Research Reports

11/2017 Fp2 - Maximal Curves with Many Automorphisms are Galois-Covered by the Hermitian Curve
Daniele Bartoli, Maria Montanucci , Fernando Torres

Let F be the finite field of order q2, q = ph with p prime. It is commonly
atribute to J.P. Serre the fact that any curve F-covered by the Hermitian curve Hq+1 :
yq+1 = xq + x is also F-maximal. Nevertheless, the converse is not true as the Giulietti-
Korchm´aros example shows provided that q > 8 and h ≡ 0 (mod 3). In this paper, we
show that if an F-maximal curve X of genus g ≥ 2 where q = p is such that |Aut(X)| >
84(g − 1) then X is Galois-covered by Hp+1. Also, we show that the hypothesis on the
order of Aut(X) is sharp, since there exists an F-maximal curve X for q = 71 of genus
g = 7 with |Aut(X)| = 84(7 − 1) which is not Galois-covered by the Hermitian curve

PDF icon rp-2017-11.pdf
10/2017 Generalized Weierstrass Semigroups and their Poincaré Series
J. J. Moyano-Fernández, W. Tenório , F. Torres

We investigate the structure of the generalized Weierstraß semigroups at several points on a curve defined over a finite field. We present a description of these
semigroups that enables us to deduce properties concerned with the arithmetical structure of divisors supported on the specified points and their corresponding Riemann-Roch
spaces. This characterization allows us to show that the Poincar´e series associated with generalized Weierstraß semigroups carry essential information to describe entirely their
respective semigroups.

PDF icon rp-2017-10.pdf
9/2017 Zero-one Augmented Beta and Zero Inflated Discrete Models with Heterogeneous Dispersion: An Application to Students’ Academic Performance
Hildete P. Pinheiro, Rafael P. Maia, Eufrásio A. Lima-Neto, Mariana Rodrigues-Motta

The purpose of this work is to present suitable statistical methods to study the performance of undergraduate students based on the incidence/proportion of failed courses. Some approaches are considered: in one of them the incidence of failed courses is modeled using zero in ated discrete distributions with heteroscedasticity, considering
the logarithm of the total number of courses as an o set; in another, the proportion of failed courses is modeled considering a zero-one augmented
beta distribution with heterogeneous dispersion parameter. A detailed residual analysis is performed to investigate the best model to  t the data. The zero-one augmented beta model with heteroscedasticity presents a better t based on residual analysis. Moreover, the model for the proportion brings us more information as it is straight
forward to interpret its results. The database consists of records of 3,699 students with Engineering major who entered the State University of Campinas, Brazil, from 2000 to 2005. The entrance exam scores, academic and demographic variables and their socioeconomic status are considered as covariates in the models.

PDF icon rp-2017-09.pdf
8/2017 Multidimensional Multiple Group IRT Models with Skew Normal Latent Trait Distributions
Juan L. Padilla, Caio L. N. Azevedo, Victor H. Lachos

Item response theory (IRT) models are one of the most important statistical tools for psychometric data analysis. Their applicability goes from educational
assessment to biological essays. The IRT models combine, at least, two sets of unknown quantities: the latent traits (person parameters) and item parameters (related to measurement instruments of interest). The multidimensional item response theory (MIRT) models are quite useful to analyze data sets involving multiple skills or latent traits, which occurs in many of the applications. However, most of the works in the literature consider the usual assumption of multivariate (symmetric) normal distribution to the latent traits and do not deal with the multiple group framework (few groups with many of subjects in each one). They, in general, consider a limited
number of model t assessment tools, and do not investigate the measurement instrument dimensionality in a detailed way, while also dealing with the model nonidenti ability in a di erent way than that we presented here and only for one group model. In this work, we propose a MIRT multiple group model with multivariate skew normal distributions for modeling the latent traits of each group under the centered parameterization, presenting simple and feasible conditions for model identi cation. A full Bayesian approach for parameter estimation, structural selection (model comparison and determination of the dimensionality of the measurement instrument) and model
t assessment are developed through Markov Chain Monte Carlo (MCMC) algorithms. The developed tools are illustrated through the analysis of a real data set related to the rst stage of the University of Campinas 2013 admission exam.

PDF icon rp-2017-08.pdf
7/2017 Likelihood-based Inference for Zero-or-one Augmented Rectangular Beta Regression Models
Ana R.S. Santos, Caio L. N. Azevedo, Jorge L. Bazan, Juvêncio S. Nobre

A new zero-and/or-one augmented beta rectangular regression model is introduced in this work, which is based on a new parameterization of the rectangular beta distribution. Maximum likelihood estimation is performed by using a combination of the EM algorithm (for the continuous part) and Fisher scoring algorithm (for discrete part). Also, we develop techniques of model t assessment, by using the randomized quantile residuals and model selection, considering criteria, such as AIC and BIC.We conducted several simulation studies, considering some situations of practical interest, in order to evaluate the parameter recovery of the proposed model and estimation method, the impact of transforming the observed zeros and ones with the use of non-augmented models and the behavior of the model selection criteria. A psychometric real data set was analyzed to illustrate the performance of the new approach considering the model studied.

PDF icon rp-2017-07.pdf
6/2017 Bayesian Inference for a Birnbaum-Saunders Regression Model Based on the Centered Skew Normal Distribution
Nathalia L. Chaves, Caio L N Azevedo, Filidor Vilca-Labra and Juvêncio S. Nobre
PDF icon rp-2017-6.pdf
5/2017 A Copula Based Modeling for Longitudinal IRT Data with Skewed Latent Distributions
José Roberto Silva dos Santos, Caio Lucidius Naberezny Azevedo
PDF icon rp-2017-5.pdf
4/2017 Bayesian General Cholesky Decomposition Based Modeling of Longitudinal Multiple-Group IRT Data with Skewed Latent Distributions and Growth Curves
José Roberto Silva dos Santos , Caio Lucidius Naberezny Azevedo
PDF icon rp-2017-4.pdf
3/2017 A General Cholesky Decomposition Based Modeling of Longitudinal IRT Data: Handling Skewed Latent Traits Distributions
José Roberto Silva dos Santos, Caio Lucidius Naberezny Azevedo
PDF icon rp-2017-3.pdf
2/2017 A General Cholesky Decomposition Based Modeling of Longitudinal IRT Data.
José Roberto Silva dos Santos, Caio Lucidius Naberezny Azevedo
PDF icon rp-2017-2.pdf