This paper demonstrates the feasibility of applying nonlinear programming methods to solve the classification problem in discriminant analysis. The application represents a useful extension of previously proposed line...
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This paper demonstrates the feasibility of applying nonlinear programming methods to solve the classification problem in discriminant analysis. The application represents a useful extension of previously proposed linear programming-based solutions for discriminant analysis. The analysis of data obtained by conducting a Monte Carlo simulation experiment shows that these new procedures are promising. Future research that should promote application of the proposed methods for solving classification problems in a business decision-making environment is discussed. [ABSTRACT FROM AUTHOR]
Standard errors of the coefficients of a logistic regression (a binary response model) based on the asymptotic formula are compared to those obtained from the bootstrap through Monte Carlo simulations. The computer in...
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Standard errors of the coefficients of a logistic regression (a binary response model) based on the asymptotic formula are compared to those obtained from the bootstrap through Monte Carlo simulations. The computer intensive bootstrap method, a nonparametric alternative to the asymptotic estimate, overestimates the true value of the standard errors while the asymptotic formula underestimates it. However, for small samples the bootstrap estimates are substantially closer to the true value than their counterpart derived from the asymptotic formula. The methodology is discussed using two illustrative data sets. The first example deals with a logistic model explaining the log-odds of passing the ERA amendment by the 1982 deadline as a function of percent of women legislators and the percent vote for Reagan. In the second example, the probability that an ingot is ready to roll is modelled using heating time and soaking time as explanatory variables. The results agree with those obtained from the simulations. The value of the study to better decision making through accurate statistical inference is discussed. [ABSTRACT FROM AUTHOR]
This paper develops an explicit relationship between sample size, sampling error, and related costs for the application of multiple regression models in observational studies. Graphs and formulas for determining optim...
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This paper develops an explicit relationship between sample size, sampling error, and related costs for the application of multiple regression models in observational studies. Graphs and formulas for determining optimal sample sizes and related factors are provided to facilitate the application of the derived models. These graphs reveal that, in most cases, the imprecision of estimates and minimum total cost are relatively insensitive to increases in sample size beyond n=20. Because of the intrinsic variation of the regression model, even if larger samples are optimal, the relative change in the total cost function is small when the cost of imprecision is a quadratic function. A model-utility approach, however, may impose a lower bound on sample size that requires the sample size be larger than indicated by the estimation or cost-minimization approaches. Graphs are provided to illustrate lower-bound conditions on sample size. Optimal sample size in view of all considerations is obtained by the maximin criterion, the maximum of the minimum sample size for all approaches. [ABSTRACT FROM AUTHOR]
作者：
KOEHLER, GJUNIV FLORIDA
COLL BUSINESS ADMDEPT DECIS & INFORMAT SCIGAINESVILLEFL 32611 USA
Discriminant analysis methods are used to study the differences between 2 or more mutually exclusive groups that are based on one or more quantitative variables and to classify new observations into an appropriate gro...
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Discriminant analysis methods are used to study the differences between 2 or more mutually exclusive groups that are based on one or more quantitative variables and to classify new observations into an appropriate group. Recent research indicates that mathematical programming models used to determine linear discriminant classifiers show promise when compared to classical methods. Several authors have presented increasingly sophisticated mathematical programming models to determine linear discriminant classifiers. This progression of new models was largely motivated by anomalies in earlier formulations. Glover, Keene, and Duea (1988) provided the hybrid discriminant model (HDM), which purportedly resolves all of the anomalies of previous models. The claim that the HDM avoids unacceptable solutions is examined. It is concluded that the HDM overcomes some problems of earlier linear programming models, but it does not generally prevent unacceptable solutions.
ABSTRACTThis paper presents a new linear model methodology for clustering judges with homogeneous decision policies and differentiating dimensions which distinguish judgment policies. This linear policy capturing mode...
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ABSTRACTThis paper presents a new linear model methodology for clustering judges with homogeneous decision policies and differentiating dimensions which distinguish judgment policies. This linear policy capturing model based on canonical correlation analysis is compared to the standard model based on regression analysis and hierarchical agglomerative clustering. Potential advantages of the new methodology include simultaneous instead of sequential consideration of information in the dependent and independent variable sets, decreased interpretational difficulty in the presence of multicollinearity and/or suppressor/moderator variables, and a more clearly defined solution structure allowing assessment of a judge\'s relationship to all of the derived, ideal policy types. An application to capturing policies of information systems recruiters responsible for hiring entry‐level personnel is used to compare and contrast the two technique
Recently developed large sample inference procedures for least absolute value (LAV) regression are examined via Monte Carlo simulation to determine when sample sizes are large enough for the procedures to work effecti...
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Recently developed large sample inference procedures for least absolute value (LAV) regression are examined via Monte Carlo simulation to determine when sample sizes are large enough for the procedures to work effectively. A variety of different experimental settings were created by varying the disturbance distribution, the number of explanatory variables and the way the explanatory variables were generated. Necessary sample sizes range from as small as 20 when disturbances are normal to as large as 200 in extreme outlier-producing distributions. [ABSTRACT FROM AUTHOR]
The matched-pairs methodology is becoming increasingly popular as a means of controlling extraneous factors in business research. This paper develops discriminant procedures for matched data and examines the propertie...
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The matched-pairs methodology is becoming increasingly popular as a means of controlling extraneous factors in business research. This paper develops discriminant procedures for matched data and examines the properties of these methods. Data from a recent study by Hunt on the determinants of inventory method choice are used to contrast the performance of the different methods. While all of the methods yield the same set of discriminating variables, those procedures that allow for the dependence among observations within a pair provide greater classificatory power than traditional multivariate techniques. [ABSTRACT FROM AUTHOR]
Four discriminant models were compared in a simulation study: Fisher's linear discriminant function [14], Smith's quadratic discriminant function [34], the logistic discriminant model, and a model based on lin...
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The bootstrap method is used to compute the standard error of regression parameters when the data are non-Gaussian distributed. Simulation results with L1 and L2 norms for various degrees of 'non-Gaussianess' ...
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The bootstrap method is used to compute the standard error of regression parameters when the data are non-Gaussian distributed. Simulation results with L1 and L2 norms for various degrees of 'non-Gaussianess' are provided. The computationally efficient L2 norm, based on the bootstrap method, provides a good approximation to the L1 norm. The methodology is illustrated with daily security return data. The results show that decisions can be reversed when the ordinary least-squares estimate of standard errors is used with nonGaussian data. [ABSTRACT FROM AUTHOR]
The two-group discriminant problem has applications in many areas, for example, differentiating between good credit risks and poor ones, between promising new firms and those likely to fail, or between patients with s...
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The two-group discriminant problem has applications in many areas, for example, differentiating between good credit risks and poor ones, between promising new firms and those likely to fail, or between patients with strong prospects for recovery and those highly at risk. To expand our tools for dealing with such problems, we propose a class of nonparametric discriminant procedures based on linear programming (LP). Although these procedures have attracted considerable attention recently, only a limited number of computational studies have examined the relative merits of alternative formulations. In this paper we provide a detailed study of three contrasting formulations for the two-group problem. The experimental design provides a variety of test conditions involving both normal and nonnormal populations. Our results establish the LP model which seeks to minimize the sum of deviations beyond the two-group boundary as a promising alternative to more conventional linear discriminant techniques. [ABSTRACT FROM AUTHOR]
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