Nonmetric Data Research Articles

Elements of Dual Scaling: An Introduction to Practical Data Analysis.

Quantification methodology of categorical data is a popular topic in many branches of science. Most books, however, are either too advanced for those who need it, or too elementary to gain insight into its potential. This book fills the gap between these extremes, and provides specialists with an easy and comprehensive reference, and others with a complete treatment of dual scaling methodology -- starting with motivating examples, followed by an introductory discussion of necessary quantitative skills, and ending with different perpsectives on dual scaling with examples, advanced topics, and future possibilities. This book attempts to successively upgrade readers' readiness for handling analysis of qualitative, categorical, and non-metric data, without overloading them. The writing style is very friendly, and difficult topics are always accompanied by simple illlustrative examples. There are a number of topics on dual scaling which were previously addressed only in journal articles or in publications that are not readily available. Integration of these topics into the standard framework makes the current book unique, and its extensive coverage of relevant topics is unprecedented. This book will serve as both reference and textbook for all those who want to analyze categorical data effectively.

Automating the quantitative analysis of 2-D neural dendritic trees

Neurons in the central and peripheral nervous system vary widely in their dendritic branching patterns. Quantification of the morphological characteristics used to identify different classes of neurons and relate neural structure to function requires that accurate metric and non-metric data be obtained from neural images obtained by camera-lucida drawing or from digitized video images made with transmitted, fluorescence or confocal microscopy. This paper describes a largely automated procedure for determining the dendritic tree structure of largely planar cells (such as retinal ganglion cells or cells in tissue culture monolayers) from an initial pictorial representation or digitized image. From this structure, non-metric data (such as the ordered ‘tree’ of branches) and metric information (such as total dendritic length and dendritic field area) can be automatically computed. The use of this method is specifically illustrated in the capture of the dendritic tree structure of retinal ganglion cells from the rabbit retina.

Skeletal Morphology of the Okhotsk People on Sakhalin Island.

Morphological data of human skeletal remains of the prehistoric Okhotsk culture in Sakhalin were presented. The Okhotsk people in Sakhalin are quite similar to the Okhotsk people in Hokkaido in terms of not only cranial metric and nonmetric data but also limb bone measurements. The Sakhalin Okhotsk people show a close affinity in morphology with peoples in the northern Sakhalin and Amur Basin and differ from the Ainu in Hokkaido and Sakhalin.

The Origin and Microevolution of Ainu as Viewed from Dentition: The Basic Populations in East Asia. VIII.

Metric and non-metric dental variation among several Ainu samples was analyzed. Recent Ainu samples from Hokkaido and Sakhalin form a tight cluster. The sample from the people of the Okhotsk culture, or Omisaki sample, shows a quite dispersed arrangement. Extending the comparisons to include East and Southeast Asian and the Pacific samples validates the relatively homogeneous dental pattern of recent Ainu. The Omisaki sample has dental characteristics similar to those of sinodont populations. Discriminant function analyses based on metric and non-metric data indicate that some Omisaki individuals are classified as part of the members of sundadont populations, and others as those from sinodont populations. These findings suggest that the people of the Okhotsk culture were likely migrants from the north. However, they might have exerted little genetic influence on the formation of the physical characteristics of recent Ainu. The results obtained in the present study re-confirm that Ainu may be direct descendants of the Neolithic Jomon people. They share the ancestral ties with the generalized Asiatic populations, as represented by Negritos. It is quite likely that members of the late Pleistocene Sundaland populations could have colonized the continental shelf of East Asia, extending to Hokkaido and Sakhalin in the north and western Micronesia and Polynesia in the east.

Morphological Data on the Skeletons of the KANASEKI-Family.

Metric and non-metric data on the skeletons of the KANASEKI-family, the late Dr. T. KANASEKI and his father, Mr. K. KANASEKI, are presented. Photographs of bones are also shown in plates.

Cortical asymmetries in frontal lobes of Rhesus monkeys ( Macaca mulatta)

Cortical sulci were digitized and their lenghts determined with 3-dimensional computer technology on 335 endocranial casts from rhesus monkeys with known maternal genealogies, ages at death, and sex. Non-metric data were also collected from 403 endocasts. Frontal lobes were directionally asymmetrical with lengths of the left central, right rectus (principal), and right lateral orbital sulci significantly longer. The positions of the medial and lateral ends of the central sulcus were significantly different in the two hemispheres, and there was significant protrusion of the frontal lobe (petalia) on the right side. Together, these data indicate elongation of the right orbital and dorsolateral frontal lobe. The asymmetries reported here probably involve short-term memory for visual information. This raises interesting questions about the extent to which macaques are right hemisphere dominant for processing visual information as compared to humans.

