Application Of Discriminant Function Analysis Research Articles

Estimation of sex using dimensions around the metatarsal diaphyseal nutrient foramen: Application of discriminant function analysis and logistic regression models

Sex estimation equations are population-specific, and a wider use of multiple bones to generate equations will increase the accuracy of sex estimation in forensic settings. The metatarsal bones have been used previously, however the dimensions around the diaphyseal nutrient foramen have not been utilised in sex estimation. The current study aimed to determine the utility of the dimensions around the nutrient foramen of metatarsal bones in estimating sex in the South Africans of European descent (SAED). Five measurements around the nutrient foramen were taken from a total of 876 metatarsal bones (first to fifth) from 186 individual skeletons (99 males, 87 females) obtained from the Raymond A. Dart Modern Skeletal Collection. Measurements subjected to direct and stepwise discriminant function (DFA) and logistic regression (LRA) analyses included total length, distance from proximal end to nutrient foramen, circumference, and mediolateral and dorsoplantar diameters at the level of the nutrient foramen. The original classification accuracies for multivariable functions of the stepwise and direct DFA ranged from 83.1–88.3% to 85.5–88.3%, respectively. The original classification accuracies for multivariable functions of the stepwise and direct LRA ranged from 83.3%–88.7% to 86.2%–88.3%, respectively. The cross-validation classifications showed a drop of 0–2.4% for DFA and 0.2–1.1% for LRA. The width measurements were better predictors of sex than length. The dimensions around the metatarsal bone nutrient foramen exhibit sexual dimorphism in the SAED. The generated DFA and LRA functions produced high average classification accuracies which are useful in sex estimation during forensic human identification.

Forecasting of pre-harvest crop yield using discriminant function analysis of meteorological parameters

In the present paper, an application of discriminant function analysis of meteorological parameters for developing suitable statistical models to forecast wheat yield in Faizabad district of Eastern Utter Pradesh has been demonstrated. Time series data on wheat yield for 20 years (1990-91 to 2009-10) have been divided into three groups, viz. congenial, normal, and adverse based on de-trended yield distribution. Considering these groups as three populations, discriminant function analysis using weekly data of crop season on five meteorological parameters has been carried out. The discriminant scores obtained from this have been used as regressor variables along with time trend in development of statistical models. In all six procedures using weekly weather data have been proposed. The models developed have been used to forecast the wheat yield for the year 2008-09 and 2009-10 which were not included in the development of the models. It has been found that most of the models provide reliable forecast of the wheat yield about two months before the harvest. However, the model-5 has been found to be the most suitable among all the models developed.

Forecasting of Pre-harvest Wheat Yield using Discriminant Function Analysis of Meteorological Parameters of Kurukshetra District of Haryana

In the present paper, an application of discriminant function analysis of meteorological parameters for developing suitable statistical models to forecast wheat yield in Kurukshetra district of Haryana has been demonstrated. Time series data on wheat yield for 35 years (1985-86 to 2019-20) have been divided into three groups, viz. congenial, normal, and adverse based on de-trended yield distribution. Considering these groups as three populations, discriminant function analysis using weekly data of crop season on five meteorological parameters has been carried out. The discriminant scores obtained from this have been used as regressor variables along with time trend in development of statistical models. In all six procedures using weekly weather data have been proposed. The models developed have been used to forecast the wheat yield for the year 2017-18 and 2019-20 which were not included in the development of the models. It has been found that most of the models provide reliable forecast of the wheat yield about two months before the harvest. However, the model-5 has been found to be the most suitable among all the models developed.

