bluuebunny/crossref_metadata_2025 huggingface dataset:
Simulation of Human Problem-Solving Behavior
Authors: Laughery K. R. , Gregg L. W.
Published: January 2006

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.
Mathematical Analysis of the Durations of Reinforced Inter-Response Times during Variable Interval Reinforcement
Authors: Revusky Samuel H.
Published: January 2006

In a free-responding situation in which reinforcements are scheduled by a variable interval program, the durations of reinforced inter-response times are shown to be a function of the durations of all inter-response times produced by S and of the frequency of reinforcement.
The Analysis of Proximities: Multidimensional Scaling with an Unknown Distance Function. I.
Authors: Shepard Roger N.
Published: January 2006

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.
Scaling a Simplex
Authors: Kaiser Henry F.
Published: January 2006

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.
Matrix Reduction and Approximation to Principal Axes
Authors: Horst Paul
Published: January 2006

A modification of Hotelling’s iteration method of factor analysis is presented which is much more rapid and almost as accurate. At any stage of the approximation for a factor vector its major product moment reduces the rank of the residual matrix by precisely one. Each approximation to an eigenvalue is larger than the preceding one. By observing the decline in these increments one can often stop the iterations at early stages without serious loss. If subsequent rotational procedures are used, the method gives practically the same results as the more exact methods and in a small fraction of the time.
Sample and Population Score Matrices and Sample Correlation Matrices from an Arbitrary Population Correlation Matrix
Authors: Kaiser Henry F. , Dickman Kern
Published: January 2006

A method for generating sample and population score matrices and sample correlation matrices from a given population correlation matrix is developed. An example giving the desired matrices for a population Guttman simplex correlation matrix is presented.
Abacs for Determination of a Correlation Coefficient Corrected for Restriction of Range
Authors: Michael William B. , Jones Robert A. , Gaddis L. Wesley , Kaiser Henry F.
Published: January 2006

Abacs approximating the product-moment correlation for both explicit and implicit selection are presented. These abacs give accuracy to within .01 of the corresponding analytic estimate.
On the Statistical Treatment of Residuals in Factor Analysis
Authors: Jöreskog K. G.
Published: January 2006

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.
A General Approach to Nonlinear Factor Analysis
Authors: McDonald Roderick P.
Published: January 2006

The method presented attempts to allow for nonlinear, possibly nonmonotonic relations between manifest and latent variates. An attempt is made to provide a workable criterion for choosing between alternative models on the basis of observable data as well as for constructing the appropriate function. An idealized numerical example is given.
The Relation between Factor Loadings and Biserial Correlations in Item Analysis
Authors: Henrysson Sten
Published: January 2006

The first centroid factor loadings obtained from various interitem relations are compared with item discrimination indices commonly used in item analysis. Depending upon what type of matrix is factored, the factor loadings are shown to be related to point biserial and biserial correlations.
A Comparison of Four Methods of Constructing Factor Scores
Authors: McDonald Roderick P. , Burr E. J.
Published: January 2006

Four least-squares methods for constructing factor scores have been described in the literature. The formal properties of these scores are developed, and they are compared in terms of four generally desirable properties of constructed factor scores. In particular, it is shown that two of the methods yield scores that are conditionally unbiassed, and univocal in the sense of Guilford and Michael, though not orthogonal, while one of the other methods yields orthogonal scores.

It is shown that constructed factor scores cannot be simultaneously univocal and orthogonal, unless we choose the special basis in factor space given by Canonical Factor Analysis.

The general problem of choosing between the methods is discussed, on the basis of the theoretical relations obtained.
A Correction for Replicated Error in Correlation Coefficients
Authors: Bashaw W. L. , Anderson Harry E.
Published: January 2006

A solution is presented to the problem of determining a proper correction for spuriousness in correlation coefficients. The general case developed is the estimate of correlation between u and v, both being linear functions of the same set of variables. Special formulae relate to overlapping scales correlations, part-whole correlations, and item-total test correlations.
Cutting Scores and Errors of Measurement
Authors: Lord Frederic M.
Published: January 2006

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.
Regression Analysis of Linear Composite Variance
Authors: Creager John A. , Valentine Lonnie D.
Published: January 2006

