Giovanni C. Porzio

Examining the effect of social influence on student performance through network autocorrelation models

The paper investigates the link between student relations and their performances at university. A social influence mechanism is hypothesized as individuals adjusting their own behaviors to those of others with whom they are connected. This contribution explores the effect of peers on a real network formed by a cohort of students enrolled at a graduate level in an Italian University. Specifically, by adopting a network effects model, the relation between interpersonal networks and university performance is evaluated assuming that student performance is related to the performance of the other students belonging to the same group. By controlling for individual covariates, the network results show informal contacts, based on mutual interests and goals, are related to performance, while formal groups formed temporarily by the instructor have no such effect.

Archetypal Analysis for Data Driven Benchmarking

In this work, adopting an exploratory and graphical approach, we suggest to consider archetypal analysis as a basis for a data driven benchmarking procedure. The procedure is aimed at defining some reference performers, at understanding their features, and at comparing observed performances with them. Being archetypes some extreme points, we propose to consider them as reference performers. Then, we offer a set of graphical tools in order to describe these archetypal benchmarks, and to evaluate the observed performances with respect to them.

Exploring the Periphery of Data Scatters: Are There Outliers?

Outliers are observations that are particularly discordant with respect to others, lying hence on the periphery of the data region. In the literature, many tools have been proposed with the aim of detecting multiple outliers. Most of the recent and attractive methods are based on some measure of the distance of each data point from a center. However, they are really effective only if the shape of the data scatter is symmetrical with respect to such a center. Otherwise, asymmetry will make these measures misleading. For this reason, we propose a method that allows direct exploration of the periphery of the data scatter, without considering any center. The methodology we propose is based on a two-step procedure that exploits the sample convex hull and radial projections. It explores gaps in the data scatter and proximities to its boundary, highlighting how the data structure is sparse at its periphery. A complementary graphical display is finally offered as a useful tool to visualize boundary features.

Minimum volume peeling

Among the measures of a distributions location, the mode is probably the least often used, although it has some appealing properties. Estimators for the mode of univariate distributions are widely available. However, few contributions can be found for the multivariate case. A consistent direct multivariate mode estimation procedure, called minimum volume peeling, can be outlined as follows. The approach iteratively selects nested subsamples with a decreasing fraction of sample points, looking for the minimum volume subsample at each step. The mode is then estimated by calculating the mean of all points in the final set. The robustness of the method is investigated by analyzing its finite sample breakdown point and algorithms to determine minimum volume sets are discussed. Simulation results confirm that using minimum volume peeling leads to efficient mode estimates both in uncontaminated as well as contaminated situations.

Dynamic Graphics and Model Validation: An Application to Best-Practice Production Functions

The aim of this work is to show how dynamic graphics can supplement, and in some instances even surrogate, techniques of model validation traditionally adopted in economic and business applications. A case study considers a production function estimated over an unbalanced panel of technically efficient countries, where standard validation tools cannot be applied. Yet, the dynamic use of the summary plot and the added variable plot allows even in this case to assess the role of potentially influential observations. Through these procedures, a simple intervention model is implemented, obtaining coefficient values more in line with a priori expectations. Copyright

Finite Sample Behavior of MLE in Network Autocorrelation Models

This work evaluates the finite sample behavior of ML estimators in network autocorrelation models, a class of auto-regressive models studying the network effect on a variable of interest. Through an extensive simulation study, we examine the conditions under which these estimators are normally distributed in the case of finite samples. The ML estimators of the autocorrelation parameter have a negative bias and a strongly asymmetric sampling distribution, especially for high values of the network effect size and the network density. In contrast, the estimator of the intercept is positively biased but with an asymmetric sampling distribution. Estimators of the other regression parameters are unbiased, with heavy tails in presence of non-normal errors. This occurs not only in randomly generated networks but also in well-established network structures.

Testing Circular Antipodal Symmetry Through Data Depths

This work discusses how to test antipodal symmetry of circular distributions through depth functions. Two notions of depths for circular data are adopted, and their performances are evaluated and compared through a simulation study.

A boxplot for circular data: A Boxplot for Circular Data

The box-and-whiskers plot is an extraordinary graphical tool that provides a quick visual summary of an observed distribution. In spite of its many extensions, a really suitable boxplot to display circular data is not yet available. Thanks to its simplicity and strong visual impact, such a tool would be especially useful in all fields where circular measures arise: biometrics, astronomy, environmetrics, Earth sciences, to cite just a few. For this reason, in line with Tukeys original idea, a Tukey-like circular boxplot is introduced. Several simulated and real datasets arising in biology are used to illustrate the proposed graphical tool.

Regression analysis by example

the book. Brief chapters on advanced topics such as nonlinear regression, robust regression, regression models for time series and bootstrapping complete the book. The book is aimed at use in statistics and engineering courses at the upper-undergraduate and graduate level. The authors stress the importance of integrating statistical computations into such courses. Throughout the book, they use examples in both a number of commercial software packages as well as R – all datasets that are used in the examples can be downloaded from the publisher’s website. Personally, I would have preferred it if the book would have been restricted to the use of R, both for consistency and the fact that it is freely available and thus best suited for classroom use. This is certainly a good choice as a text book for the targeted classes, as long as the students have a sufficiently strong background in statistics and linear algebra, but the book is suitable for self-study as well.

Multivariate Control Charts from a Data Mining Perspective

This chapter aims at presenting our data mining vision on Statistical Process Control (SPC) analysis, specifically on the design of multivariate control charts for individual observations in the case of independent data and continuous variables. We first argue why the classic multivariate SPC tool, namely the Hotelling T 2 chart, might not be appropriate for large data sets, and then we provide an up-to-date critical review of the methods suitable for dealing with data mining issues in control chart design. In order to address new SPC issues such as the presence of multiple outliers and incorrect model assumptions in the context of large data sets, we suggest exploitation of some multivariate nonparametric statistical methods. In a model-free environment, we present the way we handle large data sets: a multivariate control scheme based on the data depth approach. We first present the general framework, and then our specific idea on how to design a proper control chart. There follows an example, a simulation study, and some remarks on the choice of the depth function from a data mining perspective. A brief discussion of some open issues in data mining SPC closes the chapter.