Use Of Discriminant Functions Research Articles

Identification of origins of lesser snow geese by X-ray spectrometry

An attempt to apply computer-controlled. X-ray spectrometric methods for the identification of origins of waterfowl, through the analysis of chemical elements in their primary flight feathers, is described. Materials were gathered from three geographically distinct populations of wild lesser snow geese (Chen caerulescens). They were laundered, dried, and irradiated by 25 mCi (1 Ci = 37 GBq) Americium 241. Chemical spectra were developed using a lithium-drifted silicon detector, and a computer-controlled pulse-height analyzer that provided results in 512 channels of emission energy between about 2.3 and 40 keV. Computer programs were written or adapted to process our data. Multivariate discriminant functions were used (among other techniques) to examine potential significant differences between populations, and between different year classes within one population. Attempts were made to classify unknown feathers through use of discriminant functions. Best results were obtained by measuring the areas under K alpha peaks of emission energy for recognizable chemical elements in the spectra and using those, and the times for analysis, as significant variables. Two other methods of using the data are compared with that method. Efforts to discriminate geographically different populations, and to classify unknowns are encouraging. However, there are residual problems to be dealt with.

Use of Discriminant Function in Taxonomic Determination of Canids from Missouri

Skulls of 30 dogs ( Canis familiaris ), 29 coyotes ( Canis latrans ), 18 gray wolves ( Canis lupus ), 27 red wolves ( Canis rufus ), and 20 canids of doubtful taxonomic position were measured in 14 dimensions. Multivariate analysis showed complete separation of coyote, dog, gray wolf, and red wolf. Several unknowns fell within the parameters; others fell between and indicate hybridization. Apparent infusion of red wolf genes into the coyote population was occurring in the 1940's and 1950's as the red wolf was being exterminated in Missouri. Five of seven animals with red wolf genes were either black or associated with black animals.

Beyond averaging: The use of discriminant functions to recognize event related potentials elicited by single auditory stimuli

A test of the stepwise discriminant analysis (SWDA) procedure for assessing single-trial event related potentials (ERPs) is presented. Discriminant functions (DFs) were built from a data base composed of single-trial ERPs from sixteen subjects who were presented trains of loud and soft tones. Loud tones occurred randomly on 10% of the trials. Subjects either counted the rare-loud stimuli or solved a hidden-word puzzle. Various DFs at three electrode sites (F z, C z and P z) were obtained to assess the feasibility of performing pairwise discriminations between the various combinations of events which are defined by this procedure. For the pair of events which yielded the most striking differences between their average ERP waveforms it was possible to classify correctly, an average of 84% of the events using information from one electrode site, and 89% of the events if information from multiple electrode sites was used. A “subject-independent” DF was developed from these data and applied to data obtained from seven new subjects. This subject-independent function proved to be sufficiently generalized to classify correctly 81% of the trials. The nature of classification errors by this procedure is discussed.

Further experience with discriminant functions in differential diagnosis of hypercalcaemia

Summary Further experience has been obtained in the use of discriminant functions in the differential diagnosis of hypercalcaemia from the study of 140 new patients. The discriminant functions described in an earlier paper were derived from the results for plasma inorganic phosphate, alkaline phosphatase, chloride, bicarbonate and urea obtained from hypercalcaemic patients on admission to hospital. They indicated the correct diagnosis in ninety-two of 103 new hypercalcaemic patients (89·3%) admitted to University College Hospital and in thirty-one of thirty-seven hypercalcaemic patients at two other hospitals. Revised discriminant functions have been calculated including the erythrocyte sedimentation rate as a sixth variable. These revised functions have led to some improvement in diagnostic accuracy. The correct diagnosis was indicated in ninety-three of ninety-eight patients (94·9%) at University College Hospital and in thirty-three of the thirty-seven patients at the two other hospitals.

The nicotinic cholinergic receptor: Different compositions evidenced by statistical analysis

Summary The available acetylcholine receptor proteins from the electric organs of Electrophoridae and Torpedinidae are analysed in respect of quantitative statistical parameters. These parameters take into account the hydrophilic and hydrophobic moieties of the membrane proteins. The statistical analysis, based on the use of discriminant functions, brings out clear differences between the cholinergic receptor proteins, on the one hand, and non-membrane and loosely bound, peripheral membrane proteins, on the other. Subtle differences between the receptor proteins are also observed. The significance of the findings is discussed in the light of the physico-chemical properties of these proteins.

