A simple model for fluctuating interresponse times is developed and studied. It involves a mechanism that generates regularly spaced excitations, each of which can trigger off a response after a random delay. The excitations are not observable, but their periodicity is reflected in a regular patterning of responses. The probability distribution of the time between responses is derived and its properties are analyzed. Several limiting cases are also examined.

The first in the present series of two papers described a computer program for multidimensional scaling on the basis of essentially nonmetric data. This second paper reports the results of two kinds of test applications of that program. The first application is to artificial data generated by monotonically transforming the interpoint distances in a known spatial configuration. The purpose is to show that the recovery of the original metric configuration does not depend upon the particular transformation used. The second application is to measures of interstimulus similarity and confusability obtained from some actual psychological experiments.

Arguments for using multiple cutting scores are theoretically inapplicable when the selection measures are fallible. The effect of errors of measurement in altering the shape of some optimum selection regions is here investigated mathematically, with numerical illustrations, for the case of two selection variables.

A computer program is described that is designed to reconstruct the metric configuration of a set of points in Euclidean space on the basis of essentially nonmetric information about that configuration. A minimum set of Cartesian coordinates for the points is determined when the only available information specifies for each pair of those points—not the distance between them—but some unknown, fixed monotonic function of that distance. The program is proposed as a tool for reductively analyzing several types of psychological data, particularly measures of interstimulus similarity or confusability, by making explicit the multidimensional structure underlying such data.

The problem of defining and determining the effective contribution of a component variable to the variance of a composite is briefly reviewed. Another method of dealing with this problem is proposed and illustrated with analysis of a three-component problem. The proposed method is based on systematic application of a series of regressions and is restricted in application to positive manifold systems.

A method for estimation in factor analysis is presented. The method is based on the assumption that the residual (specific and error) variances are proportional to the reciprocal values of the diagonal elements of the inverted covariance (correlation) matrix. The estimation is performed by a modification of Whittle's least squares technique. The method is independent of the unit of scoring in the tests. Applications are given in the form of nine reanalyses of data of various kinds found in earlier literature.

An examination of the determinantal equation associated with Rao's canonical factors suggests that Guttman's best lower bound for the number of common factors corresponds to the number of positive canonical correlations when squared multiple correlations are used as the initial estimates of communality. When these initial communality estimates are used, solving Rao's determinantal equation (at the first stage) permits expressing several matrices as functions of factors that differ only in the scale of their columns; these matrices include the correlation matrix with units in the diagonal, the correlation matrix with squared multiple correlations as communality estimates, Guttman's image covariance matrix, and Guttman's anti-image covariance matrix. Further, the factor scores associated with these factors can be shown to be either identical or simply related by a scale change. Implications for practice are discussed, and a computing scheme which would lead to an exhaustive analysis of the data with several optional outputs is outlined.

A statistical model for verbal learning is presented and tested against experimental data. The model describes a Markov process with a realizable absorbing state, allowing complete learning on some finite trial as well as imperfect retention prior to this trial.

This paper deals with the determination of optimal weights for points on scoring scales for subjective comparative experiments. A scoring scale with a specific number of points is considered, and it is assumed that verbal or other indications imply an order to the scale points. The optimal spacing for the scale points is obtained in the sense that treatment or item differences are maximized relative to error or within-treatment variation. The method is presented in sufficiently generalized form to be used directly with any experimental design leading to the analysis of variance. An iterative procedure, suitable for computer use, yields the optimal differences among the ordered scale points. Properties of this procedure are discussed.

A least-squares solution for scaling the variables of a Guttman simplex is developed. The procedure yields a ratio scale, two varieties of interval scale, and orders the variables. A measure of the goodness of fit of the scale to the data is suggested. An example of the application of the method is given. The problem of non-positive correlations is discussed.

Indexes of skewness and kurtosis for a test-score distribution are expressed in terms of item parameters. Both are shown to depend, in part, on item means, variances, and covariances. The index of skewness depends also on trivariances. A trivariance is a product moment involving first powers of deviation scores for three items. The index of kurtosis depends on quadrivariances, as well as trivariances. A quadrivariance is a product moment involving first powers of deviation scores for four items. Empirical data are presented for responses of groups of subjects to 25 triads and 25 tetrads of items from five tests.

In the simulation of human behavior on a digital computer, one first attempts to discover the manner in which subjects (Ss) internally represent the environment and the rules that they employ for acting upon this representation. The interaction between the rules and the environmental representation over a period of time constitutes a set of processes. Processes can be expressed as flow charts which, in turn, are stated formally in terms of a computer program. The program serves as a theory which is tested by executing the program on a computer and comparing the machine's performance with S's behavior.

The choice model considered by Luce in an earlier work is stated in terms of unobservable parameters. In this paper a consequence of the model, involving only observables, is shown to be equivalent to the model.

A derivation is presented for correcting correlations for indirect restriction of range when correlations between one selection variable and non-interval measures are involved. Following a systematic investigation of special cases, formulas are given for practical application in validation work. Procedures for the case with several selection variables are briefly discussed.

A statistical theory of choice is developed using a sequential sampling assumption. Response latency distributions for certain simple reaction-time situations are derived and tested. Both response probability and response latency measures are developed for a two-alternative judgment situation and the relationship between the two measures explored. The sampling parameter is proposed as a means of representing incentive conditions in choice situations and ROC curves are obtained by appropriate manipulations of this parameter. A solution to the overlap problem in simple discrimination-learning situations is also derived.

It is suggested that a number of theoretical models for non-test data can be tested by factor analysis. A traditional method for transforming principal-axis factor solutions is used as an aid in making such tests; a modification of this method is suggested. Means of using all of the information in a model for the purpose of determining the transformation of the arbitrary factor solution are presented, and an illustrative example is given.