Journal of Data Science

This study investigates whether Support Vector Machine (SVM) can be used to predict the problem solving performance of students in the computerbased learning environment. The SVM models using RBF, linear, polynomial and sigmoid kernels were developed to estimate the probability for middle school students to get mathematics problems correct at their first attempt without using hints available in the computer-based learning environment based on their problem solving performance observed in the past. The SVM models showed better predictions than the standard Bayesian Knowledge Tracing (BKT) model, one of the most widely used prediction models in educational data mining research, in terms of Area Under the receiver operating characteristic Curve (AUC). Four SVM models got AUC values from 0.73 to 0.77, which is approximately 29% improvement, compared to the standard BKT model whose AUC was 0.58.

Abstract: In longitudinal studies where the same individuals are followed over time, bias caused by unobserved data raises a serious concern, particularly when the data are missing in a non-ignorable manner. One approach to deal with non-ignorable missing data is a pattern mixture model. In this paper, we combine the pattern mixture model with latent trajectory analysis using the SAS TRAJ procedure, which offers a practical solution to many problems of the same nature. Our model assumes a stochastic process that categorizes a relative large number of missing-data patterns into several latent groups, each of which has unique outcome trajectory, which allows patterns with missing values to share information with patterns with more data points. We estimated the longitudinal trajectories of a memory test over 12 years of follow-up, using data from the prospective epidemiological study of dementia. Missing data patterns were created conditional on survival, and final marginal response was obtained by excluding those who had died at each time point. The approach presented here is appealing since it can be easily implemented using common software.

Abstract: We introduce a new class of the slash distribution using folded normal distribution. The proposed model defined on non-negative measure ments extends the slashed half normal distribution and has higher kurtosis than the ordinary half normal distribution. We study the characterization and properties involving moments and some measures based on moments of this distribution. Finally, we illustrate the proposed model with a simulation study and a real application.

Abstract: To analyze skewed data, skew normal distribution is proposed by Azzalini (1985). For practical problems of estimating the skewness parame ter of this distribution, Gupta and Gupta (2008) suggested power normal dis tribution as an alternative. We search for another alternative, named tilted normal distribution following the approach of Marshall and Olkin (1997) to add a positive parameter to a general survival function and taking survival function is of normal form. We have found out different properties of this distribution. Maximum likelihood estimate of parameters of this distribu tion have been found out. Comparison of tilted normal distribution with skew normal and power normal distribution have been made.

Abstract: This paper provides a Bayesian approach to estimating the interest rate term structures of Treasury and corporate debt with a penalized spline model. Although the literature on term structure modeling is vast, to the best of our knowledge, all methods developed so far belong to the frequentist school. In this paper, we develop a two-step estimation procedure from a Bayesian perspective. The Treasury term structure is first estimated with a Bayesian penalized spline model. The smoothing parameter is naturally embedded in the model as a ratio of posterior variances and does not need to be selected as in the frequentist approach. The corporate term structure is then estimated by adding a credit spread to the estimated Treasury term structure, incorporating knowledge of the positive credit spread into the Bayesian model as an informative prior. In contrast to the frequentist method, the small sample size of the corporate debt poses no particular difficulty to the proposed Bayesian approach.

Compositional data consist of known compositions vectors whose components are positive and defined in the interval (0,1) representing proportions or fractions of a “whole”. The sum of these components must be equal to one. Compositional data is present in different knowledge areas, as in geology, economy, medicine among many others. In this paper, we propose a new statistical tool for volleyball data, i.e., we introduce a Bayesian anal- ysis for compositional regression applying additive log-ratio (ALR) trans- formation and assuming uncorrelated and correlated errors. The Bayesian inference procedure based on Markov Chain Monte Carlo Methods (MCMC). The methodology is applied on an artificial and a real data set of volleyball.

The Birnbaum-Saunders generalized t (BSGT) distribution is a very flflexible family of distributions that admits different degrees of skewness and kurtosis and includes some important special or limiting cases available in the literature, such as the Birnbaum-Saunders and BirnbaumSaunders t distributions. In this paper we provide a regression type model to the BSGT distribution based on the generalized additive models for location, scale and shape (GAMLSS) framework. The resulting model has high flflexibility and therefore a great potential to model the distribution parameters of response variables that present light or heavy tails, i.e. platykurtic or leptokurtic shapes, as functions of explanatory variables. For different parameter settings, some simulations are performed to investigate the behavior of the estimators. The potentiality of the new regression model is illustrated by means of a real motor vehicle insurance data set.