Influence-Based Diagnostics for Finite Mixture Models
Murray A. Jorgensen · Biometrics · 1990
SUMMARY In the fitting of finite mixtures of distributions to empirical data it is often felt necessary to exclude certain observations in order to achieve a satisfactory fit. This is particularly true of fisheries lengthfrequency data where the object is to model a discrete number of age classes by a mixture of normal components and the presence of outliers in the sample can have a large effect on the parameter estimates and the fit. This paper develops diagnostic tools to measure the effect of individual observations on the parameter estimates and the fit in order to make the data rejection decision of the data-analyst less ad hoc. Specifically, we show how to compute the parameter influence curves and introduce a statistic similar to Cook's distance used in regression diagnostics.