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"Simonoff, Jeffrey S"
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Handbook of regression analysis
\"Written by two established experts in the field, the purpose of this handbook is to provide a practical, one-stop reference on regression analysis. The focus is on the tools that both practitioners and researchers use in real life. It is intended to be a comprehensive collection of the theory, methods, and applications of the subject matter, but it is deliberately written at an accessible level. The handbook will provide a quick and convenient reference or \"refresher\" on ideas and methods that are useful for the accurate analysis of data and its resulting interpretations. Students can use the book as an introduction to and/or summary of key concepts in regression and related course work (such as linear, nonlinear, and nonparametric regressions). Plentiful references are supplied for the more motivated readers. Theory is presented when necessary, and always supplemented by hands-on examples. Software routines are available via an author-maintained web site\"-- Provided by publisher.
Book
Handbook of regression analysis
\"Written by an established expert in the field, the purpose of this handbook is to provide a practical, one-stop reference on regression analysis. The focus is on the tools that both practitioners and researchers use in real life. It is intended to be a comprehensive collection of the theory, methods, and applications of the subject matter, but it is deliberately written at an accessible level. The handbook will provide a quick and convenient reference or \"refresher\" on ideas and methods that are useful for the accurate analysis of data and its resulting interpretations. Students can use the book as an introduction to and/or summary of key concepts in regression and related course work (such as linear, nonlinear, and nonparametric regressions). Plentiful references are supplied for the more motivated readers. Theory is presented when necessary, and always supplemented by hands-on examples. Software routines are available via an author-maintained web site\"--
eBook
RE-EM trees: a data mining approach for longitudinal and clustered data
Longitudinal data refer to the situation where repeated observations are available for each sampled object. Clustered data, where observations are nested in a hierarchical structure within objects (without time necessarily being involved) represent a similar type of situation. Methodologies that take this structure into account allow for the possibilities of systematic differences between objects that are not related to attributes and autocorrelation within objects across time periods. A standard methodology in the statistics literature for this type of data is the mixed effects model, where these differences between objects are represented by so-called “random effects” that are estimated from the data (population-level relationships are termed “fixed effects,” together resulting in a mixed effects model). This paper presents a methodology that combines the structure of mixed effects models for longitudinal and clustered data with the flexibility of tree-based estimation methods. We apply the resulting estimation method, called the RE-EM tree, to pricing in online transactions, showing that the RE-EM tree is less sensitive to parametric assumptions and provides improved predictive power compared to linear models with random effects and regression trees without random effects. We also apply it to a smaller data set examining accident fatalities, and show that the RE-EM tree strongly outperforms a tree without random effects while performing comparably to a linear model with random effects. We also perform extensive simulation experiments to show that the estimator improves predictive performance relative to regression trees without random effects and is comparable or superior to using linear models with random effects in more general situations.
Journal Article
Smoothing parameter selection in nonparametric regression using an improved Akaike information criterion
Many different methods have been proposed to construct nonparametric estimates of a smooth regression function, including local polynomial, (convolution) kernel and smoothing spline estimators. Each of these estimators uses a smoothing parameter to control the amount of smoothing performed on a given data set. In this paper an improved version of a criterion based on the Akaike information criterion (AIC), termed AICC, is derived and examined as a way to choose the smoothing parameter. Unlike plug-in methods, AICC can be used to choose smoothing parameters for any linear smoother, including local quadratic and smoothing spline estimators. The use of AICC avoids the large variability and tendency to undersmooth (compared with the actual minimizer of average squared error) seen when other `classical' approaches (such as generalized cross-validation or the AIC) are used to choose the smoothing parameter. Monte Carlo simulations demonstrate that the AICC-based smoothing parameter is competitive with a plug-in method (assuming that one exists) when the plug-in method works well but also performs well when the plug-in approach fails or is unavailable.
Journal Article
Non-White, No More: Effect Coding as an Alternative to Dummy Coding With Implications for Higher Education Researchers
The purpose of this article is to describe effect coding as an alternative quantitative practice for analyzing and interpreting categorical, race-based independent variables in higher education research. Unlike indicator (dummy) codes that imply that one group will be a reference group, effect codes use average responses as a means for interpreting information. This technique is especially appropriate for examining race, as such a process enables raced subgroups to be compared to each other and does not position responses of any raced group as normative--the standard against which all other race effects are interpreted. The issues raised here apply in any research context where a categorical variable without a natural reference group (e.g., college major) is a potential predictor in a regression model.
