RESUMO
In recent decades, the use of regression models with random effects has made great progress. Among these models' attractions is the flexibility to analyze correlated data. In various situations, the distribution of the response variable presents asymmetry or bimodality. In these cases, it is possible to use the normal regression with random effect at the intercept. In light of these contexts, i.e. the desire to analyze correlated data in the presence of bimodality or asymmetry, in this paper we propose a regression model with random effect at the intercept based onthe generalized inverse Gaussian distribution model with correlated data. The maximum likelihood is adopted to estimate the parameters and various simulations are performed for correlated data. A type of residuals for the new regression is proposed whose empirical distribution is close to normal. The versatility of the new regression is demonstrated by estimating the average price per hectare of bare land in 10 municipalities in the state of São Paulo (Brazil). In this context, various databases are constantly emerging, requiring flexible modeling. Thus, it is likely to be of interest to data analysts, and can make a good contribution to the statistical literature.
RESUMO
We propose a new continuous distribution in the interval ( 0 , 1 ) based on the generalized odd log-logistic-G family, whose density function can be symmetrical, asymmetric, unimodal and bimodal. The new model is implemented using the gamlss packages in R. We propose an extended regression based on this distribution which includes as sub-models some important regressions. We employ a frequentist and Bayesian analysis to estimate the parameters and adopt the non-parametric and parametric bootstrap methods to obtain better efficiency of the estimators. Some simulations are conducted to verify the empirical distribution of the maximum likelihood estimators. We compare the empirical distribution of the quantile residuals with the standard normal distribution. The extended regression can give more realistic fits than other regressions in the analysis of proportional data.
RESUMO
We define the odd log-logistic exponential Gaussian regression with two systematic components, which extends the heteroscedastic Gaussian regression and it is suitable for bimodal data quite common in the agriculture area. We estimate the parameters by the method of maximum likelihood. Some simulations indicate that the maximum-likelihood estimators are accurate. The model assumptions are checked through case deletion and quantile residuals. The usefulness of the new regression model is illustrated by means of three real data sets in different areas of agriculture, where the data present bimodality.