Studies on selection for yield in wheat. An application of genotypic and phenotypic correlations, path-coefficient analysis and discriminant functions

SUMMARYGrain yield in wheat, as in other crops, is a complex character, made up of many subcharacters. In the present investigation the study of genotypic and phenotypic correlations and path-coefficient analysis indicated that 250-grain wt. and ear number were two important component characters in wheat. Under these circumstances it would be desirable to select those plants which produce large number of tillers and very large and bold sized grains. The greater the number of tillers on a plant the greater would be the number of grains/plant. Again large and bold type of grain would obviously give higher seed wt.With the use of discriminant functions it was observed that a maximum genetic gain of 7·44% was obtained when grain yield/plant, 250-grain wt., no. of ears/plant and ear length were included in the function. This would suggest that the discriminant function is superior to straight selection in wheat. However, an expected gain of 4·13% was realized when only 250-grain wt. and grain yield/plant were taken into account. In the present analysis it appeared that relatively more emphasis should be given to grain wt. during selection. To make proper use of such characters in selection, their importance must be considered in the definition of economic worth. Progress measured in terms of yield alone will be less when the economic importance of plant type is ignored.

Is computerized diagnosis possible?

Many mathematical approaches to medical diagnosis have been tested in the past fifteen years. These approaches all have a similar mathematical basis—namely, that of pattern recognition through the use of discriminant functions. When the ten most commonly used mathematical diagnostic models are applied to the same large set of data, their diagnostic accuracy is more sensitive to variations between the diseases than variations between the mathematical models. This is not surprising given the models' close mathematical relationships. The result of the theoretical and empirical comparisons of the models suggests that in the future researchers should take a new direction—not continue experiments with increasingly sophisticated mathematical techniques. Future research should tackle the real obstacles to practical computer-aided medical diagnosis: 1. 1. lack of standard medical definitions, 2. 2. lack of large, reliable medical data bases, and 3. 3. lack of acceptance of computer-aided diagnosis by the medical profession. The author suggests the formation of a liaison group from organizations involved in operations research, computer science, information systems, and medicine to attack these problems on a national level.

A commentary on the use of multivariate statistical methods in anthropometric research.

AbstractA critical review of the increasing emphasis being placed on the use of multivariate statistical methods in anthropometric research is given. Particular attention is paid to multivariate techniques for testing hypotheses concerning mean vectors, principal components analysis and the use of discriminant functions, but some more general comments about the proper role of statistics in research are included. It is argued that multivariate techniques often do not allow the effective description and communication of the informational content of a body of data and that much additional research — both from the standpoint of theory and from the standpoint of practice — must be done before multivariate analysis can fulfill the promise it holds for the physical anthropologist.

Estimation of the multivariate logistic risk function: A comparison of the discriminant function and maximum likelihood approaches

We have considered the case in which the multivariate logistic model holds for risk of disease. That is, we assume the probability that a person with independent variable values X 1,… , x k develops the disease is given by P(X 1,…X k)=[1+e −a− ∑ i=1 k β ix i ] −1 for some constants α and β i . Truett, Cornfield and Kannel [1] have proposed the use of the linear discriminant function in estimating the coefficients α and β i. Their method is theoretically correct if the distribution of ( x 1,…, x k) is multivariate normal both for the well and for the diseased populations, with equal variance-covariance matrices in the two populations, or if the linear compound α + Σβ i x i is univariate normal for the two populations, again with equal variance-covariance matrices, where the β i are now the population values of the linear discriminant coefficients. Walker and Duncan [3] suggest an iterative procedure which gives maximum likelihood estimates for the coefficients. On theoretical grounds the maximum likelihood method is preferable, since it does not assume any particular distribution for ( x 1,…, x k) and it gives results which asymptotically converge to the proper values if the logistic model holds [5]. On the other hand, the discriminant function approach is computationally simpler and may be more convenient to apply for very large amounts or data or when computer facilities are limited. We have compared the two methods theoretically, for the case when all independent variables are of the attribute type, and empirically, using Framingham 12-yr incidence data for (1) coronary heart disease and (2) CHD death or myocardial infarction. Our results suggest the following if the logistic model holds but the normality assumptions on the independent variables are violated: 1. (a) β i which are zero will tend to be estimated as zero for large samples by the method of maximum likelihood, but not necessarily by the discrimination function method; 2. (b) if any β i are non-zero they will tend to be estimated as non-zero by either method, but the discriminant function approach will give asymptotically biased estimates for those β i and for α; 3. (c) empirically, the assessment of significance for a variable, as measured by the ratio of the estimated coefficient to its estimated standard error, is apt to be about the same whichever method is used; 4. (d) empirically, the maximum likelihood method usually gives slightly better fits to the model, as evaluated from observed and expected numbers of cases per decile of risk; 5. (e) there is a theoretical basis for the possibility that the discriminant function will give a very poor fit, even if the model holds. Of course we are not able to show that conclusion (c) will hold generally, even though it holds for our examples. Moreover, conclusion (a) warns that use of the discriminant function technique can give misleading results regarding significance. Hence, it would seem that use of the maximum likelihood method would be preferable, whenever practical, in situations where the normality assumptions are violated, especially when many of the independent variables are qualitative.

