Regressão Simplex aplicada a delineamentos de mistura e utilização do Algoritmo Boosting

In the composition of this work are present two parts. The first part contains the theory used. The second part contains the two articles. The first article examines two models of the class of generalized linear models for analyzing a mixture experiment, which studied the effect of different diets consist of fat, carbohydrate, and fiber on tumor expression in mammary glands of female rats, given by the ratio mice that had tumor expression in a particular diet. Mixture experiments are characterized by having the effect of collinearity and smaller sample size. In this sense, assuming normality for the answer to be maximized or minimized may be inadequate. Given this fact, the main characteristics of logistic regression and simplex models are addressed. The models were compared by the criteria of selection of models AIC, BIC and ICOMP, simulated envelope charts for residuals of adjusted models, odds ratios graphics and their respective confidence intervals for each mixture component. It was concluded that first article that the simplex regression model showed better quality of fit and narrowest confidence intervals for odds ratio. The second article presents the model Boosted Simplex Regression, the boosting version of the simplex regression model, as an alternative to increase the precision of confidence intervals for the odds ratio for each mixture component. For this, we used the Monte Carlo method for the construction of confidence intervals. Moreover, it is presented in an innovative way the envelope simulated chart for residuals of the adjusted model via boosting algorithm. It was concluded that the Boosted Simplex Regression model was adjusted successfully and confidence intervals for the odds ratio were accurate and lightly more precise than the its maximum likelihood version.

Componentes principais na elaboração de índices de provas de desempenho em bovinos

The principal component analysis assists the producers in making decision of which evaluated features must be maintained in performance tests indexes, according to the variation present in these animals evaluated. The objective in this study was to evaluate a set of characteristics measured in a performance test in semifeedlot cattle of the Simmental and Angus breeds, by means principal component analysis (PC), aim to identify the features that represent most of the phenotypic variation for preparation of indexes. It was used data from 39 Angus and 38 Simmental bulls from the Santa Éster farm, located in Silvianópolis - MG. The performance test period was from october 2014 to february 2015. The features evaluated in the test were: final weight (FW), average daily gain weight (GW), respiratory rate (RR), haircoat temperature (HT) and rectal (RT), hair number (HN), hair length (HL), hair thickness (HT), muscularity (MUSC), racial characteristics, angulation, reproductive and balance (BAL), height of the front and back, width and length of croup, body length, depth and heart girth, subcutaneous fat thickness and rump (FTR), loin eye area and marbling (MAR). It was used PRINCOMP from SAS program for procedure the PC analysis. It was found that of the 27 features evaluated, the first four PC for Simmental breed explained 74% total variation data. The four PC selected with the corresponding weighting coefficients formed the following index: (0.27 * FW) + (0.47 * MUSC) + (0.50 * HL) + (0.39 * HT). Since the characteristics related to the adaptability of great importance for the studied breed, it was decided to keep the index of evidence for the Angus breed, the feature hair number, because there is a feature that presented a great variability and occupied one of the first principal component. Thus, the Angus index was composed by five features, with 79% total variation data, resulting in the following formula: (0.26 * FW) + (0.33 * BAL) + (0.58 * MAR) - (0.43 * FTR) – (0.38 * HN). By the principal component analysis it was possible to minimize the features number to be evaluated on performance tests from that farm, making the animal selection rapidly and accurate.