Bayesian non-linear regression models with skew-elliptical errors: Applications to the classification of longitudinal profiles |
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| Affiliation: | 1. St. Mary''s University, United States;2. University of Texas at San Antonio, United States;3. SeaWorld San Antonio, United States;4. University of Alaska Fairbanks, United States;5. University of Washington''s Joint Institute for the Study of the Atmosphere and Ocean, National Oceanic and Atmospheric Association, Alaska Fisheries Science Center''s Marine Mammal Laboratory, United States;1. Department of Psychology, University of Lethbridge, Lethbridge, Canada;2. Odum School of Ecology, University of Georgia, Athens, USA;3. Department of Pathobiological Sciences and School of Veterinary Medicine, University of Wisconsin-Madison, Madison, USA;4. Department of Geography, McGill University, Montreal, Canada;5. Department of Anthropology and McGill School of Environment, McGill University, Montreal, Canada;6. Wildlife Conservation Society, Bronx, NY, USA;1. Laboratory of Metrology of Nuclear Irradiations, V.G. Khlopin Radium Institute, Saint-Petersburg, 194021, Russia;2. Laboratory of Theoretical Chemistry, V.G. Khlopin Radium Institute, Saint-Petersburg, 194021, Russia;3. Department of Radiochemistry, Saint-Petersburg State University, Saint-Petersburg, 199034, Russia |
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| Abstract: | Typically, the fundamental assumption in non-linear regression models is the normality of the errors. Even though this model offers great flexibility for modeling these effects, it suffers from the same lack of robustness against departures from distributional assumptions as other statistical models based on the Gaussian distribution. It is of practical interest, therefore, to study non-linear models which are less sensitive to departures from normality, as well as related assumptions. Thus the current methods proposed for linear regression models need to be extended to non-linear regression models. This paper discusses non-linear regression models for longitudinal data with errors that follow a skew-elliptical distribution. Additionally, we discuss Bayesian statistical methods for the classification of observations into two or more groups based on skew-models for non-linear longitudinal profiles. Parameter estimation for a discriminant model that classifies individuals into distinct predefined groups or populations uses appropriate posterior simulation schemes. The methods are illustrated with data from a study involving 173 pregnant women. The main objective in this study is to predict normal versus abnormal pregnancy outcomes from beta human chorionic gonadotropin data available at early stages of pregnancy. |
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