Tatiene Correia de Souza

Inference Under Heteroskedasticity and Leveraged Data

We evaluate the finite-sample behavior of different heteros-ke-das-ticity-consistent covariance matrix estimators, under both constant and unequal error variances. We consider the estimator proposed by Halbert White (HC0), and also its variants known as HC2, HC3, and HC4; the latter was recently proposed by Cribari-Neto (2004). We propose a new covariance matrix estimator: HC5. It is the first consistent estimator to explicitly take into account the effect that the maximal leverage has on the associated inference. Our numerical results show that quasi-t inference based on HC5 is typically more reliable than inference based on other covariance matrix estimators.

Testing inference in variable dispersion beta regressions

The class of beta regression models proposed by Ferrari and Cribari-Neto [Beta regression for modelling rates and proportions, Journal of Applied Statistics 31 (2004), pp. 799–815] is useful for modelling data that assume values in the standard unit interval (0, 1). The dependent variable relates to a linear predictor that includes regressors and unknown parameters through a link function. The model is also indexed by a precision parameter, which is typically taken to be constant for all observations. Some authors have used, however, variable dispersion beta regression models, i.e., models that include a regression submodel for the precision parameter. In this paper, we show how to perform testing inference on the parameters that index the mean submodel without having to model the data precision. This strategy is useful as it is typically harder to model dispersion effects than mean effects. The proposed inference procedure is accurate even under variable dispersion. We present the results of extensive Monte Carlo simulations where our testing strategy is contrasted to that in which the practitioner models the underlying dispersion and then performs testing inference. An empirical application that uses real (not simulated) data is also presented and discussed.

Heteroskedasticity-Robust Inference in Linear Regressions

The assumption that all errors share the same variance (homoskedasticity) is commonly violated in empirical analyses carried out using the linear regression model. A widely adopted modeling strategy is to perform point estimation by ordinary least squares and then perform testing inference based on these point estimators and heteroskedasticity-consistent standard errors. These tests, however, tend to be size-distorted when the sample size is small and the data contain atypical observations. Furno (1996) suggested performing point estimation using a weighted least squares mechanism in order to attenuate the effect of leverage points on the associated inference. In this article, we follow up on her proposal and define heteroskedasticity-consistent covariance matrix estimators based on residuals obtained using robust estimation methods. We report Monte Carlo simulation results (size and power) on the finite sample performance of different heteroskedasticity-robust tests. Overall, the results favor inference based on HC0 tests constructed using robust residuals.

Modelagem da Proporção de Obesos nos Estados Unidos Utilizando o Modelo de Regressão Beta

Neste artigo tivemos como objetivo modelar a proporcao de adultos obesos nos estados dos Estados Unidos considerando os individuos que apresentaram IMC (Indice de Massa Corporal) maior ou igual a 30.0 kg/m2. Utilizamos o modelo de regressao beta com finalidade de explicar a proporcao de adultos obesos, uma vez que os dados apresentam assimetria e estao restritos ao intervalo (0,1). Os resultados mostraram que a falta de atividade fisica, o pouco consumo de vegetais por dia, o habito de fumar e as taxas de inseguranca alimentar nos estados, apresentam um efeito positivo no aumento da proporcao media de adultos obesos, por outro lado as taxas de desemprego e o escore de bem-estar, exibem uma relacao negativa com o desfecho. Estimamos o impacto das taxas de inatividade fisica sobre a proporcao media de adultos obesos e os resultados revelaram que o efeito desse impacto e positivo e apresenta uma forma acelerada para valores de inatividade fisica menores do que 0.85.