Sexual dimorphism of foramen magnum: An Egyptian study

BackgroundHuman identification is of a paramount forensic concern. It includes sex determination which becomes extremely complex and tricky especially in fragmentary remains.Purpose of the studyWe aimed to evaluate the accuracy of ten dimensions of foramen magnum (FM) and occipital condyles in determination of sex among 367 subjects (204 females and 163 males), their ages ranged between 18-75 years. Multislice Computed Tomography images of skulls of the studied patients were obtained from the Radiology Department. Ten different anatomical variables of the FM were measured by two independent experienced radiologists blinded to the study.ResultsFM dimensions are unique and show significant sexual dimorphism in the studied Egyptian population especially with application of discriminant function analysis. These landmarks include foramen magnum length and width (FML, FMW), FM index, FM area, length of the right and left occipital condyles (LROC, LLOC), width of the right occipital condyle (WROC), maximum bicondylar distance (MBD) and minimum intercondylar distance (MnICD). LROC and FMW are highly significant discriminating variables predicting sex.ConclusionsIt is concluded that all the studied FM parameters showed significant differences between males and females except the left occipital condylar width with higher male values when compared to females. Additionally, the right occipital condylar length and FM width are highly significant discriminating variables which are strongly beneficial in prediction of sex. FM dimensions would provide a reliable additional tool for identification of sex among adult population and could be specific for Egyptians in case of fragmentary remains or damaged skulls.

Pre-harvest forecast of pigeon-pea yield using discriminant function analysis of weather variables

In the present paper, an application of discriminant function analysis of weather variables (minimum & maximum temperature, Rainfall, Rainy days, Relative humidity 7 hr & 14 hr, Sunshine hour and Wind velocity )for developing suitable statistical models to forecast pigeon-pea yield in Faizabad district of Eastern Uttar Pradesh has been demonstrated. Time series data on pigeon-pea yield for 22 years (1990-91 to 2011-12) have been divided into three groups, viz., congenial, normal, and adverse based on de-trended yield distribution. Considering these groups as three populations, discriminant function analysis using weekly data on eight weather variables in different forms has been carried out. The sets of discriminant scores obtained from such analysis have been used as regressor variables along with time trend variable and pigeon-pea yield as regressand in development of statistical models. In all nine models have been developed. The forecast yield of pigeon-pea have been obtained from these models for the year 2009-10, 2010-11 and 2011-12, which were not included in the development of the models. The model 4 and 9 have been found to be most appropriate on the basis of R2adj, percent deviation of forecast, percent root mean square error (%RMSE) and percent standard error (PSE) for the reliable forecast of pigeon-pea yield about two and half months before the crop harvest.

Estimation of crop production for smaller geographical area: An application of discriminant function analysis

ABSTRACTCrop production statistics for small areas like Community Development Blocks (generally referred to as blocks) and panchayat level (smaller than blocks) have become essential in view of policy formulation for making development plans at the micro level in India. Presently, the crop production or yields through crop-cutting experiments (CCES) are obtained at the district level and these estimates are aggregated at the state and the country level. Conducting the requisite number of CCEs for a specific area is neither operationally feasible nor economically viable. Following the prediction approach of Singh et al. (2012), we have explored an application of discriminant function analysis of the auxiliary variables related to crop yield for estimation of crop production at the block level in this article. Time-series data on crop yield, along with auxiliary variables, have been used in the study. The discriminant scores obtained from estimated discriminant functions have been used as an explanatory var...

Identification of Pollution Sources and Classification of Apulia Region Groundwaters by Multivariate Statistical Methods and Neural Networks

<abstract><title><italic>Abstract.</italic></title> Multivariate statistical techniques, including discriminant function analysis (DFA), cluster analysis (CA), principal component analysis (PCA), absolute principal component score (APCS), and radial basis function neural network (RBF-NN), were applied to a data set formed by 905 samples and 15 parameters, including pH, electrical conductivity (EC), total dissolved solids (TDS), dissolved oxygen (O₂), chemical oxygen demand (COD), Na⁺, Ca²⁺, Mg²⁺, K⁺, Cl^-, NO₃^-, SO₄^2-, HCO₃, and vital organism at 22°C and 36°C, of groundwater samples collected in the Apulia region (southern Italy). Among all collected samples, only samples showing values for all parameters were used to compose the data set on which the multivariate statistical techniques were applied. PCA and APCS allowed us to identify, for each province as well as the sites diverging from the main cluster, the pollution sources pressuring the sampling sites investigated: they were identified as fertilizer applications, the use of unpurified irrigation water, marine water intrusion, and calcareous characteristics of the soil. We found that the groundwater pollution sources pressuring the sites were similar among the five Apulian provinces (Foggia, Bari, Brindisi, Lecce, and Taranto). Moreover, for each province, marine water intrusion showed the highest contribution. The application of DFA to the data set allowed us to obtain good results in discriminating among four provinces, with the exception of Taranto. The model also gave good performance results in forecasting. However, RBF-NN provided more accurate results than DFA and confirmed that EC had the greatest relative importance. This is probably due to the different salinity among the sites (Na⁺ also showed good discriminant importance). In fact, with PCA and APCS, it was possible to observe that EC, together with Na⁺, Cl^-, and TDS, was the parameter that most often showed high loading values, and the scattered samples with these loading values were collected at sites in which marine water intrusion had been hypothesized. The results obtained by multivariate statistical methods can be useful both in guiding stakeholders and in providing a valid tool to authorities for assessing and managing groundwater resources.