Cosomys primus: a case for stasis

The first lower molar length, width, and posterior loop width were analyzed for tenCosomys primuspopulations from horizontal deposits ranging in elevation from 3,000 to 3,295 feet. Sedimentation rates based on radiometric dates for two ashes and rates derived in previous studies suggest that these sediments span an interval of time that ranges from 45,000 to 164,000 years ago. Nonmetric data included the presence of enamel pits, prism folds, and crenulations; the number of triangles; and relative dentine tract heights. Coefficients of variation for the metrics were low, 4 to 7, and a one-way ANOVA revealed no significant differences between any of the populations. Changes in the mean phenotype were less than two phenotypic standard deviations and were not correlated with elevation. The presence of enamel pits, prism folds, and crenulations correlated only with less occlusal wear.Thus, these microtine rodent populations appear to exhibit stasis over a time period of at least 45,000 and possibly as much as 164,000 years, unless the deposits accumulated more rapidly than previously estimated.

Interspecific relations of African crocidurine shrews (Mammalia: Soricidae) based on multivariate analysis of mandibular data

Eighteen graded non-metric characters and 30 measurements of the mandible and lower dentition were used to investigate the grouping of African species of the genera Crocidura, Suncus and Sylvisorex. Seventy-seven taxa (species, subspecies and synonyms), including four European species, were represented by one to nine mandibles (147 mandibles in all), and the means of four Pleistocene African species were also included. The metric data were subjected to principal component and canonical variate analyses, and the non-metric data to principal component analysis. Grouping was detected by comparing the results of the three analyses. Six groups are recognized within the genus Crocidura, typified by C. fumosa, C. turba, C. russula, C. fuscomurina, C. hirta and C. flavescens. Sylvisorex is divisible into two groups, typified by S. lunaris and S. granti. The African species of Suncus (but not the introduced species, S. murinus) form a single group, which is linked to the Sylvisorex granti group. Suncus is closely related to, or convergent with, the Crocidura fuscomurina group. The first non-metric principal component, the second metric principal component and the second canonical variate are significantly correlated. It is considered that these together represent a general trend of evolutionary advance. Phylogenetic relations are discussed in the light of this; Crocidura may be diphylefic.

Comparative studies of dental characteristics in the Aogashima islanders.

Metric and non-metric data of the dental traits of the Aogashima Islanders were compared with those from the Honshu Japanese (Tokyo and Kyoto areas), the Okinawa Islanders, the Ainu, the Jomon and the Yayoi populations using multivariate analysis methods. The overall tooth size of the Aogashima Islanders is closest to the Tokyo residents, larger than the Jomon population, the Okinawa Islanders and the Ainu, and smaller. than the Yayoi population. On the other hand, the Aogashima Islanders are similar to the Okinawa Islanders in the shape factors of the tooth crown measurements. In the non-metric dental characters, the Aogashima Islanders show a closer affinity to the Okinawa Islanders than to any other populations compared. As a whole, the Aogashima Islanders are similar to the Jomon population as well as those who show close affinities to the latter, and largely differ from the Yayoi population in dental morphology. This finding seems to suggest that the dental traits in isolated populations such as the Aogashima Islanders may give important informations about the geographic variations which are supposed to reflect the history of formation processes of the Japanese population.

Towards a New Approach to Vision: Applications to Robots and Humans

A description of a novel and very speculative approach to new research directions for human vision with application to robotic vision is described. The goal of the approach is to propose a plausible, implementable, spatial perception model for human vision and apply this model to a stereo robot vision system. The model is based on computer algorithms variously called “Multidimensional Scaling”, well known in psychology and sociology but relatively unknown in engineering. These algorithms can reconstruct a spatially accurate model to a high level of metric precision of a “configuration of points” from low quality, error prone non-metric data about the configuration. ALSCAL – a general purpose computer package adaptable for this purpose is being presently evaluated. This is a departure from typical engineering approaches which are directed toward gathering a low volume of highly precise referenced data about the positions of selected points in the visual scene and substitutes instead an approach of gathering a high volume of very low precision relative data about the interpoint spacings. It would seem that the latter approach is the one actually used by the human vision system. The results are highly encouraging in that the agreement between test configurations of two and three dimensional configurations of points are very faithfully reconstructed from as low as 10 points in a configuration using only rank ordered (i.e. nonmetric) information about interpoint spacings. The reconstructions are remarkably robust even under human-like “fuzzy” imprecision in visual measurements.

The use of nonmetric variation in estimating human population admixture: a test case with Brazilian blacks, whites, and mulattos.

Measurements in populations which serve as valid indicators of biological relationship should be proportional to genetic distance. In order to test the utility of discrete cranial traits for estimating genetic distances among populations, estimates of admixture are obtained for gene frequency data and nonmetric cranial data in São Paulo mulattos (M). The gene frequency data serve as a control that the three populations are related as stated: estimates of admixture are obtained by using São Paulo whites (W) and blacks (B) as parental populations and by estimating the parameter of admixture, m, in the model pM = (1 - m) pW + mpB (Elston, 1971) where the p's are either gene frequencies or nonmetric trait frequencies. A test of goodness of fit of the model provides a means of ascertaining whether or not the data fit this linear model. While the gene frequency data indicate distances among the three populations which are highly compatible with the linear model of admixture, the nonmetric data show significant deviations from the model. This implies that the frequencies of the nonmetric traits in the populations used in this analysis are not a linear function of genetic distance. This discourages the use of nonmetric traits in making quantitative conclusions about genetic relationships. It also suggests the need for investigation of the use of other skeletal characters for estimating genetic distance, as well as approaches for such investigations through the study of hybrid individuals.