Journal Article
Efficiency for Regularization Parameter Selection in Penalized Likelihood Estimation of Misspecified Models
It has been shown that Akaike information criterion (AIC)-type criteria are asymptotically efficient selectors of the tuning parameter in nonconcave penalized regression methods under the assumption that the population variance is known or that a consistent estimator is available. We relax this assumption to prove that AIC itself is asymptotically efficient and we study its performance in finite samples. In classical regression, it is known that AIC tends to select overly complex models when the dimension of the maximum candidate model is large relative to the sample size. Simulation studies suggest that AIC suffers from the same shortcomings when used in penalized regression. We therefore propose the use of the classical corrected AIC (AIC c) as an alternative and prove that it maintains the desired asymptotic properties. To broaden our results, we further prove the efficiency of AIC for penalized likelihood methods in the context of generalized linear models with no dispersion parameter. Similar results exist in the literature but only for a restricted set of candidate models. By employing results from the classical literature on maximum-likelihood estimation in misspecified models, we are able to establish this result for a general set of candidate models. We use simulations to assess the performance of AIC and AIC c, as well as that of other selectors, in finite samples for both smoothly clipped absolute deviation (SCAD)-penalized and Lasso regressions and a real data example is considered. Supplementary materials for this article are available online.
Journal Article
Effect Coding as a Mechanism for Improving the Accuracy of Measuring Students Who Self-Identify with More than One Race
The purpose of this paper is to describe effect coding as an alternative quantitative practice for analyzing and interpreting categorical, multi-raced independent variables in higher education research. Not only may effect coding enable researchers to get closer to respondents' original intentions, it allows for more accurate analyses of all race based categories.
Journal Article
On the Sensitivity of the Lasso to the Number of Predictor Variables
The Lasso is a computationally efficient regression regularization procedure that can produce sparse estimators when the number of predictors (p) is large. Oracle inequalities provide probability loss bounds for the Lasso estimator at a deterministic choice of the regularization parameter. These bounds tend to zero if p is appropriately controlled, and are thus commonly cited as theoretical justification for the Lasso and its ability to handle high-dimensional settings. Unfortunately, in practice the regularization parameter is not selected to be a deterministic quantity, but is instead chosen using a random, data-dependent procedure. To address this shortcoming of previous theoretical work, we study the loss of the Lasso estimator when tuned optimally for prediction. Assuming orthonormal predictors and a sparse true model, we prove that the probability that the best possible predictive performance of the Lasso deteriorates as p increases is positive and can be arbitrarily close to one given a sufficiently high signal to noise ratio and sufficiently large p. We further demonstrate empirically that the amount of deterioration in performance can be far worse than the oracle inequalities suggest and provide a real data example where deterioration is observed.
Journal Article
Exploring Innovative Entrepreneurship and Its Ties to Higher Educational Experiences
The purpose of this paper was to explore innovative entrepreneurship and to gain insight into the educational practices and experiences that increase the likelihood that a student would graduate with innovative entrepreneurial intentions. To this end, we administered a battery of assessments to 3,700 undergraduate seniors who matriculated in the spring of 2007; these students attended one of five institutions participating in this study. Results showed that, after controlling for a host of personality, demographic, educational, and political covariates, taking an entrepreneurial course and the assessments faculty use as pedagogical strategies for teaching course content were significantly related to innovation intentions. Implications for higher education stakeholders are discussed.
Journal Article
Cultivating Innovative Entrepreneurs for the Twenty-First Century: A Study of U.S. and German Students
The purpose of this exploratory study was to examine the cultivation of innovative entrepreneurial intentions among students in three distinctive educational settings: a U.S. undergraduate four-year environment, a U.S. M.B.A. two-year environment, and a German five-year business and technology environment. Results suggested that innovative entrepreneurial intentions varied based on educational setting. Implications for theory, research, and practice are discussed.
Journal Article