Showing papers on "Linear discriminant analysis published in 1985"

Introducing Recursive Partitioning for Financial Classification: The Case of Financial Distress

Abstract: The purpose of this study is to present a new classification procedure, Recursive Partitioning Algorithm (RPA), for financial analysis and to compare it with discriminant analysis within the context of firm financial distress. RPA is a computerized, nonparametric technique based on pattern recognition which has attributes of both the classical univariate classification approach and multivariate procedures. RPA is found to outperform discriminant analysis in most original sample and holdout comparisons. We also observe that additional information can be derived by assessing both RPA and discriminant analysis results.

Maximum likelihood estimation for mixed continuous and categorical data with missing values

Abstract: SUMMARY Maximum likelihood procedures for analysing mixed continuous and categorical data with missing values are presented. The general location model of Olkin & Tate (1961) and extensions introduced by Krzanowski (1980, 1982) form the basis for our methods. Maximum likelihood estimation with incomplete data is achieved by an application of the EM algorithm (Dempster, Laird & Rubin, 1977). Special cases of the algorithm include Orchard & Woodbury's (1972) algorithm for incomplete normal samples, Fuchs's (1982) algorithms for log linear modelling of partially classified contingency tables, and Day's (1969) algorithm for multivariate normal mixtures. Applications include: (a) imputation of missing values, (b) logistic regression and discriminant analysis with missing predictors and unclassified observations, (c) linear regression with missing continuous and categorical predictors, and (d) parametric cluster analysis with incomplete data. Methods are illustrated using data from the St Louis Risk Research Project. Some key word8: Cluster analysis; Discriminant analysis; EM algorithm; Incomplete data; Linear regression; Logistic regression; Log linear model; Mixture model.

Discrimination of Groundwater Sources Using Cluster Analysis, MANOVA, Canonical Analysis and Discriminant Analysis

Abstract: Multivariate statistical analysis of water chemistry variables provides an empirical method of establishing relationships and/or differences among groundwater samples taken spatially or temporally. Careful application of cluster analysis, multivariate analysis of variance, canonical analysis, and discriminant analysis provides insight into possible segregation among groundwater sources or mixing among aquifers and a subsequent test of that conjecture. The methods have been applied successfully to two field studies discussed herein. The statistically distinct groups of samples identified by the above methods are supported by structural and geochemical stratification mapping.

Discriminant analysis of amphibian habitat determinants in South-East England

Abstract: 203 ponds and their environs in south-east England were studied with respect to the distribution of amphibians and to a number of specific habitat features A discriminant analysis was carried out to identify the most important habitat features for each species and to derive discriminant functions capable of separating used and unused sites into characteristic groups

An Evaluation of Smoothed Classification Error- Rate Estimators

Abstract: This article examines the properties of smoothed estimators of the probabilities of misclassification in linear discriminant analysis and compares them with those of the resubstitution, leave-one-out, and bootstrap estimators. Smoothed estimators are found to have smaller variance than the other estimators and bias that is a function of the amount of smoothing. An algorithm is presented for determining a reasonable level of smoothing as a function of the training sample sizes and the number of dimensions in the observation vector. Using the criterion of unconditional mean squared error, this particular smoothed estimator, called the NS method, appears to offer a reasonable alternative to existing nonparametric estimators.

A Robust Credit Screening Model Using Categorical Data

Abstract: Motivated by an application in a public utility, the credit screening problem is re-examined from a decision theoretic viewpoint. The relationships between several alternative problem formulations are explored, and compared to the classical linear discriminant analysis LDA approach. Several mathematical programming based solution methods are proposed when the data are binary, and an efficient algorithm is developed for the case when the screening function must also have binary weights. Actual results of both the mathematical programming and LDA methods are presented and compared. The resulting mathematical programming rules are effective, robust, and flexible to administer. Practical advantages of the resulting "n out of N" type rules are discussed. These screening rules have been widely implemented by a major public utility and have resulted in substantial benefits to the utility and to the public.

Classification and Multiple Regression through Projection Pursuit

Abstract: : Projection pursuit regression is generalized to multivariate responses. By viewing classification as a special case, this generalization serves to extend classification and discriminant analysis via the projection pursuit approach.

