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.

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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).

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Objective: We describe the implementation and evaluation of an integrated, stepped care model aimed to identify and address the concerns of adolescents with type 1 diabetes (T1D) associated with diabetes-related quality of life (DRQoL), emotional wellbeing, and depression. Research Design and Methods: The care model with 4 steps: (1) Systematic identification and discussion of concerns salient to adolescents; (2) Secondary screening for depressive symptoms when indicated; (3) Developing collaborative treatment plans with joint physical and mental health goals; and (4) Psychiatric assessment and embedded mental health treatment; was implemented into an ambulatory pediatric diabetes clinic and evaluated using quantitative and qualitative methods.Results: There were 236 adolescents (aged 13-18 years) with T1D that were enrolled in the care model. On average adolescents identified three concerns associated with their DRQoL and 25% indicated low emotional well-being. Fifteen adolescents received a psychiatric assessment and embedded mental health treatment.Both adolescents and caregivers were appreciative of a broader, more holistic approach to their diabetes care and to the greater focus of the care model on adolescents, who were encouraged to self-direct the conversation. Parents also appreciated the extra level of support and the ability to receive mental health care for their adolescents from their own diabetes care team. Conclusion:The initial findings from this project indicate the acceptability and, to limited extent, the feasibility of an integrated stepped care model embedded in an ambulatory pediatric diabetes clinic led by an interdisciplinary care team. The care model facilitated the identification and discussion of concerns salient to youth and provided a more holistic approach.

A new approach for the estimation and the validation of a Structural Equation Model with a formative-reflective scheme is presented. The basis of the paper is a proposal for overcoming a potential deficiency of PLS Path Modeling. In the PLS approach the reflective scheme assumed for the endogenous latent variables is inverted; moreover, the model errors are not explicitly taken into account for the estimation of the endogenous latent variables. The proposed approach utilizes all the relevant information in the formative manifest variables providing solutions which respect the causal structure of the model. The estimation procedure is based on the optimization of the redundancy criterion. The new approach, entitled Redundancy Analysis approach to Path Modeling is compared with both traditional PLS Path Modeling and LISREL methodology, on the basis of real and simulated data.

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