Home > Research > Publications & Outputs > Not quite normal: Consequences of violating the...
View graph of relations

Not quite normal: Consequences of violating the assumption of normality with regression mixture models

Research output: Contribution to Journal/MagazineJournal articlepeer-review

Published

Standard

Not quite normal: Consequences of violating the assumption of normality with regression mixture models. / Van Horn, M. Lee; Smith, Jessalyn; Fagan, Abigail et al.
In: Structural Equation Modeling, Vol. 19, No. 2, 2012, p. 227-249.

Research output: Contribution to Journal/MagazineJournal articlepeer-review

Harvard

Van Horn, ML, Smith, J, Fagan, A, Jaki, T, Maysn, K, Hawkins, D, Feaster, D & Howe, G 2012, 'Not quite normal: Consequences of violating the assumption of normality with regression mixture models', Structural Equation Modeling, vol. 19, no. 2, pp. 227-249. https://doi.org/10.1080/10705511.2012.659622

APA

Van Horn, M. L., Smith, J., Fagan, A., Jaki, T., Maysn, K., Hawkins, D., Feaster, D., & Howe, G. (2012). Not quite normal: Consequences of violating the assumption of normality with regression mixture models. Structural Equation Modeling, 19(2), 227-249. https://doi.org/10.1080/10705511.2012.659622

Vancouver

Van Horn ML, Smith J, Fagan A, Jaki T, Maysn K, Hawkins D et al. Not quite normal: Consequences of violating the assumption of normality with regression mixture models. Structural Equation Modeling. 2012;19(2):227-249. doi: 10.1080/10705511.2012.659622

Author

Van Horn, M. Lee ; Smith, Jessalyn ; Fagan, Abigail et al. / Not quite normal: Consequences of violating the assumption of normality with regression mixture models. In: Structural Equation Modeling. 2012 ; Vol. 19, No. 2. pp. 227-249.

Bibtex

@article{95b9f24ecaed44f19e0f750f1ddcd20f,
title = "Not quite normal: Consequences of violating the assumption of normality with regression mixture models",
abstract = "Regression mixture models, which have only recently begun to be used in applied research, are a new approach for finding differential effects. This approach comes at the cost of the assumption that error terms are normally distributed within classes. This study uses Monte Carlo simulations to explore the effects of relatively minor violations of this assumption. The use of an ordered polytomous outcome is then examined as an alternative that makes somewhat weaker assumptions, and finally both approaches are demonstrated with an applied example looking at differences in the effects of family management on the highly skewed outcome of drug use. Results show that violating the assumption of normal errors results in systematic bias in both latent class enumeration and parameter estimates. Additional classes that reflect violations of distributional assumptions are found. Under some conditions it is possible to come to conclusions that are consistent with the effects in the population, but when errors are skewed in both classes the results typically no longer reflect even the pattern of effects in the population. The polytomous regression model performs better under all scenarios examined and comes to reasonable results with the highly skewed outcome in the applied example. We recommend that careful evaluation of model sensitivity to distributional assumptions be the norm when conducting regression mixture models.",
keywords = "regression mixtures, differential effects , moderation , distributional assumptions , latent class analysis",
author = "{Van Horn}, {M. Lee} and Jessalyn Smith and Abigail Fagan and Thomas Jaki and Katherine Maysn and D. Hawkins and Daniel Feaster and George Howe",
year = "2012",
doi = "10.1080/10705511.2012.659622",
language = "English",
volume = "19",
pages = "227--249",
journal = "Structural Equation Modeling",
issn = "1070-5511",
publisher = "Psychology Press Ltd",
number = "2",

}

RIS

TY - JOUR

T1 - Not quite normal: Consequences of violating the assumption of normality with regression mixture models

AU - Van Horn, M. Lee

AU - Smith, Jessalyn

AU - Fagan, Abigail

AU - Jaki, Thomas

AU - Maysn, Katherine

AU - Hawkins, D.

AU - Feaster, Daniel

AU - Howe, George

PY - 2012

Y1 - 2012

N2 - Regression mixture models, which have only recently begun to be used in applied research, are a new approach for finding differential effects. This approach comes at the cost of the assumption that error terms are normally distributed within classes. This study uses Monte Carlo simulations to explore the effects of relatively minor violations of this assumption. The use of an ordered polytomous outcome is then examined as an alternative that makes somewhat weaker assumptions, and finally both approaches are demonstrated with an applied example looking at differences in the effects of family management on the highly skewed outcome of drug use. Results show that violating the assumption of normal errors results in systematic bias in both latent class enumeration and parameter estimates. Additional classes that reflect violations of distributional assumptions are found. Under some conditions it is possible to come to conclusions that are consistent with the effects in the population, but when errors are skewed in both classes the results typically no longer reflect even the pattern of effects in the population. The polytomous regression model performs better under all scenarios examined and comes to reasonable results with the highly skewed outcome in the applied example. We recommend that careful evaluation of model sensitivity to distributional assumptions be the norm when conducting regression mixture models.

AB - Regression mixture models, which have only recently begun to be used in applied research, are a new approach for finding differential effects. This approach comes at the cost of the assumption that error terms are normally distributed within classes. This study uses Monte Carlo simulations to explore the effects of relatively minor violations of this assumption. The use of an ordered polytomous outcome is then examined as an alternative that makes somewhat weaker assumptions, and finally both approaches are demonstrated with an applied example looking at differences in the effects of family management on the highly skewed outcome of drug use. Results show that violating the assumption of normal errors results in systematic bias in both latent class enumeration and parameter estimates. Additional classes that reflect violations of distributional assumptions are found. Under some conditions it is possible to come to conclusions that are consistent with the effects in the population, but when errors are skewed in both classes the results typically no longer reflect even the pattern of effects in the population. The polytomous regression model performs better under all scenarios examined and comes to reasonable results with the highly skewed outcome in the applied example. We recommend that careful evaluation of model sensitivity to distributional assumptions be the norm when conducting regression mixture models.

KW - regression mixtures

KW - differential effects

KW - moderation

KW - distributional assumptions

KW - latent class analysis

U2 - 10.1080/10705511.2012.659622

DO - 10.1080/10705511.2012.659622

M3 - Journal article

VL - 19

SP - 227

EP - 249

JO - Structural Equation Modeling

JF - Structural Equation Modeling

SN - 1070-5511

IS - 2

ER -