On Selecting Variables and Assessing Their Performance in Linear Discriminant Analysis

Ganeshanandam, S.; Krzanowski, W. J.

doi:10.1111/j.1467-842x.1989.tb00988.x

Cited by 29 publications

(10 citation statements)

References 25 publications

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“…Likewise, the asymptotic tests discussed in Section 3 are not applicable in the case of a relatively small sample size and, more generally, both exact and aymptotic tests may not be applied when stepwise procedures are inappropriately employed, as in the case of confirmatory studies. However, in the case of a small sample size, alternative variable selection procedures based on estimated error rates may be used (e.g., Costanza and Afifi, 1979;Van Ness, 1979;Ganeshanandam and Krzanowski, 1989). Techniques in addressing both the problems of error-rate estimation and variable selection procedures for small samples are not further discussed because they are straightforward to apply, as in the case of standard discriminant models.…”

Section: Discussionmentioning

confidence: 98%

Generalized Covariance-Adjusted Discriminants: Perspective and Application

Kowalski²,

Randall

et al. 1997

Biometrics

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When discriminant analysis is used in practice for assessing the usefulness of diagnostic markers, the lack of control over covariates motivates the need for their adjustment in the analysis. This necessity for adjustment arises especially when the researcher's aim is classification based on a set of diagnostic markers and is not based on a set of covariates for which there exists known heterogeneity among the subjects with respect to the groups under consideration. The traditional covariance-adjusted approach is restrictive for such applications in that they assume linear covariates and a normal distribution for the the feature vector. Further, there is no available method for variable selection in using such covariance-adjusted models. In this paper, we generalize the traditional covariance-adjusted model to a general normal and logistic model, where these generalized models not only relax the distributional assumptions on the feature vector but also allow for nonlinear covariates. Exact and asymptotic tests are also derived for the problem of variable selection for these new models. The methodology is illustrated with both simulated data and an actual data set from a psychiatric study on using the Social Rhythm Metric for patients with anxiety disorders.

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Section: Discussionmentioning

confidence: 98%

Generalized Covariance-Adjusted Discriminants: Perspective and Application

Kowalski²,

Randall

et al. 1997

Biometrics

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“…Although holdout estimators of misclassification probabilities and their (co)variances have been used here, theoretically they could be replaced by leave-one-out/jackknife, bootstrap/resampling, or cross-validatory estimators (Ganeshanandam and Krzanowski 1989;Hand 1986); and their (co)variances in the derivation of z,.,. But holdout/error-count estimators will continue to be used here for the sake of simplicity in the derivation and computation of error rates and their (co)variances due to the independence of the test sample from the reference sample.…”

Section: Other Estimatorsmentioning

confidence: 99%

A Test of Additional Accuracy for Selecting Groups of Allocation Variables

Evans¹,

Schwager

1994

Technometrics

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The standardized difference in estimated Bayes risk between two subsets of groups of allocation variables is proposed as a test statistic for additional classification accuracy. This test is used in a minimal-best-subset algorithm that aims to select the optimal subset for the data at hand-that is, the smallest subset retaining most of the classification accuracy. A multivariate normal example confirms that all-possible-subsets and minimal-best discrimination procedures based on Wilks's lambda and Rao's test usually do not identify the best subsets according to estimated Bayes risk. The minimal-best discrimination subset was suboptimal in all of 100 bootstrapped samples: It contained too many groups in every case. In contrast, the minimal-best classification selected an optimal subset for 82 out of 100 bootstrap examples; appending a test of additional accuracy of the minimal-best subset versus the overall-best subset led to an optimal subset in the other 18 cases by suggesting the addition of more groups.

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“…This remark, of course, does not imply that LDF or QDF may break down in nonnormality. In fact, it is generally accepted (Marriott, 1974 andHawkins, 1981) that LDF is fairly robust to minor departures from the homoscedastic normal model, and moreover, the derivation in Fisher (1936) shows LDF to be a robust discriminant function over a wide variety of data types (Ganeshanandam and Krzanowski, 1989). Perhaps these reasons are the impetus for its use in the overwhelming majority of routine applications of discrimination.…”

Section: Introductionmentioning

confidence: 96%

A simulation study of imputation techniques in linear quadratic and kernel discriminant analyses

Bello

1993

Journal of Statistical Computation and Simulation

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The problem of incomplete training data crops up fairly frequently in discriminant analysis. A timehonoured solution is to impute (fill in) data to the missing values. Working under the assumption that missing values are missing at random (MAR), this paper examines the effects of imputed values on the classification performance of linear (LDF)-, quadratic (QDF)-, and kernel (KDF)-discriminant functions. Five deterministic imputation techniques are studied and the problem of correctly implementing these techniques is addressed using normal and non-normal data. Monte Carlo results indicate that imputed values do not affect the underlying assumptions of discriminant analyses and, as the proportion of missing values increases, the efficiency of imputation techniques depends on the implementation procedure used.

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On Selecting Variables and Assessing Their Performance in Linear Discriminant Analysis

Cited by 29 publications

References 25 publications

Generalized Covariance-Adjusted Discriminants: Perspective and Application

Generalized Covariance-Adjusted Discriminants: Perspective and Application

A Test of Additional Accuracy for Selecting Groups of Allocation Variables

A simulation study of imputation techniques in linear quadratic and kernel discriminant analyses

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