Generating Correlated, Non-normally Distributed Data Using a Non-linear Structural Model

Auerswald, Max; Moshagen, Morten

doi:10.1007/s11336-015-9468-7

Cited by 16 publications

(18 citation statements)

References 26 publications

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“…This is particularly noteworthy concerning the Hull method and the EKC, given that these methods explicitly assume a normal distribution (Braeken & van Assen, 2017; Lorenzo-Seva et al, 2011). SMT was the only extraction criterion that was adversely affected by non-normality in the latent variables in some conditions, consistent with evidence from confirmatory factor analysis (e.g., Auerswald & Moshagen, 2015; Foldnes & Grønneberg, 2015; Mair et al, 2012). In the present study, we only considered SMT using uncorrected ML-based χ 2 , so a natural extension is to investigate SMT under non-normality with appropriate corrections, such as the Satorra-Bentler correction (Satorra & Bentler, 1994).…”

Section: Discussionsupporting

confidence: 72%

“…Three types of distributions were used (normal, non-normal based on non-normal errors, non-normal based on non-normal latent factors). The two types of non-normal distributions were included because recent evidence suggests that the performance of factor-based models may vary depending on whether the non-normality in the observed variables arises from non-normal correlated variables (such as factors) or from non-normal independent variables (such as errors; Auerswald & Moshagen, 2015; Foldnes & Grønneberg, 2015; Mair, Satorra, & Bentler, 2012). Normally distributed data were generated using Cholesky decomposition.…”

Section: Methodsmentioning

confidence: 99%

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How to determine the number of factors to retain in exploratory factor analysis: A comparison of extraction methods under realistic conditions.

Auerswald¹,

Moshagen²

2019

Psychological Methods

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240

187

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Exploratory factor analyses are commonly used to determine the underlying factors of multiple observed variables. Many criteria have been suggested to determine how many factors should be retained. In this study, we present an extensive Monte Carlo simulation to investigate the performance of extraction criteria under varying sample sizes, numbers of indicators per factor, loading magnitudes, underlying multivariate distributions of observed variables, as well as how the performance of the extraction criteria are influenced by the presence of cross-loadings and minor factors for unidimensional, orthogonal, and correlated factor models. We compared several variants of traditional parallel analysis (PA), the Kaiser-Guttman Criterion, and sequential 2 model tests (SMT) with 4 recently suggested methods: revised PA, comparison data (CD), the Hull method, and the Empirical Kaiser Criterion (EKC). No single extraction criterion performed best for every factor model. In unidimensional and orthogonal models, traditional PA, EKC, and Hull consistently displayed high hit rates even in small samples. Models with correlated factors were more challenging, where CD and SMT outperformed other methods, especially for shorter scales. Whereas the presence of cross-loadings generally increased accuracy, non-normality had virtually no effect on most criteria. We suggest researchers use a combination of SMT and either Hull, the EKC, or traditional PA, because the number of factors was almost always correctly retrieved if those methods converged. When the results of this combination rule are inconclusive, traditional PA, CD, and the EKC performed comparatively well. However, disagreement also suggests that factors will be harder to detect, increasing sample size requirements to N Ն 500.

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Section: Discussionsupporting

confidence: 72%

Section: Methodsmentioning

confidence: 99%

How to determine the number of factors to retain in exploratory factor analysis: A comparison of extraction methods under realistic conditions.

Auerswald¹,

Moshagen²

2019

Psychological Methods

Self Cite

240

187

View full text Add to dashboard Cite

show abstract

“…Therefore, the user is given a choice to either simulate from theoretical distributions or from a particular dataset of interest. Auerswald and Moshagen (2015) as well as Mattson (1997) have considered the problem by restating it under a latent variable framework and inducing the non-normality through the latent variables. Methods like this would allow the users to more accurately control the distributional assumptions of latent variables, which could be of interest to researchers in Structural Equation Modelling or Item Response Theory.…”

Section: Alternative Approachesmentioning

confidence: 99%

Issues, problems and potential solutions when simulating continuous, non-normal data in the social sciences

Astivia¹

2020

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Computer simulations have become one of the most prominent tools for methodologists in the social sciences to evaluate the properties of their statistical techniques and to offer best practice recommendations. Amongst the many uses of computer simulations, evaluating the robustness of methods to their assumptions, particularly univariate or multivariate normality, is crucial to ensure the appropriateness of data analysis. In order to accomplish this, quantitative researchers need to be able to generate data where they have a degree of control over its non-normal properties. Even though great advances have been achieved in statistical theory and computational power, the task of simulating multivariate, non-normal data is not straightforward. There are inherent conceptual and mathematical complexities implied by the phrase "non-normality" which are not always reflected in the simulations studies conduced by social scientists. The present article attempts to offer a summary of some of the issues concerning the simulation of multivariate, non-normal data in the social sciences. An overview of common algorithms is presented as well as some of the characteristics and idiosyncrasies that implied in them which may exert undue influence in the results of simulation studies. A call is made to encourage the meta-scientific study of computer simulations in the social sciences in order to understand how simulation designs frame the teaching, usage and practice of statistical techniques within the social sciences.

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“…Qu, Liu and Zhang (2019) Therefore, the user is given a choice to either simulate from theoretical distributions or from a particular dataset of interest. Auerswald and Moshagen (2015) as well as Mattson (1997) In spite of these modern advances, the NORTA approaches in general (and the 3 rd…”

Section: Alternative Approachesmentioning

confidence: 99%

Issues, problems and potential solutions when simulating continuous, non-normal data in the social sciences

Olo¹

2019

Preprint

View full text Add to dashboard Cite

Computer simulations have become one of the most prominent tools for methodologists in the social sciences to evaluate the properties of their statistical techniques and to offer best practice recommendations. Amongst the many uses of computer simulations, evaluating the robustness of methods to their assumptions, particularly univariate or multivariate normality, is crucial to ensure the appropriateness of data analysis. In order to accomplish this, quantitative researchers need to be able to generate data where they have a degree of control over its non-normal properties. Even though great advances have been achieved in statistical theory and computational power, the task of simulating multivariate, non-normal data is not straightforward. There are inherent conceptual and mathematical complexities implied by the phrase ``non-normality'' which are not always reflected in the simulations studies conduced by social scientists. The present article attempts to offer a summary of some of the issues concerning the simulation of multivariate, non-normal data in the social sciences. An overview of common algorithms is presented as well as some of the characteristics and idiosyncrasies that implied in them which may exert undue influence in the results of simulation studies. A call is made to encourage the meta-scientific study of computer simulations in the social sciences in order to understand how simulation designs frame the teaching, usage and practice of statistical techniques within the social sciences.

show abstract

Generating Correlated, Non-normally Distributed Data Using a Non-linear Structural Model

Cited by 16 publications

References 26 publications

How to determine the number of factors to retain in exploratory factor analysis: A comparison of extraction methods under realistic conditions.

How to determine the number of factors to retain in exploratory factor analysis: A comparison of extraction methods under realistic conditions.

Issues, problems and potential solutions when simulating continuous, non-normal data in the social sciences

Issues, problems and potential solutions when simulating continuous, non-normal data in the social sciences

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