Statistical analysis of fuzzy-set data from neuronal networks

In this study, we describe the process of transforming neuron polarization values that meet the assumptions of ratio data into ordinal data. This is a crisp-to-fuzzy set transformation. A computerized simulation of the application of this process is discussed and nonparametric methods of analyzing fuzzy-set data are presented.     

Statistical analysis of binary relational data: Parameter estimation

Binary interaction data, measuring the presence or absence of a relation between pairs of actors in a “dyadic interaction situation,” are commonly gathered to study the social structure of the group of actors. Recent developments have made the statistical analysis of such data statistically easier and more substantively sophisticated. These developments allow researchers to simultaneously study several sociometric structural properties, such as reciprocity, differential popularity, and equivalence of actors. Building on this research, we review the stochastic models responsible for this breakthrough, and discuss methods for estimating expected values and model parameters. Throughout, we also highlight recent advances designed to incorporate nodal or actor attribute data into the relational data analysis. We conclude with an example illustrating these ideas based on conversational activities among actors in a group of eight people.     

Frog skin,time series,and other kinds of data: Nonisomorphic representation and analysis

Representational art is spatially congruent, or isomorphic, with objects in the world. In other words, they are the same in some important way. But not all representation is isomorphic. Data graphs are a type of nonisomorphic representation. A major goal of data graphs is to facilitate the rapid comprehension of differences or relations. This is done by providing a kind of analogy between something that can be “seen” (the relative heights of points) and some relevant information. This article discusses some rules about data graphing, then some new visualization tools are briefly critiqued.     

Processing locational and orientational information

In choice reaction time (RT) tasks, college students verified the truth of displays expressing spatial relations between two objects. The relations werelocational (A is left of B) ororientational (A and B are horizontal). The objects were names of states in the United States, symbols, or letter arrays. The objects were memorized prior to the display (states and letters) or were presented as part of the display (symbols and letters). In the location tasks with both states and symbols, locatives were spatial (right, left, above, below) or compass (north, south, east, west). Distance between states was also varied. When location was judged, horizontally aligned stimuli resulted in slower responses than vertically aligned stimuli, independently of materials and locative set. Reaction time was inversely related to distance. When orientation was judged, responses to horizontal pairs of states were slower than responses to vertical pairs of states, responses to horizontal pairs of letters were faster than responses to vertical pairs, and RT did not depend upon the orientation of symbols. This pattern of results suggests that orientational judgments are influenced by type of materials and the entext to which the material has been encoded (i.e., memorized). Locational judgments reflect a potent source of difficulty not present in orientation tasks, namely, telling left from right. Alternative explanations of the right-left effect are discussed.     

An analysis of generative representation systems

Three ideas are basic to generative theory: (a) Subjects are assumed to attend to the relations among stimuli, extracting the transformations relating pairs of stimuli; (b) the set of abstracted transformations is decomposed or reduced to an elementary set of generators; (c) subjects use the elementary generators as the basis for judging similarity. The purpose of this paper is to illustrate these ideas with an experiment in which subjects were asked to rate the similarity between stimulus pairs. The stimulus materials consisted of the permutations of a 4-item pattern with the properties of a dihedral group which insured the existence of sets of elementary transformations. Three analytic techniques were used to determine the generator set of transformations abstracted by subjects. The first analysis consisted of a monotonic regression between dissimilarity ratings and the number of elementary generators of a given permutation. The residual variance of this monotone regression, suitably normalized, was used as a quantitative goodness-of-fit measure. For the stochastic analysis, cumulative distributions of dissimilarity ratings were obtained for permutations requiring one, two, or three generators. The idea was that permutations requiring fewer generators should be associated with distributions of lower dissimilarity values (higher similarity scores) as compared to permutations predicted to be transformationally more complex. The final analysis, a multidimensional scaling of dissimilarity ratings, converted subjects' ratings into spatial structures to determine whether individual subjects' ratings exhibited the predicted spatial arrangement. The monotone regression and stochastic analyses abstracted similar generator sets for individual subjects, some of which provided perfect fits to the data. Although the scaling analysis yielded similar estimates of generators, for some subjects, transformations with the same number of generators yielded unequal “cognitive” distances resulting in some-what deformed spatial structures for these subjects. It was concluded that the results generally supported a generative model as an approximation to subjects' representations of interstimulus relationships.     