Error-Rate Estimation in Discriminant Analysis

Abstract: A new derivation for a method to estimate error rates in discriminant analysis is presented. Known as the Shrunken D or DS method, the technique is evaluated in a sampling experiment, along with seven other parametric methods, as a means for estimating both the optimal and conditional error rates. The results show that the “best” estimators are not the same for the two types of error rates and that sample size should influence the choice of an estimator.

On Extensions to Fishers Linear Discriminant Function

Abstract: : This Memorandum describes how Fisher's Linear Discriminant can be combined with the Fukunaga-Koontz transform to give a useful technique for reduction f feature space from many to two or three dimensions. Performance is seen to be superior in general to the Foley-Sammon extension to fisher's method. The technique is then extended to show how a new radius vector (or pair of radius vectors) can be combined with fisher's vector to produce a classifier with even more power of discrimination. Illustrations of the technique show that good discrimination can be obtained even if there is considerable overlap of classes in any single projection. Keywords include: Index Terms; Dimensionality reduction, Discriminant vectors, Feature selection, Fisher criterion, Linear transformations, Separability. (Great Britain)

A linear programming alternative to discriminant analysis in credit scoring

Abstract: The typical technique used to construct credit scoring models is discriminant analysis. This paper presents a descriptive example and empirical analysis to illustrate how linear programming might be used to solve discriminant type problems. Results of the analysis indicated that the linear programming procedure performs well in solving the example credit scoring problem. In addition, the structure of the linear programming model was such that changes could be readily made to reflect either conservative or liberal lending policies.

T 2 Tests, the Linear Two-Group Discriminant Function, and Their Computation by Linear Regression

Abstract: Tests for redundancy of variables in linear two-group discriminant analysis are well known and frequently used. We give a survey of similar tests, including the one-sample T 2 as a special case, in the situation in which only the mean vector (but no covariance matrix) is available in one sample. Then we show that a relation between linear regression and discriminant functions found by Fisher (1936) can be generalized to this situation. Relating regression and discriminant analysis to a multivariate linear model sheds more light on the relationship between them. Practical and didactical advantages of the regression approach to T 2 tests and discriminant analysis are outlined.

Correlation between soil characters and forest types: a study in multiple discriminant analysis*

Abstract: Multiple discriminant analysis is a useful multivariate technique in vegetation studies that can be employed for several purposes, even if the underlying statistical assumptions are not satisfied. An example of application of this method is discussed: multiple discriminant analysis was successfully used for evaluating the predictivity of forest types defined by numerical classification of vegetation data with respect to soil variables.

Selecting risk factors: a comparison of discriminant analysis, logistic regression and Cox's regression model using data from the Tromsø Heart Study.

Abstract: For comparative evaluation, discriminant analysis, logistic regression and Cox's model were used to select risk factors for total and coronary deaths among 6595 men aged 20-49 followed for 9 years. Groups with mortality between 5 and 93 per 1000 were considered. Discriminant analysis selected variable sets only marginally different from the logistic and Cox methods which always selected the same sets. A time-saving option, offered for both the logistic and Cox selection, showed no advantage compared with discriminant analysis. Analysing more than 3800 subjects, the logistic and Cox methods consumed, respectively, 80 and 10 times more computer time than discriminant analysis. When including the same set of variables in non-stepwise analyses, all methods estimated coefficients that in most cases were almost identical. In conclusion, discriminant analysis is advocated for preliminary or stepwise analysis, otherwise Cox's method should be used.

Maximum Shannon information content of diagnostic medical testing. Including application to multiple non-independent tests.

Abstract: The increase in Shannon information available from a diagnostic test associated with grading of the test results into many outcomes, rather than simply positive or negative, was examined to determine its upper limit as the number of test outcomes is increased indefinitely. Numerical methods were employed to find the optimal locations of outcome boundaries when a single normally distributed test variable is classified into 2, 3, 4, 5, 6, 8, 14, or 20 outcome categories. In each case Shannon information was computed for values of prior probability between 0.01 and 0.99 and for distances between the means in diseased and nondiseased populations ranging from 0.5 to 5.0 standard deviations. There is an important improvement in Shannon information as the number of outcomes defined is increased, but the increment in information diminishes rapidly with each additional category. A 20%-30% increment in information may be achieved with three outcomes instead of two. A further important increase in information occurs with four to seven outcomes, but beyond this the increment in inforation is negligible. The findings were similar over a wide range of prior probabilities and distances between the means. The analysis was extended to the case of multiple nonindependent tests by demonstrating their application to a Fisher discriminant function incorporating such tests. It was concluded that for normally distributed test variables: grading of test results significantly improves the information content of both single and multiple tests; the value of information content for 8-20 outcomes represents very nearly the maximum information content of a test; there is little value in using more than five to seven test outcomes; multiple grading should not be neglected for discriminant functions.

