Resíduos desempenham um papel importante na verificação do ajuste do modelo e na idenfiticação de observações discrepantes e/ou influentes. Neste trabalho, estudamos duas classes de resíduos para os modelos de regressão gama inflacionados no zero (ZAGA) e gaussiana inversa inflacionados no zero (ZAIG). Essas classes de resíduos são uma função de um resíduo para o componente contínuo do modelo e da estimativa de máxima verossimilhança da probabilidade da observação assumir o valor zero. Estudos de simulação de Monte Carlo foram realizados para examinar as propriedades dessas classes de resíduos em ambos os modelos de regressão (ZAGA e ZAIG). Os resultados mostraram que um resíduo de uma dessas classes tem algumas propriedades semelhantes à da distribuição normal padrão nos modelos estudados. Além desse objetivo principal, descrevemos os modelos de regressão ZAGA e ZAIG, estudamos propriedades de alguns resíduos em modelos lineares generalizados com resposta gama e gaussiana inversa e discutimos outros aspectos de análise de diagnóstico nos modelos ZAGA e ZAIG. Para finalizar, foi feita uma aplicação com dados reais de fundos de investimentos, em que ajustamos o modelo ZAIG, para exemplificar os tópicos discutidos e mostrar a importância desses modelos e as vantagens de um dos resíduos estudados na análise de dados reais. / Residuals play an important role in checking model adequacy and in the identification of outliers and influential observations. In this paper, we studied two class of residuals for the zero adjusted gamma regression model (ZAGA) and the zero adjusted inverse Gaussian regression model (ZAIG). These classes of residuals are function of a residual for the continuous component of the model and the maximum likelihood estimate of the probability of the observation assuming the zero value. Monte Carlo simulation studies are performed to examine the properties of this class of residuals in both models (ZAGA and ZAIG). Results showed that a residual of one of these class has some similar properties to the standard normal distribution in the studied models. We also described ZAGA and ZAIG regression models, studied properties of some residuals in generalized linear models with response gamma and inverse Gaussian and discussed other aspects of diagnostic analysis in ZAGA and ZAIG models. To finsih,we presented a real data set application from invesment funds of Brazil. We fitted the ZAIG model to illustrate the topics discussed and showed the importance of these models and the advantages of one of the studied residuals in the analysis of real dataset.

Background: Shifting the healthcare payment system from a volume-based to a value-based model has been a significant effort to improve the quality of care and reduce healthcare costs in the US. In 2018, Massachusetts Medicaid launched Accountable Care Organizations (ACOs) as part of the effort. Constructing, assessing, and risk-adjusting quality measures are integral parts of the reform process. Methods: Using data from the MassHealth Data Warehouse (2016-2019), we assessed the loss of community tenure (CTloss) as a potential quality measure for patients with bipolar, schizophrenia, or other psychotic disorders (BSP). We evaluated various statistical models for predicting CTloss using deviance, Akaike information criterion, Vuong test, squared correlation and observed vs. expected (O/E) ratios. We also used logistic regression to investigate risk factors that impacted medication nonadherence, another quality measure for patients with bipolar disorders (BD). Results: Mean CTloss was 12.1 (±31.0 SD) days in the study population; it varied greatly across ACOs. For risk adjustment modeling, we recommended the zero-inflated Poisson or doubly augmented beta model. The O/E ratio ranged from 0.4 to 1.2, suggesting variation in quality, after adjusting for differences in patient characteristics for which ACOs served as reflected in E. Almost half (47.7%) of BD patients were nonadherent to second-generation antipsychotics. Patient demographics, medical and mental comorbidities, receiving institutional services like those from the Department of Mental Health, homelessness, and neighborhood socioeconomic stress impacted medication nonadherence. Conclusions: Valid quality measures are essential to value-based payment. Heterogeneity implies the need for risk adjustment. The search for a model type is driven by the non-standard distribution of CTloss.