A Note on the Equivalency of Two Discrimination Procedures

Kshirsagar, A. M.; Arseven, E.

doi:10.2307/2683679

Cited by 11 publications

(6 citation statements)

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“…Farber & Kadmon 2003). Mahalanobis distances to the mean vector of a class are equivalent to Fisher’s discriminant functions (Kshirsagar & Arseven 1975).…”

Section: Methodsmentioning

confidence: 99%

Bioclimate envelope model predictions for natural resource management: dealing with uncertainty

Mbogga

Wang

Hamann

2010

Journal of Applied Ecology

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Summary1. Bioclimate envelope models are widely used to predict the potential distribution of species under climate change, but they are conceptually also suitable to match policies and practices to anticipated or observed climate change, for example through species choice in reforestation. Projections of bioclimate envelope models, however, come with large uncertainties due to different climate change scenarios, modelling methods and other factors. 2. In this paper we present a novel approach to evaluate uncertainty in model-based recommendations for natural resource management. Rather than evaluating variability in modelling results as a whole, we extract a particular statistic of interest from multiple model runs, e.g. species suitability for a particular reforestation site. Then, this statistic is subjected to analysis of variance, aiming to narrow the range of projections that practitioners need to consider. 3. In four case studies for western Canada we evaluate five sources of uncertainty with two to five treatment levels, including modelling methods, interpolation type for climate data, inclusion of topo-edaphic variables, choice of general circulation models, and choice of emission scenarios. As dependent variables, we evaluate changes to tree species habitat and ecosystem distributions under 144 treatment combinations. 4. For these case studies, we find that the inclusion of topo-edaphic variables as predictors reduces projected habitat shifts by a quarter, and general circulation models had major main effects. Our contrasting modelling approaches primarily contributed to uncertainty through interaction terms with climate change predictions, i.e. the methods behaved differently for particular climate change scenarios (e.g. warm & moist scenarios) but similar for others. 5. Synthesis and applications. Partitioning of variance components helps with the interpretation of modelling results and reveals how models can most efficiently be improved. Quantifying variance components for main effects and interactions among sources of uncertainty also offers researchers the opportunity to filter out biologically and statistically unreasonable modelling results, providing practitioners with an improved range of predictions for climate-informed natural resource management.

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“…Farber & Kadmon 2003). Mahalanobis distances to the mean vector of a class are equivalent to Fisher’s discriminant functions (Kshirsagar & Arseven 1975).…”

Section: Methodsmentioning

confidence: 99%

Bioclimate envelope model predictions for natural resource management: dealing with uncertainty

Mbogga

Wang

Hamann

2010

Journal of Applied Ecology

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“…Though predictive and separatory discrimination methods differ theoretically and operationally, they are nonetheless closely related (Williams 1982(Williams , 1983. Under assumptions described below, both approaches yield mathematically equivalent classification procedures (Kshirsager andArseven 1975, Williams 1982).…”

Section: Introductionmentioning

confidence: 99%

Assessment of Sampling Stability in Ecological Applications of Discriminant Analysis

Williams¹,

Titus²

1988

Ecology

132

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JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. A simulation study was undertaken to assess the sampling stability of the variable loadings in linear discriminant function analysis. A factorial design was used for the factors of multivariate dimensionality, dispersion structure, configuration of group means, and sample size. A total of 32 400 discriminant analyses were conducted, based on data from simulated populations with appropriate underlying statistical distributions. Ecological Society of AmericaResults from the simulations suggest that minimum sample sizes must exceed multivariate dimensionality by at least a factor of three to achieve reasonable levels of stability in discriminant function loadings. However, the requisite sample size would vary with respect to each of the design factors and, especially, with the overall amount of system variation.A review of 60 published studies and 142 individual analyses indicated that sample sizes in ecological studies often have met that requirement. However, individual group sample sizes frequently were very unequal, and checks of assumptions usually were not reported. We recommend that ecologists obtain group sample sizes that are at least three times as large as the number of variables measured.

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“…. , zd by a smaller number of canonical correlations (Kshirsagar & Arsenven, 1975). This refinement is worthwhile in the case of a large number of variables as in social sciences or in economics.…”

Section: The 'Gos' Methods Of Estimationmentioning

confidence: 99%

Chance of Misclassification in the Case of Several Normal Populations

Paek¹,

Kshirsagar²

1996

Australian Journal of Statistics

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SUMMARY When a new observation is to be classified into one of several multivariate normal populations with different means and the same covariance matrix, by Rao's method of scoring, the chance of misclassification is expressed as a multiple integral. This paper gives a practical method of obtaining reasonable approximations to this integral by using tables prepared by Gibbons, Olkin & Sobel (1977) for a different task.

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A Note on the Equivalency of Two Discrimination Procedures

Cited by 11 publications

References 0 publications

Bioclimate envelope model predictions for natural resource management: dealing with uncertainty

Bioclimate envelope model predictions for natural resource management: dealing with uncertainty

Assessment of Sampling Stability in Ecological Applications of Discriminant Analysis

Chance of Misclassification in the Case of Several Normal Populations

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