Pressuposto da normalidade multivariada para o teste de razão de verossimilhança entre dois grupos de caracteres de mamoneira

Abstract

The likelihood ratio test for independence between two groups of variables allows us to identify whether there is a dependency relationship between two groups of variables, ie, if the covariance between the two groups are zero. This test assumes normality multivariate data, which limits its application, in many studies of agronomic area, times when you need use, for example, the canonical correlation analysis. The objective of this study is to evaluate the type I error and power of the likelihood ratio test (LRT) for independence between two groups of variables in different scenarios, consisting of combinations of: sample sizes 16, 40 number of combinations of two variables groups, and nine degrees of correlation between variables in matrices (for power); multivariate normal distribution under normal and contaminated, as well as compare the different scenarios, two formulas for calculating the test statistic. Thus, were evaluated the effect of 640 and 5760 scenarios on rates of type I error and power, respectively, in each one of probability distributions and formulas. The assessment of performance of LRT was performed through computational simulation by Monte Carlo method, using 2000 simulations in each of the scenarios generated. In multivariate normal situation: when the number of variables is large (p = 24), the LRT for independence between two groups of variables, controls the type I error rates and has high power in sample sizes greater than 100 and 500, with use of formulas for small and large samples, respectively; and, for sample sizes small (n = 25, 30 and 50), the test presents good performance, provided that, the number of variables does not exceed to 12; and, the formula chosen, whether for small samples. Under contaminated multivariate normal distribution, the LRT for independence between two groups of variables have high values of power, but is not robust, because it has high rates of type I error in any scenario evaluated.