The use of discriminant functions in laboratory medicine: evaluation of phosphate clearance studies in the diagnosis of hyperparathyroidism.

Discriminant functions maximize the discriminating power of a group of laboratory tests and, in addition, offer a powerful method for evaluating the contribution of a new test to our diagnostic capabilities. In this study discriminant functions were used to evaluate the contributions of the various phosphate clearance tests in distinguishing between patients with hyperparathyroidism and control patients. The routine phosphate clearance and the phosphate-creatinine clearance ratio did not add significant information to the discriminant. A small but significant amount of discriminant power was added by either the phosphate-creatinine clearance ratio or the change in phosphate-creatinine ratios after calcium infusion. This analysis demonstrates that in difficult cases the addition of one of these two clearance tests to the usual analyses of serum calcium and phosphorus increases our diagnostic capability and provides more accurate diagnoses. For the data in this study the proposed discriminant function positively distinguishes patients with hyperparathyroidism from patients without this disease. These results demonstrate that discriminant functions can optimize diagnostic classification and, equally important to the clinical laboratory scientist, provide a formal mechanism by which to evaluate the effectiveness of any laboratory procedure.

Studies on Variation in the Number of Sterile Filaments and Its Significance in Classification of Cultivated Peanut Varieties (Arachis hypogaea, L.)

This paper dealt with the results investigated on the degree of variation in the number of sterile filaments and its classificatory significance in peanut (Arachis hypogaea, L.), using 121 cultivated varieties or strains originated from various countries of the world and Japan (Table 1). Significance of classification of varieties based on the plant type was investigated by use of discriminant function evaluated by the above character and other 3 characters of varieties (Tables 3 and 4). Results and considerations obtained are as follows: 1) The rate of appearance of "10-", "9-", and "8-anthers-flower" (0, 1, and 2 in the number of sterile filaments, respectively) was characteristic of the varietal groups classified by the plant type, with one exceptional variety. "Eight-anthers-flower" appeared predominantly in all varieties examined. However, significant much higher rate of appearance of "9-anthers-flower+10-anthers-flower" (%) was observed in the erect varieties (Spanish and Valencia types), compared with that in the prostrate and semi-prostrate ones (Virginia Runner and V. Bunch types) (Table 2 and Fig. 1). No significant differences in this values were found between the 2 types in each of the above 2 varietal groups. 2) From these results, the following conclusions were derived: i) The 2 varietal groups of the cultivated peanut, i. e. the erect type and prostrate type (including the semi-prostrate type), are different markedly in the degree of variation in the number of sterile filaments, as one of the floral morphological characteristics of this plant. In other words, the characteristic presence of 2 sterile filaments has almost being stabilized in the latter varietal group than the former one. ii) It is most presumable that the androecium having no sterile filaments is most primitive and fundamental type of the androecium of this plant. And it is of great interest to find out a relationship between varietal groups and the trend of gradual decreasing and stabilization in fertile stamen number in this plant, i. e. "10→9→8" (Table 6), in connection with the assumption on degree of primitiveness or advancement of each varietal group, viewed from the "androecium-morphology". iii) More extensive studies on the "androecium-morphology" in a number of cultivated varieties and the allied species of this plant, and survey of the plant which normally have only "10-anthers-flower" may give a clue to clear up somewhat of the problems on the origin, geographic distribution, varietal differentiation, and classification of this plant. 3) Three discriminant functions, to investigate the classification of varieties based on the plant type, were evaluated by use of 4 characters: rate of appearance of "9-anthers-flower+10-anthers-flower" (%) (x1), width of terminal leaflet (x2), pod volume (x3), and length of calyxtube (x4). High significant difference (p<0.001) in mean discriminant values was recognized only between the erect varieties and the prostrate varieties (including semi-prostrate varieties), and not between prostrate and semi-prostrate, and also between Spanish and Valencia types (Fig. 2). 4) From the above-mentioned results, it appears to be reasonable to take the plant type as the primary basic character in botanical classification of the cultivated peanut varieties.

