed through Type I error. For this purpose, four experimental factors have been manipulated: the number of factors or dimensions (2, 3, 4, 5, 6), the number of response points (3, 4, 5, 6), the degree of skewness of the responses distribution (symmetric, moderately and severely asymmetric) and the sample size (100, 150, 250, 450, 650, 850) of the simulated models. According to the main results, C2 index always shows a bigger Type I error than RMSEA, regardless of the experimental factors analysed. Finally, different action alternatives are discussed and future research lines are presented.

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“…For instance, Bollen and Barb [2] show in a simulation study that if bivariate normal variables are categorized into at least five response categories, the differences between the correlation between the original variables and the correlation of the categorized variables is small (see Categorizing Data). Johnson and Creech [7] show that this also holds for parameter estimates and model fit. However, when the number of categories is smaller than five, the distortion becomes sizable.…”

Section: Dichotomous and Ordinal Datamentioning

confidence: 82%

Multilevel and SEM Approaches to Growth Curve Modeling

Hox

Stoel

2014

Wiley StatsRef: Statistics Reference Online

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Growth curve models are used to model development explicitly as a function of time. Two techniques are commonly used to construct and analyze growth curve models: structural equation modeling, with distinct measurement occasions represented by separate variables, and multilevel regression modeling, with different measurement occasions represented as nested within individuals. Both approaches are essentially the same, but they differ in the way they can be extended into models that are more complex. An example is given, and estimation methods and software are briefly discussed.

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Ordinal Measures in Multiple Indicator Models: A Simulation Study of Categorization Error

Cited by 399 publications

References 11 publications

Confirmatory factor analysis with ordinal data: Comparing robust maximum likelihood and diagonally weighted least squares

Confirmatory factor analysis with ordinal data: Comparing robust maximum likelihood and diagonally weighted least squares

Análisis factorial confirmatorio. Recomendaciones sobre mínimos cuadrados no ponderados en función del error Tipo I de Ji-Cuadrado y RMSEA

Multilevel and SEM Approaches to Growth Curve Modeling

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