A nonnormal look at polychoric correlations: modeling the change in correlations before and after discretization

Demirtaş, Hakan; Ahmadian, Robab; Atış, Sema; Can, Fatma Ezgi; Ercan, İlker

doi:10.1007/s00180-016-0653-7

Cited by 6 publications

(1 citation statement)

References 24 publications

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“…This intermediate correlation is then imposed on uncorrelated, standard-normal variates before they are transformed to non-normality via the third-order polynomial method, and that yields the full multivariate extension of this algorithm. The Fleishman (1978) method and its multivariate extension are by far the most widely used data-generating algorithms in the quantitative behavioural sciences and they have seen widespread use outside these fields as well, as can be seen in Demirtas (2016), Demirtas and Hedeker (2016), Demirtas, Ahmadian, Atis, Can, and Ercan (2016) and Demirtas and Vardar-Acar (2017). The third-order polynomial method is implemented in latent variable software packages such as EQS (Bentler, 1995), the lavaan R package (Rosseel, 2012), the simsem R package (Pornprasertmanit, Miller, & Schoemann, 2012) and the BinOrdNonNor R package (Demirtas, Wang, & Allozi, 2017).…”

Section: Introductionmentioning

confidence: 99%

On the solution multiplicity of the Fleishman method and its impact in simulation studies

Astivia

Zumbo

2018

Brit J Math & Statis

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The Fleishman third-order polynomial algorithm is one of the most-often used non-normal data-generating methods in Monte Carlo simulations. At the crux of the Fleishman method is the solution of a non-linear system of equations needed to obtain the constants to transform data from normality to non-normality. A rarely acknowledged fact in the literature is that the solution to this system is not unique, and it is currently unknown what influence the different types of solutions have on the computer-generated data. To address this issue, analytical and empirical investigations were conducted, aimed at documenting the impact that each solution type has on the design of computer simulations. In the first study, it was found that certain types of solutions generate data with different multivariate properties and wider coverage of the theoretical range spanned by population correlations. In the second study, it was found that previously published recommendations from Monte Carlo simulations could change if different types of solutions were used to generate the data. A mathematical description of the multiple solutions to the Fleishman polynomials is provided, as well as recommendations for users of this method.

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