Biochemical diagnosis of alcoholism in men psychiatric patients.

Abstract: A comparison was conducted of several discriminant models (linear, stepwise linear and quadratic) using two definitions of prior probability (proportional and equal) to detect alcoholism on the basis of routine blood test results. Discriminant functions were derived on a sample of men alcoholic (N = 407) and nonalcoholic (N = 1068) psychiatric patients, and were cross-validated on an independent sample of the same two populations (NS = 365 and 1020, respectively). Linear discriminant models generally outperformed quadratic models. The best classification was obtained by the equal stepwise linear model that retained SGOT, calcium, albumin, inorganic phosphate and BUN. The best quadratic model (equal) achieved good overall accuracy but weak sensitivity. The linear model was relatively accurate in terms of classification, and better sensitivity was achieved with the five best predictors than with all available measures.

Robustness to nonnormality of the linear discriminant function: mixtures of normal distributions

Abstract: Using the techniques developed by Subrahmaniam and Ching’anda (1978), we study the robustness to nonnormality of the linear discriminant functions. It is seen that the LDF procedure is quite robust against the likelihood ratio rule. The latter yields in all cases much smaller overall error rates; however, the disparity between the error rates of the LDF and LR procedures is not large enough to warrant the recommendation to use the more complicated LR procedure.

On the Asymptotic Distribution of the Location Linear Discriminant Function

Abstract: On presente un developpement asymptotique de la distribution de la regle «estimative» et on etudie sa performance sous diverses hypotheses relatives aux parametres

Properties of Bootstrap Samples

Abstract: SYNOPTIC ABSTRACTEfron's version of the “bootstrap” procedure was devised as a method for obtaining nonparametric estimates of Standard deviations and biases of estimators. Important applications include error rate of classifiers, non-linear regression, econometric modeling, discriminant analysis and principal components. Applications of the bootstrap procedure usually require the generation of “bootstrap samples.” This paper presents a connection between bootstrap samples and the classical occupancy problem. Small sample properties of a bootstrap sample are obtained based on the application of results on the occupancy problem. The implications of these results on the estimate of misclassification probability in discriminant analysis are addressed.

Tables for obtaining confidence bounds for realized signal to noise ratio with an estimated discriminant function

Abstract: Percentage points of a new distribution involving a confluent-hypergeometric distribution obtained by Khatri and Rao (1985) are tabulated. The use of the tabulated values in obtaining a lower confidence bound for the realized signal to noise ratio based on an estimated discriminant function for signal detection is explained.

Quadratic discriminant analysis with covariance for stock delineation and population differentiation: a study of beaked redfishes (Sebastes mentella and S. fasciatus)

Abstract: Stock delineation is of vital importance in fisheries management programs. Linear discriminant function (LDF) has been employed extensively in population differentiation studies but is of severely ...

Discrimination with Polychotomous Predictor Variables Using Orthogonal Functions

Abstract: Three discriminant functions proposed by Bahadur (1961 a, b), Martin and Bradley (1972), and Ott and Kronmal (1976) are generalized to accommodate polychotomous predictor variables. The discrete Fourier orthogonal functions used in the generalization provide computational advantages with the use of the fast Fourier transform. Data-dependent inclusion rules for each expansion's coefficients are developed to “smooth” observed frequencies and improve discrimination. The performances of these methods are compared in a simulation study, and populations in which these rules are expected to perform well are identified.

Migration Counts and Local Weather at British Bird Observatories — An Examination By Linear Discriminant Analysis

Abstract: Linear discriminant analysis is presented as an alternative to multiple regression analysis for the study of relationships between migration counts and local weather conditions. Discriminant analysis is seen to be a useful tool for this purpose since it offers straightforward interpretations of results, and it is based on assumptions that appear to be upheld by the data.