Perception as abduction: turning sensor data into meaningful representation

This article presents a formal theory of robot perception as a form of abduction. The theory pins down the process whereby low-level sensor data is transformed into a symbolic representation of the external world, drawing together aspects such as incompleteness, top-down information flow, active perception, attention, and sensor fusion in a unifying framework. In addition, a number of themes are identified that are common to both the engineer concerned with developing a rigorous theory of perception, such as the one on offer here, and the philosopher of mind who is exercised by questions relating to mental representation and intentionality.     

Statistical analysis of timing errors.

Human rhythmic activities are variable. Cycle-to-cycle fluctuations form the behavioral observable. Traditional analysis focuses on statistical measures such as mean and variance. In this article we show that, by treating the fluctuations as a time series, one can apply techniques such as power spectra and rescaled range analysis to gain insight into the mechanisms underlying the remarkable abilities of humans to perform a variety of rhythmic movements, from maintaining memorized temporal patterns to anticipating and timing their movements to predictable sensory stimuli.     

Expressivism,representation, and the nature of conceptual analysis

Philosophers often hold that the aim of conceptual analysis is to discover the representational content of a given concept such as free will, belief, or law. In From Metaphysics to Ethics and other recent work, Frank Jackson has developed a theory of conceptual analysis that is one of the most advanced systematizations of this widespread idea. I argue that this influential way of characterizing conceptual analysis is too narrow. I argue that it is possible that an expressivist account could turn out to be correct as a genuine conceptual analysis of a genuine concept. I claim that since an expressivist analysis does not aim to discover the representational content of a given concept—and, indeed, might itself be based on the idea that the concept in question is not even representational in nature—the possibility of expressivist conceptual analysis shows that Jackson’s theory of conceptual analysis is incomplete as it currently stands. I conclude that Jackson needs to either shift his basic understanding of the nature of conceptual analysis or commit to a particular normative reinterpretation of his project.     

The cerebral representation of space: insights from functional imaging data

Functional imaging techniques, such as positron emission tomography and functional magnetic resonance imaging, present a unique opportunity to examine, in humans, the cerebral representation of space in vivo. Space is ubiquitous and not a unitary phenomenon, and the brain uses visual, vestibular and proprioceptive inputs to produce multiple representations of space subserving spatial cognition, ranging from gaze control to remembering multiple complex large-scale environments. Functional imaging studies have shown the importance of the parietal cortex in perceptual, motor, attention and working memory aspects of body-centred human spatial cognition. Functional imaging has also revealed pathways in humans homologous to those found in monkeys for the separate processing of spatial location and object identity. There are further suggestions of similar differentiation in working memory. The importance of the medial temporal region in the recall of spatial location has been confirmed also and novel virtual reality paradigms are now providing insights into the cerebral representation of spatially-extended large-scale environments. We still have much to learn about the cerebral representation of space in the human brain and functional brain imaging, in concert with patient studies and animal models, will allow us to continue investigating.     

Statistical modelling of network panel data: goodness of fit

Networks of relationships between individuals influence individual and collective outcomes and are therefore of interest in social psychology, sociology, the health sciences, and other fields. We consider network panel data, a common form of longitudinal network data. In the framework of estimating functions, which includes the method of moments as well as the method of maximum likelihood, we propose score-type tests. The score-type tests share with other score-type tests, including the classic goodness-of-fit test of Pearson, the property that the score-type tests are based on comparing the observed value of a function of the data to values predicted by a model. The score-type tests are most useful in forward model selection and as tests of homogeneity assumptions, and possess substantial computational advantages. We derive one-step estimators which are useful as starting values of parameters in forward model selection and therefore complement the usefulness of the score-type tests. The finite-sample behaviour of the score-type tests is studied by Monte Carlo simulation and compared to t-type tests.     

