A comparison of some methodologies for the factor analysis of non‐normal Likert variables

Abstract

This paper considers the problem of applying factor analysis to non‐normal categorical variables. A Monte Carlo study is conducted where five prototypical cases of non‐normal variables are generated. Two normal theory estimators, ML and GLS, are compared to Browne's (1982) ADF estimator. A categorical variable methodology (CVM) estimator of Muthén (1984) is also considered for the most severely skewed case. Results show that ML and GLS chi‐square tests are quite robust but obtain too large values for variables that arc severely skewed and kurtotic. ADF, however, performs well.Parameter estimate bias appears non‐existent for all estimators. Results also show that ML and GLS estimated standard errors are biased downward. For ADF no such standard error bias was found. The CVM estimator appears to work well when applied to severely skewed variables that had been dichotomized. ML and GLS results for a kurtosis only case showed no distortion of chi‐square or parameter estimates and only a slight downward bias in estimated standard errors. The results are compared to those of other related studies.

Validation of the Organizational Culture Assessment Instrument: An Application of the Korean Version

“…Third, no statistically significant relationship between cultural types located in the two opposite quadrants (i.e., between clan and market and between adhocracy and hierarchy) was specified. According to Muthén and Kaplan (1985), Maximum Likelihood (ML) function is quite robust for observed categorical variables with skewnesses and kurtoses from -1.0 and +1.0. Because the observed categorical variables were close to normal with relatively small skewnesses and kurtoses (less than ± 0.5), the ML method was employed for estimation.…”

Dimensionalidade da escala de estresse percebido (Perceived Stress Scale, PSS-10) em uma amostra de professores

“…Considerando o nível de mensuração ordinal das variáveis e a violação do pressuposto de normalidade multivariada dos dados (Mardia = 149,040, p ≤ 0,05;Mardia, 1970), foi conduzida uma análise fatorial exploratória robusta a partir da matriz de correlações policóricas dos itens da PSS-10 (Holgado-Tello, Chacón-Moscoso, Barbero-García, & Vila-Abad, 2010; Muthén & Kaplan, 1985), com método de extração minimum rank factor analysis (MRFA; Shapiro & ten Berge, 2002). O método de extração MRFA minimiza a variância comum residual no processo de extração dos fatores, e possibilita a interpretação da proporção da variância comum explicada pelos fatores retidos (Lorenzo-Seva & Ferrando, 2006).…”

Exploring health-related quality of life determinants of New Zealand sole mothers

“…Prior to any analysis, scale summary scores were scrutinised to ensure that assumptions of parametric tests were met. Across all items, skewness and kurtosis values were generally within the commonly accepted range of −1.00 to 1.00 (Muthén & Kaplan 1985). Thirteen items across the PSS, ISEL and WHOQOL-BREF were marginally over these parameters for kurtosis (maximum −1.35), and only one item exceeded this range for skewness (−1.04).…”