Multivariate statistical analysis for race variation from foot anthropometry in the Malaysian population

Dismembered human remains are frequently found in cases of mass disasters and criminal mutilation. In order to establish personal identity, race is among the major categories of the basic biological profile, apart from sex, age, stature, anomalies and pathologies. This is the first systematic study conducted for the assessment of race variations in the Malaysian population from foot measurements. In the present study, 232 Malay (112 males and 120 females) individuals, 213 Chinese (107 males and 106 females) individuals and 204 Indian (102 males and 102 females) individuals (all consenting) who were 20 to 69 years old were randomly selected and their stature, foot length and foot breadth were measured. This study investigated the application of discriminant function analysis, principal component analysis and hierarchical cluster analysis to assess the variations in stature and foot dimensions in the Malay, Chinese and Indian subpopulations in Malaysia. Foot measurements are found to yield important predictive information about an individual's race in the Malaysian population.

Classification of fish and non-fish acoustic tracks using discriminant function analysis

Abstract Xie, Y., Michielsens, C. G. J., and Martens, F. J. 2012. Classification of fish and non-fish acoustic tracks using discriminant function analysis. – ICES Journal of Marine Science, 69: 313–322. Hydroacoustic data acquired for estimating fish populations contain information on both fish and non-fish targets, so sonar technicians traditionally rely on their knowledge of fish behaviour and experience with hydroacoustics to remove non-fish targets from the hydroacoustic data. This process is often labour-intensive and time-consuming, making real-time assessment of fish populations difficult. Simple solutions are not always available for all circumstances. However, the split-beam sonar data collected in the lower Fraser River, British Columbia, Canada, showed distinct signatures between actively swimming fish and non-fish objects such as drifting debris, surface bubbles, and stationary objects in the water column and off the river bottom. Acoustic tracks of fish and non-fish targets were characterized by differentiable statistical patterns that were amenable to discriminant function analysis (DFA). An application of DFA to segregate fish and non-fish targets detected by a split-beam sonar system in the lower Fraser River is presented, characteristics of user-identified fish and non-fish acoustic tracks being utilized as learning samples for the DFA. Also, a method to rank the discriminating power of individual variables is presented, providing guidance for constructing efficient and effective discriminant functions with variables that offer high discriminating power. The DFA yielded classification accuracies of 96% for fish and 91% for non-fish tracks and reduced the manual sorting time by 50–75%.

Sex determination by discriminant function analysis of palatal rugae from a population of coastal Andhra.

Objective:The aim of the study was to investigate differences in the palatal rugae patterns in males and females of a cross-sectional hospital-based coastal Andhra population and application of discriminant function analysis in sex identification.Materials and Methods:One hundred pre-orthodontic plaster casts, equally distributed between males and females belonging to an age range of 15-30 years, were examined for different rugae patterns. Thomas classification was adopted for analysis. Association between rugae patterns and sexual dimorphism were tested using Unpaired t test, Chi square test and discriminant function analysis developed using SAS package.Results:Difference in unification pattern among males and females was found to be statistically significant. The total number of the rugae was not statistically significant between the sexes. Association between rugae length and shape with sex determination was computed using discriminant analysis which enabled sex differentiation in this population with an accuracy of 78%.Conclusion:Palatal rugae revealed a specific pattern in unification among males and females of the coastal Andhra population. Discriminant function analysis enabled sex determination of individuals. However, these interpretations were precluded by the small sample size and further research work on larger samples and use of different classification systems is required to validate its use in forensic science.