A Quantitative Taxonomic Study or the Enderleinellus suturalis Complex (Anoplura: Hoplopleuridae)

Since the spring of 1961 the present authors have been engaged in a quantitative analytic study of the lice of the genus Hoplopleura. The data obtained from a preliminary study of Hoplopleura arboricola (unpublished) show that the populations from three species of chipmunks, Eutamias minimus, E. amoenus, and E. dorsalis, under study are distinctly different from each other when the data are analyzed by the use of discriminant functions. The use of linear discriminators using as few as five characters will serve to distinguish between members of the three populations with probabilities of misclassification in the range of 10% or less. Enderleinellus suturalis (Osborn) has been suggested to be a species complex similar to H. arboricola. For example, Werneck (1948) suggested that there might be several subspecies present in Enderleinellus suturalis (Osborn), even including E. osborni Kellogg and Ferris and E. marmotae Ferris, which are currently recognized as distinct species, distinguishable on the basis of host and locality. Ferris (1951) notes that the rather extensive materials at hand there is quite wide range of variation in various details, but a study of the material by Dr. E. F. Cook has shown no clear basis for recognizing more than one However, since Ferris's (1951) work, it has been felt by one of the authors, E. F. Cook, that the populations of lice which at the present time are known as E. suturalis (Osborn) from various species of ground squirrels differ from each other and are likely to represent different species or at least subspecies. As Ferris stated, however, there has been no clear basis for recognizing them as more than one species. As the first step, the discrimination between populations of these lice from different species of ground squirrels is here examined. Enderleinellus suturalis was first described by Osborn (1891) as Haematopinus suturalis from Citellus (Spermophilus) franklinii and C. tridecemlineatus collected at Ames, Iowa. Kellogg and Ferris (1915) put this species into the genus Enderleinellus, and designated Citellus franklinii as the type host. Ferris (1920, 1951) recorded this species from a long series of species of Citellus as follows: C. eversmanni, Altai, Siberia; C. monogolicus, Kansu, China; C. beldingi, California; C. elegans, Colorado; C. franklinii, North Dakota and Iowa; C. mollis, Nevada; C. osgoodi, near Circle, Alaska; C. townsendi, Washington; C. tridecemlineatus, Kansas, Iowa, and Oklahoma; C. madrensis (as Callospermophilus), Chihuahua, Mexico; C. nelsoni (as Ammospermophilus), California; Cynomys gunnisoni, Colorado; Cynomys leucurus, Colorado and Wyoming. In this paper three louse populations of the Enderleinellus suturalis complex from three species of ground squirrels, Citellus tridecemlineatus Mitchell, C. franklinii Sabine, and C. harrisi (Audubon and Bachman), are analyzed. The objectives of this study are to discover whether the three populations of lice found on these three host species of ground

On the Use of Discriminant Functions in Taxonomy

The most effective use of discrimninant functions presumes an expedient selection of character for measurement. Such characters should possess (a) individually, a high coefficient of discrimination, K, relating interspecific and intraspecific variability, and (b) taken in pairs, a high intraspecific correlation, with the interspecific correlation of opposite sign. A considerable increase of discrimination can be attained graphically following V. I. Romanovsky. The consideration of scatter-diagrams and correlation-ellipses suggests a new criterion, the rank of discrimination, R, whose relation to K is R = VK/2. For any two out of three species of Chaetocnema, a pair of discriminant functions, each based on three characters, provides excellent discrimination: discrimination between the species used to construct the functions and the third species is less satisfactory. Corresponding coefficients in the three pairs of functions differ appreciably, but when correlation ellipses for the three pairs are plotted, the relative positions of the ellipses for the three species are the same. New pairs of functions, whose coefficients are arithmetic or (Figure 9) geometric means of the coefficients in the separate pairs permit a clean separation of all three species in one figure. The results obtained indicate the possibility of measuring taxonomic likeness, and of developing objective criteria for the construction of a natural system of

The Use of Discriminant Functions in Biological Sampling

The Use of Discriminant Functions in Biological Sampling

The descriptive use of discriminant functions in physical anthropology.