Statistical analysis of sets of congeneric tests

Various models for sets of congeneric tests are considered, including models appropriate for the analysis of multitrait-multimethod data. All models are illustrated with real data. The special cases when two or more tests within a set are tau-equivalent or parallel are also considered. All data analyses are done within the framework of a general model by Jöreskog [1970].Research reported in this paper has been supported by Grant NSF-GB-12959 from National Science Foundation. The writer wishes to thank Gunnar Gruvaeus and Marielle van Thillo, who wrote the computer program and assisted in all aspects of the computational work.     

Statistical inference of minimum rank factor analysis

For any given number of factors, Minimum Rank Factor Analysis yields optimal communalities for an observed covariance matrix in the sense that the unexplained common variance with that number of factors is minimized, subject to the constraint that both the diagonal matrix of unique variances and the observed covariance matrix minus that diagonal matrix are positive semidefinite. As a result, it becomes possible to distinguish the explained common variance from the total common variance. The percentage of explained common variance is similar in meaning to the percentage of explained observed variance in Principal Component Analysis, but typically the former is much closer to 100 than the latter. So far, no statistical theory of MRFA has been developed. The present paper is a first start. It yields closed-form expressions for the asymptotic bias of the explained common variance, or, more precisely, of the unexplained common variance, under the assumption of multivariate normality. Also, the asymptotic variance of this bias is derived, and also the asymptotic covariance matrix of the unique variances that define a MRFA solution. The presented asymptotic statistical inference is based on a recently developed perturbation theory of semidefinite programming. A numerical example is also offered to demonstrate the accuracy of the expressions.This work was supported, in part, by grant DMS-0073770 from the National Science Foundation.     

Statistical analysis on a large time-sharing system

A set of statistical routines for strictly conversational use is discussed. The routines are being developed at Carnegie-Mellon University, where the main time-sharing system is TSS installed on an IBM 360/67, and they exist at several levels.     

Statistical aspects of a three-mode factor analysis model

A special case of Bloxom's version of Tucker's three-mode model is developed statistically. A distinction is made between modes in terms of whether they are fixed or random. Parameter matrices are associated with the fixed modes, while no parameters are associated with the mode representing random observation vectors. The identification problem is discussed, and unknown parameters of the model are estimated by a weighted least squares method based upon a Gauss-Newton algorithm. A goodness-of-fit statistic is presented. An example based upon self-report and peer-report measures of personality shows that the model is applicable to real data. The model represents a generalization of Thurstonian factor analysis; weighted least squares estimators and maximum likelihood estimators of the factor model can be obtained using the proposed theory.This investigation was supported in part by a Research Scientist Development Award (K02-DA00017) and a research grant (DA01070) from the U. S. Public Health Service. The very helpful comments of several anonymous reviewers are gratefully acknowledged.     

The use of computer networks in data gathering and data analysis

In our research, the data are gathered in the laboratory on a DEC PDP-11/24 minicomputer. Once the data are gathered, they are analog-to-digital (A/D) converted and sent by the PDP to an IBM 370-3031. The data are submitted to a Fast Fourier Transform (FFT) on the IBM computer. Once the FFT is completed, the data are accessed by an IBM PC-XT that is equipped with an IRMA system. The PC is used in its emulation mode to access the data in the mainframe. In the mainframe, SPSS or SAS is used to do the initial statistical analyses. When necessary, subsets of the data are transferred to the PC, where other computer programs are used to analyze the data. In many instances, they are returned to the mainframe from the PC, where they are submitted to multivariate statistical analysis. Finally, all of the data are stored on floppy disks, which are prepared on the PC.