title: Modelling non-normal data: The relationship between the skew-normal factor model and the quadratic factor model.
abstract: Maximum likelihood estimation of the linear factor model for continuous items assumes normally distributed item scores. We consider deviations from normality by means of a skew-normally distributed factor model or a quadratic factor model. We show that the item distributions under a skew-normal factor are equivalent to those under a quadratic model up to third-order moments. The reverse only holds if the quadratic loadings are equal to each other and within certain bounds. We illustrate that observed data which follow any skew-normal factor model can be so well approximated with the quadratic factor model that the models are empirically indistinguishable, and that the reverse does not hold in general. The choice between the two models to account for deviations of normality is illustrated by an empirical example from clinical psychology.
authors.affiliation: Heymans Institute for Psychological Research, Department of Psychometrics and Statistics, University of Groningen, The Netherlands.
authors.forename: Iris A M
authors.initials: IA
authors.lastname: Smits
authors.affiliation: Heymans Institute for Psychological Research, Department of Psychometrics and Statistics, University of Groningen, The Netherlands.
authors.forename: Marieke E
authors.initials: ME
authors.lastname: Timmerman
authors.affiliation: Heymans Institute for Psychological Research, Department of Psychometrics and Statistics, University of Groningen, The Netherlands.
authors.forename: Alwin
authors.initials: A
authors.lastname: Stegeman
mesh_terms: D000328:Adult; D000465:Algorithms; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D005260:Female; D006801:Humans; D008297:Male; D001523:Mental Disorders / Q000175:diagnosis*; D015233:Models, Statistical; D017711:Nonlinear Dynamics; D011569:Psychiatric Status Rating Scales / Q000592:standards*; D011594:Psychometrics / Q000379:methods; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D016008:Statistical Distributions
keywords: non-normality; nonlinear factor model; skew-normal distribution; skew-normal factor model