A random effect regression based on the odd log-logistic generalized inverse Gaussian distribution

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 Sao 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.

Automated summary

This paper proposes a regression model with random effect at the intercept based on the generalized inverse Gaussian distribution model for analyzing correlated data. The versatility of the model is demonstrated by estimating the average price per hectare of bare land in municipalities in Sao Paulo, Brazil.