Cluster Weighted Modeling (CWM) is a mixture approach regarding the modelisation of the joint probability of data coming from a heterogeneous population. Under Gaussian assumptions, we investigate statistical properties of CWM from both the theoretical and numerical point of view; in particular, we show that CWM includes as special cases mixtures of distributions and mixtures of regressions. Further, we introduce CWM based on Student-t distributions providing more robust fitting for groups of observations with longer than normal tails or atypical observations. Theoretical results are illustrated using some empirical studies, considering both real and simulated data.
A novel family of twelve mixture models with random covariates, nested in the linear t cluster-weighted model (CWM), is introduced for model-based clustering. The linear t CWM was recently presented as a robust alternative to the better known linear Gaussian CWM. The proposed family of models provides a unified framework that also includes the linear Gaussian CWM as a special case. Maximum likelihood parameter estimation is carried out within the EM framework, and both the BIC and the ICL are used for model selection. A simple and effective hierarchical random initialization is also proposed for the EM algorithm. The novel model-based clustering technique is illustrated in some applications to real data. Finally, a simulation study for evaluating the performance of the BIC and the ICL is presented.
Background Visual acuity alone has limitations in assessing a patient's appropriateness and prioritization for cataract surgery. Several tools, including the Catquest-9SF questionnaire and the electronic cataract appropriateness and priority system (eCAPS) have been developed to evaluate patients-reported visual function as related to day-today tasks. The aim of this study was to validate Catquest-9SF and eCAPS in a Canadian population and propose a shorter version of each, in an attempt to extend their applicability in clinical practice. Methods The English translation of the Swedish Catquest-9SF and eCAPS were self-administered separately in pre-operative patients in tertiary care in Peel region, Ontario. Rasch analysis was used to validate both scales and assess their psychometric properties, such as category threshold order, item fit, unidimensionality, precision, targeting, and differential item functioning. Results A total of 313 cataract patients (mean age = 69.1, 56.5% female) completed the Catquest-9SF and eCAPS. Catquest-9SF had ordered response thresholds, adequate precision (person separation index = 2.09, person reliability = 0.81), unidimensionality and no misfits (infit range 0.75-1.35, outfit range 0.83-1.36). There mean for patients was equal to-1.43 (lower than the mean for items which is set automatically at zero), meaning that tasks were relatively easy for respondent ability. eCAPS had 3 items that misfit the Rasch model and were excluded (infit range 0.82-1.30, outfit range 0.75-1.36). Precision was inadequate (person separation index = 0.19, person reliability = 0.04). 78.8% of subjects scored�9 (answered that they had no issues for most questions).
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.