Bruce E. Barrett

Software development cost estimation using function points

This paper presents an assessment of several published statistical regression models that relate software development effort to software size measured in function points. The principal concern with published models has to do with the number of observations upon which the models were based and inattention to the assumptions inherent in regression analysis. The research describes appropriate statistical procedures in the context of a case study based on function point data for 104 software development projects and discusses limitations of the resulting model in estimating development effort. The paper also focuses on a problem with the current method for measuring function points that constrains the effective use of function points in regression models and suggests a modification to the approach that should enhance the accuracy of prediction models based on function points in the future. >

The efficacy of SMARTER — Simple Multi-Attribute Rating Technique Extended to Ranking

Abstract A key component in the development of an additive multiattribute value model for selecting the best alternative is obtaining the attribute weights. In this paper, we assume the decision makers weight information set consists of ranked swing weights, that is, a ranking of the importance of the attribute ranges, and in this context use ‘surrogate weights’ derived from this ranking. The particular surrogate weights are called ROC , for rank order centroid weights. The paper presents three sets of results: (1) a summary of the efficacy of using ROC weights to select a best alternative; (2) an extension of the method of analysis underlying the efficacy studies to assess the applicability of ROC weights for the analysts specific value matrix; (3) methods for sensitivity analyses of a specific value matrix. A comprehensive example illustrates all analyses.

General Classes of Influence Measures for Multivariate Regression

Abstract Many of the existing measures for influential subsets in univariate ordinary least squares (OLS) regression analysis have natural extensions to the multivariate regression setting. Such measures may be characterized by functions of the submatrices H I of the hat matrix H, where I is an index set of deleted cases, and Q I , the submatrix of Q = E(E T E)−1 E T , where E is the matrix of ordinary residuals. Two classes of measures are considered: f(·)tr[H I Q I (I − H I − Q I ) a (I − H I ) b ] and f(·)det[(I − H I − Q I ) a (I − H I ) b ], where f is a scalar function of the dimensions of matrices and a and b are integers. These characterizations motivate us to consider separable leverage and residual components for multiple-case influence and are shown to have advantages in computing influence measures for subsets. In the recent statistical literature on regression analysis, much attention has been given to problems of detecting observations that, individually or jointly, exert a disproportionate ...

Leverage, residual, and interaction diagnostics for subsets of cases in least squares regression

Abstract Leverage and residual values are useful general diagnostics in least squares regression because all single-case influence measures are functions of these two basic components. Recent work in the area of robust diagnostics has suggested that ordinary leverage and residual values can be ineffective in the presence of “masking” and other multiple case effects, but Kempthorne and Mendel (1990) and others have pointed out that satisfactory definitions of “leverage” and “residual” for subsets of cases might overcome these problems. In this article, we propose a set of three simple, yet general and comprehensive, subset diagnostics (referred to as leverage, residual, and interaction) that have the desirable characteristics of single-case leverage and residual diagnostics. Most importantly, the proposed measures are the basis of several existing subset influence measures, including Cooks distance. We illustrate how these basic diagnostics usefully complement existing multiple outlier detection procedures and subset influence measures in understanding the influence structure within a regression data set.

A computational framework for variable selection in multivariate regression

Stepwise variable selection procedures are computationally inexpensive methods for constructing useful regression models for a single dependent variable. At each step a variable is entered into or deleted from the current model, based on the criterion of minimizing the error sum of squares (SSE). When there is more than one dependent variable, the situation is more complex. In this article we propose variable selection criteria for multivariate regression which generalize the univariate SSE criterion. Specifically, we suggest minimizing some function of the estimated error covariance matrix: the trace, the determinant, or the largest eigenvalue. The computations associated with these criteria may be burdensome. We develop a computational framework based on the use of the SWEEP operator which greatly reduces these calculations for stepwise variable selection in multivariate regression.

Efficient Computation of Subset Influence in Regression

Abstract The detection of influential cases is now accepted as an essential component of regression diagnostics. It is also well established that two or more cases that are individually regarded as noninfluential may act in concert to achieve a high level of joint influence. However, for the majority of data sets it is computationally infeasible to calculate the influence for all subsets of a given size. In this article we address this problem and suggest an algorithm that greatly reduces the computational effort by making use of a sequence of upper bounds on the influence value. These upper bounds are much less costly to evaluate and greatly reduce the number of subsets for which the influence value must be explicitly determined.

Detecting Bias in Jury Selection

The process of jury selection typically requires opposing counsel to reduce a pool of prospective jurors to the prescribed jury size by alternately excusing or striking individuals from service. These decisions, called peremptory strikes, are executed without the need of revealing any underlying rationale. However, recent U.S. Supreme Court rulings have held that attorneys may not exercise their peremptory strikes to systematically exclude prospective jurors on the basis of race or gender. The first step in establishing a charge of such improper bias requires the challenging party to show evidence that his or her opponents strikes are inconsistent with random consideration of these protected characteristics. Since court procedure dictates that there is some alternating between Prosecution and Defense in the striking process, choices for each side impact those of the other, and a simple comparison of the jury pool with the peremptory strikes is insufficient for establishing any inference of bias. For these situations, we present a methodology for assessing the neutrality of juror strikes, based on the Poisson binomial distribution.

Computation of determinantal subset influence in regression

One of the important goals of regression diagnostics is the detection of cases or groups of cases which have an inordinate impact on the regression results. Such observations are generally described as ‘influential’. A number of influence measures have been proposed, each focusing on a different aspect of the regression. For single cases, these measures are relatively simple and inexpensive to calculate. However, the detection of multiple-case or joint influence is more difficult on two counts. First, calculation of influence for a single subset is more involved than for an individual case, and second, the sheer number of subsets of cases makes the computation overwhelming for all but the smallest data sets.Barrett and Gray (1992) described methods for efficiently examining subset influence for those measures that can be expressed as the trace of a product of positive semidefinite (psd) matrices. There are, however, other popular measures that do not take this form, but rather are expressible as the ratio of determinants of psd matrices. This article focuses on reducing the computation for the determinantal ratio measures by making use of upper and lower bounds on the influence to limit the number of subsets for which the actual influence must be explicitly determined.

Understanding Influence in Multivariate Regression

Abstract Multivariate regression influence measures contain a dimension of synergistic interaction not present in univariate regression. This is primarily due to the covariance structure among the multiple dependent variables. Even considering only single cases, the influence can be decomposed into a leverage component and a residual component. This residual term can be further decomposed into residual effects due to the individual dependent variates, and an additional component that measures the joint contribution due to the covariance. Such a decomposition is useful to the investigator in attributing the cause and recommending accommodation of influential cases.

Linear Inequalities and the Analysis of Multi-Attribute Value Matrices

Barron and Barrett, 1996(b) demonstrate empirically that a surrogate weight vector, rank order centroid (ROC) weights, based only on ranked swing weights, is surprisingly efficacious in general in selecting a best multi-attribute alternative. An Excel-based simulation, EMAR, allows one to assess the applicability of the general result to any particular value matrix. In this paper we extend EMAR to partial information sets of weights other than a strict ranking. We also apply these procedures to examine the effect of reducing the number of attributes.