The evolutionary status of the fossil Australopithecinae and of the fossil apes belonging to the genus Proconsul has stimulated considerable discussion. Particular attention has been paid to the teeth of the fossils, and many statements appear in the literature comparing their overall dimensions with those of human beings and of the extant great apes. By way of placing such statements on a sound basis, measurements designed to describe the main features of the teeth have been taken on series of skulls of three types of modern man (British, West African native, Australian aboriginal) and of the three living great apes (gorilla, orang-outang and chimpanzee). The statistical treatment of multivariate data of this type is considered. If p measurements are taken on a tooth, the results may be considered as points in a p -dimensional space. If we replace the original measurements by k &lt; p linear functions, we can represent the values of the functions in a space of k dimensions. We choose the linear functions so as to maintain the greatest possible separation between the populations which are being compared. These functions are the solutions of the equation (B - λ W) x = 0, when B and W are the dispersion matrices between and within populations; the latent roots λ are proportional to the between-population variances of the corresponding linear functions. The measurements were transformed to logarithms before analysis, as this rendered the within-population dispersion matrices roughly equal. It proved that all but two of the λ ’s were small for the nine teeth considered, so that the measurements could be plotted without loss of information on plane diagrams. The positions of the fossils were plotted on the same diagrams, and by computing the values of the remaining linear functions it could be tested whether the points representing the fossils in fact lay close to the planes of the diagrams. It was found that in the measurements examined, Pithecanthropus pekinensis resembled the Australian aboriginal more closely than any ape. Proconsul africanus and P. nyanzae resembled the chimpanzee more closely than any type of man. The Australopithecinae, on the other hand, differed from both men and apes. Their incisors, canines and lower first premolars resembled those of man more closely than those of any ape, whereas their molars and remaining premolars were in these features more ape-like than human. The arithmetical labour of the method of analysis adopted is very considerable and would not be practicable without the use of electronic computing equipment. The results, however, are more trustworthy and also more easily appreciated than those obtained from the alternative technique of examining the measurements one at a time.

The Analysis of Variation in a Natural Population of Lady Beetles

Biometric and taxonomic studies of quantitative characters in natural populations have led to the discovery of cases of continuous geographic variation, or lines, and of subpopulations displaying various degrees of reproductive and morphological intergradation. Because of the empirical fact that two or more natural entities may bear any degree of relationship along the spectrum of reproductive isolation, from complete intersterility to complete interfertility, regardless of their absolute or partial geographic coexistence, only an arbitrary point can be established on that spectrum for the taxonomic convenience of division of such entities into subgroups. The polytypic species concept (lVayr, 1942, Chap. 6) is a function of great subjectivity when applied to geographically separated, and especially morphologically similar, populations. The danger lies in the necessity of classifying microevolutionary units for ease of handling and in the implicit assumption by many taxonomists that such classifications reflect the true biological order of nature. Many authors have vainly sought a species definition for lack of realization of this latter point (see discussion by Gilmour, 1951). One of the most objective methods for investigating the systematic relationships between evolutionary units is that of Womble (1951), even though some subjectivity may enter the picture in the weighting of various characters. Fisher (1936) has dealt with such weightings by the use of discriminant functions. In order to apply Womble's differential systematics, a good deal of information first must be accumulated on the distribution of points on the geno-, pheno-, or ecocline. The genocline iq the most fundamental of the three and much work

The Use of Discriminant Functions in Comparing Judges' Scores concerning Potatoes

The Use of Discriminant Functions in Comparing Judges' Scores concerning Potatoes

The Use of Discriminant Functions in Comparing Judges' Scores Concerning Potatoes

The Use of Discriminant Functions in Comparing Judges' Scores Concerning Potatoes

Use of Discriminant Function in Comparison of Proximate Coal Analyses

Use of Discriminant Function in Comparison of Proximate Coal Analyses