title: Robust model fitting for the non linear structural equation model under normal theory.
abstract: Structural equation modelling has been widely applied in behavioural, educational, medical, social, and psychological research. The classical maximum likelihood estimate is vulnerable to outliers and non-normal data. In this paper, a robust estimation method for the nonlinear structural equation model is proposed. This method gives more weight to data that are likely to occur based on the structure of the posited model, and effectively downweights the influence of outliers. An algorithm is proposed to obtain the robust estimator. Asymptotic properties of the proposed method are investigated, which include the asymptotic distribution of the estimator, and some statistics for hypothesis testing. Results from a simulation study and a real data example show that our procedure is effective.
authors.affiliation: Department of Statistics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong.
authors.forename: Ye-Mao
authors.initials: YM
authors.lastname: Xia
authors.forename: Xin-Yuan
authors.initials: XY
authors.lastname: Song
authors.forename: Sik-Yum
authors.initials: SY
authors.lastname: Lee
mesh_terms: D003627:Data Interpretation, Statistical; D005163:Factor Analysis, Statistical; D006801:Humans; D016013:Likelihood Functions; D008432:Mathematical Computing; D015233:Models, Statistical; D017711:Nonlinear Dynamics; D011584:Psychology / Q000706:statistics & numerical data*; D011594:Psychometrics / Q000706:statistics & numerical data; D012016:Reference Values; D012945:Social Values; D012984:Software; D013223:Statistics as Topic; D018709:Statistics, Nonparametric