Wine differentiation of vineyard management regimes

The possibility of discrimination between wines was examined based on different vineyard management regimes as a potential source of differences in wine quality. The analysis covered three years in a Chardonnay vineyard, where different irrigation and fertigation regimes were applied. The basis for wines differentiation was measurements of selected volatile organic compounds in wines (GC-MS) and wine sensory assessment using 20-point wine quality scale. It was shown that wine differentiation could be successfully performed based on measurements of selected volatile alcohols and esters in wine with the application of Discriminant Function Analysis (DFA). Also, sensorial assessment could provide for some wine differentiation between vineyard treatment regimes. Both approaches, the instrumental and sensorial, could be successful in wine discrimination, provided single vintage is considered.

Employer-Based Facilitators of Return to Work Following Disabling Injury

AbstractPostinjury vocational achievement is an important index of successful vocational rehabilitation. This study involved the identification of factors reported to facilitate labour-force participation of people with spinal cord injury (SCI) who, even though lacking the personal characteristics found to correlate with labour-force participation, were actually members of the labour force. The empirically identified subjects comprised the 20 most extreme prediction errors from the application of discriminant function analysis, which was conducted with the aim of predicting vocational achievement (in the labour force vs. not in the labour force) following SCI. Subjects were interviewed to gain an understanding of their explanations for their erroneously predicted labour-force status. Principal factors nominated as most influencing the postinjury labour-force achievements were the assistance of family, friends and representatives of preinjury employers. Implications of these findings for the delivery of rehabilitation services are presented, including the need for more community-based and employer-related services.

A statistical approach for the integrated analysis of mine induced seismicity and numerical stress estimates, a case study—Part II: evaluation of the relations

Integrated analyses at a number of underground operations have suggested that qualitative relations may exist between microseismic variable values estimated in real-time from mine seismic systems and the stress estimates provided by numerical models. In this study, multivariate statistical techniques were used to evaluate whether quantitative relations could be formed using data from the Creighton Mine in Sudbury, Ontario. It is believed that if sufficiently reliable relations could be developed, they might then be exploited to better characterize the state of the rock mass and provide insight beyond what could be obtained from either data set in isolation. This insight could then be used to eventually impact both short- and long-term mine design decisions. This paper represents the second part of a two part series and describes the evaluation of the 11 statistically significant relations that were formed in the first paper between variables within the stress and seismic databases. Specifically, the model adequacy and the stability of each relation was evaluated. In addition, the prediction capabilities of each relation were evaluated and the relations were interpreted relative to prior experience and physical theory. The results of this component of the study indicated that all but three of the developed relations met the statistical requirements for relations of this type and all were shown to be quite stable. In terms of prediction, it was demonstrated that this could best be achieved through the application of Discriminant Function Analysis. This technique was shown to be capable of suggesting which events were generated under relatively high-stress conditions, though the technique was less successful at correctly identifying events generated under lower stress conditions. Interpretation focussed on the relation between the stress conditions at the source and two particular variables from the seismic database and concluded that the observed variations in source strength were primarily controlled by spatial variations in confinement. The importance of a rigorous methodology was also discussed, as was potential ways in which the relations of the types formed in this study could impact mine design decisions.

Volcanic rocks of the witwatersrand triad, south Africa. I: Description, classification and geochemical stratigraphy

The Witwatersrand triad contains thick volcanic sequences confined largely to the Dominion Group at the base and the Ventersdorp Supergroup at the top. These volcanic sequences are of late-Archaean to early-Proterozoic age and are amongst the oldest supracrustal volcanic sequences erupted onto the Archaean Kaapvaal craton. The volcanic rocks have suffered low-grade greenschist facies metamorphism but primary textures and, in some samples, primary mineralogies are well preserved. Major and trace element analyses of a large number of samples of volcanic rocks from boreholes in the Klerksdorp area, Western Transvaal, indicate that the chemical compositions of the lavas are largely unmodified by secondary processes and can be used for classification, stratigraphic studies and petrogenetic interpretation. The volcanics of the Dominion Group are a bimodal tholeiitic basalt-rhyolite association with considerable compositional variation from basalt to tholeiitic andesite within the basaltic suite. The Ventersdorp Supergroup is a weakly developed bimodal tholeiitic basalt-dacite suite. Basic rocks in the Klipriviersberg Group at the base and in the overlying Platberg Group are largely basaltic, whereas those of the Allanridge Formation at the top are largely tholeiitic andesites. Within the Klipriviersberg Group the more primitive samples occur at the top of the sequence. Phenocryst-rich porphyries of the Makwassie Formation in the Platberg Group are largely of dacitic composition and have textural features suggestive of an ash flow origin. A distinct geochemical stratigraphy is present within the volcanic sequences and application of discriminant function analysis and an empirical discrimination grid based on ratios of immobile elements P, Ti, and Zr allows for unknown samples to be placed within their correct stratigraphic unit.

