Calvo-Alfaro, Adriana P.

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    Comparación de modelos de regresión semiparamétricos mixtos con distribución beta
    (2015-05) Calvo-Alfaro, Adriana P.; Macchiavelli, Raúl E.; College of Arts and Sciences - Sciences; Torres Saavedra, Pedro A.; Lorenzo González, Edgardo; Department of Mathematics; Ruiz Quiñones, Orlando E.
    Some studies generate data that are rates, proportions or probabilities, continuously restricted in the range (0, 1). The Beta regression allows to model this type of data and offers a number of advantages such as direct interpretation of results, since it is not necessary to use transformations, and the easy to model asymmetries because the distribution can take many forms if the scale and location parameters are changed. The semiparametric regression models provide an effective tool for modeling complex data structures, since the main feature is that they do not assume a specific shape for the regression function, the real purpose is to build it by using the observations for a better use of the collected information. The implementation of smooth techniques like splines in the beta regression modeling and random effects allows having a better regression curve approximation which generates more precise results. During the development of this work, three models of semiparametric regressions will be presented, and the matrices of design associated to the effects will be built by using splines. The conditional distribution from the variable of interest given the random effects is Beta and the random effects are assumed normally distributed; this Beta regression models are constructed by using the combination of B-splines in the fixed part; B-splines, P-splines or Radial Smoothing in the random part. By using simulations he chose the model that provides the better fit using Schwarz’s Criteria and the better predictive model using the Mean Integrated Absolute Error (MIAE). The obtained results are used in a study of disease severity of banana crops in Puerto Rico.