Numerical methods for polynomial models in nonlinear factor analysis

The basic concepts of nonlinear factor analysis are introduced and some extensions of the general theory are developed. An elementary account of the class of multiple-factor polynomial models is presented, using more elementary algebraic methods than have been employed in earlier accounts of this theory. Working formulas are developed for the multiple-factor polynomial model without product terms.Some empirical results are presented.This work was carried out while the author was a Visiting Research Fellow at the Educational Testing Service, Princeton, N. J. It made use of computer facilities at Princeton University that are supported in part by National Science Foundation Grant NSF-Gp579.     

Children's judgments of body size and distortion

Body size estimates of 69 children aged 5–13 years were obtained using a TV video methodology. Tasks included an adjustment procedure where children manipulated the width of their body image on a TV, and a discrete task, where they judged the accuracy of their TV image which was presented as either normal or distorted, that is, too wide or too thin. On the continuous task, judgments were more accurate on ascending trials where children had to increase the width of the image. On the discrete task, a signal detection analysis revealed older children were better in detecting size distortion in their images and that the differences were due to differences in the biological sensory system and not due to a bias to report that they were too fat or too thin. However, there were response bias differences between genders. Females were more likely to report size distortion with increasing age while males were less likely.     

TheP system: A scheme for organizing Pavlovian procedures

The present paper introduces theP system as a scheme for organizing Pavlovian procedures in an orderly and comprehensive manner. The system is defined by three temporal variables and three restrictions on their possible values. It can be used to define all standard temporal variables—namely, stimulus duration, interstimulus interval, trace interval, and intertrial interval—as well as variables C and T of scalar expectancy theory. The system also permits the definition of new independent variables through combinations of the basic temporal parameters. We exemplify this possibility by defining two ratios of temporal intervals. These ratios lead to a space where traditional Pavlovian arrangements (viz., simultaneous, forward-trace, forward-delay, backward) become points on a continuum, and optimal conditions across different experimental preparations become equivalent. Finally, the system can be used to define contingency variables such asp(US/CS),p(US/～CS), and the phi coefficient (φ). In this manner, an organization of different kinds of Pavlovian procedures is achieved on the basis of a single parametric scheme. Such an organization facilitates establishing procedural and theoretical relationships between temporal and contingency variables. The paper concludes with a discussion of certain limitations of the system and other related issues     

The effect of additional variables on factor indeterminacy in models with a single common factor

Determinate solutions for the indeterminate common factor ofp variables satisfying the single common factor model are not unique. Therefore an infinite sequence of additional variables that conform jointly with the originalp variables to the original single common factor model does not determine a unique solution for the indeterminate factor of thep variables (although the solution is unique for the factor of the infinite sequence). Other infinite sequences may be found to determine different solutions for the factor of the originalp variables. The paper discusses a number of theorems about the effects of additional variables on factor indeterminacy in a model with a single common factor and draws conclusions from them for factor theory in general.     

Constrained least squares estimators of oblique common factors

An expression is given for weighted least squares estimators of oblique common factors, constrained to have the same covariance matrix as the factors they estimate. It is shown that if as in exploratory factor analysis, the common factors are obtained by oblique transformation from the Lawley-Rao basis, the constrained estimators are given by the same transformation. Finally a proof of uniqueness is given.The research reported in this paper was partly supported by Natural Sciences and Engineering Research Council Grant No. A6346.     

Development of clinical tests of vision: Initial data on two hyperacuity paradigms

Many basic psychophysical functions offer promise as clinical tests of vision. Here, we discuss problems that one encounters in the clinical setting, how one identifies a psychophysical test for potential clinical development, and an orderly approach to development of suitable test paradigms. Parameters are selected which are relatively insensitive to variables encountered in the field (clinic) in a normal population, but which are sensitive to changes in the response system being studied. Initial data on two hyperacuity tests are presented. These tests are adaptations of hyperacuity paradigms (Westheimer, 1979) to a clinical environment. This particular test set offers promise because it exhibits a unique threshold which is dependent upon neural data processing and is relatively independent of retinal image degradation.