MODELING ADMINISTRATIVE EFFICIENCY SCORES OF BRAZILIAN MUNICIPALITIES: REGIONAL DIFFERENCES

In this paper we model the administrative efficiencies of Brazilian municipalities grouped by regions. We use the inflated beta regression model, since the efficiency indices take values in the interval (0,1]. Fully efficient units have unit efficiency scores. Except for the North of Brazil, urban counties tend to be more efficient than non-urban ones. In the Northeast and Southeast regions, counties that receive royalties in excess of 10% of their total revenue tend to be less efficient than they would be otherwise. The same holds for counties in the Northeast, Southeast and Midwest regions counties that take part in intermunicipal consortia. The South east region has the highest proportion of fully efficient units.

Errata: Inference Under Heteroskedasticity and Leveraged Data, Communications in Statistics, Theory and Methods, 36, 1877–1888, 2007

The optimal value of k is correct: k = 0 7. This value has been selected, as explained in the paper, through extensive Monte Carlo experiments. Figures 1 and 2 change accordingly. Finally, the HC2, HC3, and HC4 tests are less liberal than reported in the four tables in Sec. 4. (The results for the OLS, HC0, and HC5 tests are correct.) Table 1 corrects the incorrect null rejection rates. (We omit the 1% significance level and the intermediate level of heteroskedasticity.)

Erros de especificação no modelo de regressão beta com dispersão variável

Our goal with this article is to evaluate the effects of misspecifications in the inferences of the beta regression model with varying dispersion. For this, a simulation study was carried out. In these simulations, the response variable was generated with beta distribution assuming known covariates and link functions, thus the model has been adjusted in the correct and incorrect specification, particularly considering six kinds of specification errors. We evaluate the effects of these errors through rejection rates and coverage rates in relation to one of the average submodel parameters and, in addition, we also evaluated the relative bias and the mean square error of the estimates mean responses. We verified from the results obtained, that the specification errors involving the linear predictor of the precision regression structure had a considerable influence on the model inferences. Finally, we performed an application to real data in order to compare the effects of different ways specification on the inferences of beta regression model with varying dispersion.

Assessment of the Proportion of Obese Children Benefited by Family Allowance Program in the Regions of Brazil

Our objective is to evaluate and explain the proportion of obese children, between 0 and 5 years old, benefited by the Family Allowance Program in the year of 2014. Additionally, our aim is to map each Brazilian region focusing on the factors that influence their obesity. The beta regression model proposed by Ferrari & Cribari-Neto is used to explain the obesity facts in children for each Brazilian Region. The results show that in the North and Southeast Regions the per capita spending with the Family Allowance Program presented positive influence in the obesity, ie, the more it is spent with the assistance program, the higher the incidence of obese children. In the municipalities of the South and Midwest Regions, the per capita income had a negative influence on the obesity in children. In the Northeast Region, in the municipalities with higher rate of unemployment and higher percentage of underprivileged people, there was a tendency to present a higher incidence of obese children.

Testing Inference in Inflated Beta Regressions under Model Misspecification

We consider testing inference in inflated beta regressions subject to model misspecification. In particular, quasi-z tests based on sandwich covariance matrix estimators are described and their finite sample behavior is investigated via Monte Carlo simulations. The numerical evidence shows that quasi-z testing inference can be considerably more accurate than inference made through the usual z tests, especially when there is model misspecification. Interval estimation is also considered. We also present an empirical application that uses real (not simulated) data.

ESTIMATES OF VOTES FOR DILMA ROUSSEFF IN 2010 ELECTIONS UNDER THE SCOPE OF THE BOLSA FAMÍLIA PROGRAM

The purpose of this paper is to evaluate the impact of the Bolsa Familia program’s expenses during the presidential elections of 2010. The beta regression model was adjusted in order to explain the percentage of valid votes from the Northeast region in Dilma Rousseff during the second round of the 2010 elections. Factors such as the poverty ratio, the municipal GDP, the percentage of votes Lula got in 2006 as well as the Bolsa Familia program’s per capita spending all had a positive impact on the percentage of votes in Dilma in the 2010 elections. We’ve established the impact of the Bolsa Familia program in the 2010 elections: had the program being given no budget during the 2010 elections, President Dilma would have lost approximately 2,125 million votes from the Northeast region.