A comparison of some methodologies for the factor analysis of non‐normal Likert variables: A note on the size of the model

Abstract

This paper expands on a recent study by Muthen & Kaplan (1985) by examining the impact of non‐normal Likert variables on testing and estimation in factor analysis for models of various size. Normal theory GLS and the recently developed ADF estimator are compared for six cases of non‐normality, two sample sizes, and four models of increasing size in a Monte Carlo framework with a large number of replications. Results show that GLS and ADF chi‐square tests are increasingly sensitive to non‐normality when the size of the model increases. No parameter estimate bias was observed for GLS and only slight parameter bias was found for ADF. A downward bias in estimated standard errors was found for GLS which remains constant across model size. For ADF, a downward bias in estimated standard errors was also found which became increasingly worse with the size of the model.

Development and psychometric properties of the Birth Satisfaction Scale-Revised (BSS-R)

“…The robustness of parametric tests against violations of the fundamental parametric assumptions (Martin and Thompson, 2000) have resulted in the contemporary use of ordinal or ordered categorical data, which represents the common reality of questionnaire data, with these statistical techniques (Colman et al, 1997;Friedrich et al, 2011;Kind and Barmby, 2011;Shulruf et al, 2008). However, data exhibiting significant deviation from the normal distribution assumption can lead to an erroneous outcome of a statistical analysis based on assumed parametric acceptable data distributional characteristic and consequently, an incorrect and potentially misleading interpretation of statistical findings (Flora and Curran, 2004;Lubke and Muthen, 2004;Martin and Thompson, 2000;Muthen and Kaplan, 1992). Therefore, each of the BSS items distributional characteristics were examined in detail and evaluated to determine deviation from assumed normality which could have a deleterious impact on CFA and SEM.…”

The Need for Orientation Towards News Media: Revising and Validating a Classic Concept

“…The remedy to this problem is the use of alternative estimation procedures such as the asymptotically distribution free (ADF) estimation. However, ADF estimation requires large sample sizes to produce stable estimates (Muthén & Kaplan, 1992). Several authors recommend a sample size of at least 1,000 cases for the adequate performance of the ADF-based χ 2 -statistic (Wegener & Fabrigar, 2000, p. 422;West et al, 1995, p. 68).…”

Construct and content validity of the Greek version of the Birth Satisfaction Scale (G-BSS)

“…The robustness of parametric tests (including CFA and SEM) against violations of the fundamental parametric assumptions (Martin & Thompson, 2000) have resulted in the contemporary use of ordinal or ordered categorical data, which represents the common reality of questionnaire data, with these statistical techniques (Friedrich et al, 2011;Kind & Barmby, 2011;Shulruf et al, 2004). However, data exhibiting significant deviation from the normal distribution assumption can lead to an erroneous outcome of a statistical analysis based on assumed parametric acceptable data distributional characteristic and consequently, an incorrect and potentially misleading interpretation of statistical findings (Flora & Curran, 2004;Lubke & Muthen, 2004;Martin & Thompson, 2000;Muthen & Kaplan, 1992). Skew and kurtosis characteristics of each item were examined and those exhibiting any significant deviation from normality were rejected from the 30-item-G-BSS-LF item pool prior to further statistical analysis based on normality assumptions.…”