Discriminant function strategies for the kindergarten prediction of reading achievement

Abstract The present paper evaluates the application of discriminant function analysis to predictive strategies developed for the kindergarten prediction of reading achievement by the Florida Longitudinal Project. In an attempt to optimize the predictiveness of these classification equations, several problems arose that provide important information concerning the application of discriminant analysis to early detection research. These problems highlight the importance of carefully examining (a) statistical assumptions underlying discriminant analysis; (b) the statistical nature of the data and sample employed; and (c) alternative applications of discriminant analysis when certain assumptions cannot be met. Early detection research has considerable relevance for clinical neuropsychology, provided appropriate application of predictive tools is made. The results of the present study show that careful evaluation of the application of discriminant analysis is crucial for reliable prediction. In addition, it is...

Petrologic provinces in Jurassic tholeiites of Gondwanaland

Application of discriminant function analysis to the Jurassic tholeiites of Gondwanaland allows delineation of three petrologic subprovinces. TiO2 is the most important element in discrimination and a combination of TiO2 and P2O5 was found to be the most suitable. Tholeiites in the foredeep of the Gondwanide fold belt are distinctly different in minor-element composition from those in zones of deep fracturing associated with the Nuanetsi rift-rift-rift triple junction in southern Africa. Intermediate basalt types are found in areas of regional tension not associated with rifted plate margins. The minor-element composition of tholeiites is dependant upon the depth (pressure) from which the magma was tapped and is closely related to prevailing regional tectonic environments.

The Application of Discriminant Function Analysis to Correlated Samples

A method of applying the discriminant function to correlated samples was discussed for the researcher interested in utilizing multivariate statistics to pre-post data. By finding the linear combination that maximizes differences in the groups, the t-statistic can be computed for correlated samples.

Application of discriminant function analysis to the felsic rocks of the Bushveld Complex, South Africa

The technique of multivariate analysis was used to investigate the geochemical relationships between the felsic rocks of the Bushveld Complex. The Bushveld granite and Rooiberg felsite form two distinct geochemical groups based on their major element compositions, possibly indicating that they originated from separate and genetically unrelated magmas. A discriminant function based on six major oxides was found to be 90 percent effective in distinguishing between the two groups. These conclusions have important implications for the petrogenesis of the Bushveld Complex.

A Quantitative Method of Expressing Flex-Cracking Results

Abstract In addition to providing a means of obtaining accurate quantitative results for individual flex-cracking tests, such as the De Mattia or Du Pont tests, the application of discriminant function analysis suggests a basis for standardizing the entire test method, so that objection to the test for specification purposes is thus concerned only with the reproducibility of the results, a problem which can now be investigated with greater confidence and ease. In connection with the accuracy of the method it may be contended that much depends on the subjective attitude of the tester who grades the samples with the photographs. When half-scores were not employed, the accuracy was limited mainly by the coarseness of the scale. This suggests that the grading is objective and, although no comparison, based upon statistical methods, has been made to determine the discrepancies between operators, no circumstance has occurred to suggest that important divergencies of opinion do exist. In addition, the analysis has been repeated on a further series of fifty samples, and the values found for the scoring constants were not substantially different from those obtained in this investigation. There is thus good reason to believe that this method of assessing the results will form a valuable means of investigating the causes of variation in flex-cracking test results and of recording the conclusions from the tests. The author wishes to thank the Board of Management of the Research Association of British Rubber Manufacturers for permission to publish the results given in this paper.