In 2018, the last year of my undergraduate, I and my dear friend Wesley Furriel submitted an article in Brazilian Journal of Biometrics that was published in Vol. 37, No. 3 of 2019. This work, we conducted a empirical study to investigate the relationship between the Municipal Human Development Index (MHDI) of 2010 and some socioeconomic and spacial variables. To avoid potentials redundant relationships, we have selected variables that are not used in the construction of MHDI, but can enable explore its consonance with other measures that demonstrate aspects of cities social reality, such as, inequality, child vulnerability, housing and region.

To understand the relationship of MHDI with variables that measure the city reality is crucial for the public Brazilian administration. For instance, Kieling (2014) studied 14 public politics performed between 1998 and 2013 that evaluate how the MHDI is used, either as eligibility criterion for cities recieve a program, resource, public funding or as be part of drafting of bills.

The MHDI data as well as the other variables used are available online at Atlas do Desenvolvimento Humano.

By definition the MHDI is on unit interval, \((0, 1)\). Values near to \(1\) greater the human development of the city. For this type of variable, the usual linear regression model under Normal assumption is not suitable. This motivate us to perform a comparison between the Beta and Simplex regression models. The evaluation was achieved by information criteria, \(AIC\), \(BIC\), and Voung test, and also by means of residual analysis.

In conclusion, both models shows satisfactory fit to the data with a slight advantage for the Beta regression model. Furthermore, both models provide same conclusion in respect to the estimate effects of the explanatory variables on the MHDI. To be more specific, I highlight the following

• Cities with higher child vulnerability have lesser development. The same effect was also identified for cities with higher proportion of households with inadequate water supply and sewer.

• Cities that have a high Gini index, therefore have higher inequality in income distribution, tend to be higher MHDI.

• With respect to Brazilian regions, when compare to the South, with the exception of the Southwest, all other regions (Midwest, North, Northeast) present less MHDI.

It is noteworthy that the data source used in this studied refer to the 2010, and were collected during demographic census, which takes place every 10 years, but because Brazil has a stupid, genocide and fascist president our 2020 census was neglected and did not occur, hence we are not able to provide recent information of MHDI and its relationship with the variables in this study.