Multivariate Modellbildung für metrische Daten

Abstract The application of multiple regression and path analysis is discussed in regard to the exclusive use of the beta coefficients. Beta is one of the possible ways of controlling for the effects of the remaining predictors, others are part and partial correlation, part and partial covariance. A typology is developed for the difference between total and controlled effect. With this instrument (for controlled effect = beta) it can be shown under which conditions the sum of the total explaining power (r2y,xi) and the sum of the additional explaining power (Part correlation2) do exceed or not Multiple R2. By the criteria of sign rule and of the relative advantages of the decomposition of total effect in controlled effect and rest effect it is argued that beta is still the best way (of those considered) of control. Next some problems of the otherwise recommended LISREL approach are discussed: Estimation, data-fitting versus model test, model-fitting, standardization. Finally some parallels between models for metric and models for non-metric data are specified.

The Pipestem Burial: An Archaic Interment from Southeastern North Dakota

The Pipestem burial is the oldest known burial site in North Dakota. Radiocarbon assay dates the site at ca. 3500 B.P., a date which falls within the Archaic Period. Geomorphological conditions at the site tend to corroborate the date as do several other factors. Although limited, skeletal metric and non-metric data from the multiple interment compare favorably with other Archaic burials. Erosion at the site badly disturbed the burial context, thereby hampering definitive statements on the mode of burial. Despite this, comparative burial mode data from the region and elsewhere on the Great Plains are discussed.

The Contingency Periodogram: A Method of Identifying Rhythms in Series of Nonmetric Ecological Data

(1) Analysis of series, in time or space is a subject of growing interest in ecology, but the methods hitherto available (correlogram, periodogram, spectral analysis) were restricted to the analysis of metric (quantitative) data. Many ecological series, however, are of (or contain) essential variables which are qualitative (categorical), and many quantitative variables are more efficiently sampled as rank-ordered (ordinal) variables. There are no numerical methods to analyse series of nonmetric data. (2) In this paper, the periodogram of Whittaker & Robinson is generalized to qualitative data series, using information theoretic measures. Algorithms are also described to partition rank-ordered variables into classes, in order to analyse them using the contingency periodogram. (3) The validity of the contingency periodogram is assessed by comparing its results with those of the periodogram of Schuster, using two series of metric data. Both methods identify the same periods for a series of artificial data, and also for serial measurements of the photosynthetic capacity of estuarine phytoplankton, even when these metric data are reduced to a small number of states prior to contingency periodogram analysis. (4) The contingency periodogram is also used to analyse a multivariate (multi-species) phytoplankton series. The multivariate data are reduced to a single multi-state qualitative variate by clustering the samples. At least one of the periods revealed is surprising, but can be explained.

Sampling distributions of kruskal's measure of stress for an asymmetric matrix

In the past ten years multidimensional scaling of nonmetric data has been widely applied in behavioral and business research. This paper investigates the asymmetric data matrix and develops stress distributions based upon a null hypothesis of equal like­lihood in the ranking of a set of proximities.

The Analysis of Nonmetric Data

This article explores the statistical properties as well as the substantial interpretation of coefficients arrived at by usual regression procedures when the de pendent variable is a dichotomy. Some practical advice is offered on how this traditional technique can be used as a proxy to the more refined approach suggested by Grizzle, Starmer, and Koch.

Alternating Least Squares Optimal Scaling: Analysis of Nonmetric Data in Marketing Research

The authors discuss and illustrate the advantages and limitations of a family of new approaches to the analysis of metric and nonmetric data in marketing research. The general method, which is based on alternating least squares optimal scaling procedures, extends the analytical flexibility of the general linear model procedures (ANOVA, regression, canonical correlation, discriminant analysis, etc.) to situations in which the data (1) are measured at any mixture of the nominal, ordinal, or interval levels and (2) are derived from either a discrete or continuous distribution. The relationship of these procedures to traditional linear models and to other nonmetric approaches (such as multidimensional scaling and conjoint analysis) is reviewed.

Alternating Least Squares Optimal Scaling: Analysis of Nonmetric Data in Marketing Research

Alternating Least Squares Optimal Scaling: Analysis of Nonmetric Data in Marketing Research

Solutions to some nonlinear equations from nonmetric data

A method is presented to provide estimates of parameters of specified nonlinear equations from ordinal data generated from a crossed design. The analytic method, NOPE, is an iterative method in which monotone regression and the Gauss-Newton method of least squares are applied alternatively until a measure of stress is minimized. Examples of solutions from artificial data are presented together with examples of applications of the method to experimental results.

Errata: The Adequacy of Non-Metric Data in Geology: Tests Using a Divisive-Omnithetic Clustering Technique

Errata: The Adequacy of Non-Metric Data in Geology: Tests Using a Divisive-Omnithetic Clustering Technique