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.
Test Skewness and Kurtosis as Functions of Item Parameters
Authors: Ray William S. , Hundleby John D. , Goldstein Donald A.
Published: January 2006

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.
Methods of Correcting Correlations for Indirect Restriction of Range with Non-Interval Data
Authors: Rydberg Sven
Published: January 2006

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 Theoretical Distribution for Mental Test Scores
Authors: Keats J. A. , Lord Frederic M.
Published: January 2006

The negative hypergeometric distribution of raw scores on mental tests is derived from certain assumptions relating to test theory. This result is checked empirically in a number of examples. Further derivations lead to the bivariate distribution of parallel tests which is also verified with actual data. The bivariate distribution of raw score and true score is also derived from a further assumption. This distribution is used to set confidence limits for true scores for persons with a given raw score.
A Functional Equation Analysis of Two Learning Models
Authors: Kanal Laveen
Published: January 2006

One-absorbing barrier random walks arising from Luce's nonlinear beta model for learning and a linear commuting-operator model (called the alpha model) are considered. Functional equations for various statistics are derived from the branching processes defined by the two models. Solutions to general functional equations, satisfied by statistics of the alpha and beta models, are obtained. The methods presented have application to other learning models.
On Two-Sided Orthogonal Procrustes Problems
Authors: Schönemann Peter H.
Published: January 2006

A least squares method for approximating a given symmetric matrix B by another matrix B which is orthogonally similar to a second given matrix A is derived and then generalized to nonsymmetric (but square) A and B. A possible application to ordering problems is discussed.
A Counterexample to Two-Dimensional Varimax-Rotation
Authors: Gebhardt Friedrich
Published: January 2006

Usually, an iterative procedure based on two-dimensional rotations is employed to find the varimax solution in factor analysis. A matrix is given where this procedure does not yield the maximum value of the varimax criterion. However, random orthogonal transformations of some matrices and subsequent varimax-rotation using the iterative procedure seem to indicate that usually no local maxima exist.
Toward a Resolution of the Fechner-Thurstone Legacy
Authors: Stevens S. S.
Published: January 2006

The occasion of a symposium to honor Fechner on the centennial of the publication of his Elemente der Psychophysik (1] has provided an excuse to review the Fechnerian legacy and to ask what perversity in the nature of science or the Zeitgeist has made it possible for Fechner’s concept of error to persist for a hundred years and grow famous. The central feature of this legacy is the notion that the jnd (just noticeable difference) can serve as a unit for the measurement of sensation. Since the jnd is really a measure of the uncertainty, dispersion, or variability among a set of judgments, this proposition makes residual “noise” the yardstick of sensory magnitude–a notion as curious as it seems improbable. Why did this conception survive its inventor, and why did it become, under Thurstone's expert guidance, the foundation of psychological measurement applied to subjective values and attitudes? Thurstone’s Case V in which he assumes equal discriminal dispersions (equal subjective variabilities) matches in effect the Fechnerian assumption that all jnds are subjectively equal.
Psychometrics—A Special Case of the Brahman Theory
Authors: Dunlap Jack W.
Published: January 2006

We are gathered today to commemorate the completion of the first quarter of a century of the Society’s history, and I consider it no small honor to have been selected to address this distinguished group on this memorable occasion. When Dr. Charles Wrigley, Chairman of the Program Committee, extended the invitation, he expressed the hope that I would review the history of the formation of the Society and discuss something of its achievements to date. Today I shall only highlight the early history of the organization, since in my Presidential Address in September 1941 a rather full history was presented.
Nonmetric Multidimensional Scaling: A Numerical Method
Authors: Kruskal J. B.
Published: January 2006

We describe the numerical methods required in our approach to multi-dimensional scaling. The rationale of this approach has appeared previously.
Enumeration of Paths in Digraphs
Authors: Parthasarathy K. R.
Published: January 2006

The solution of the problem of enumeration of the n-paths in a digraph has so far been attempted through an indirect approach of enumerating the redundant chains. The approach has yielded an algorithm for determination of the general formula for the matrix of redundant n-chains and also a partial recurrence formula for the same. This paper presents a direct approach to the problem. It gives a recurrence relation expressing the matrix of n-paths of a digraph in terms of the matrices of (n − 1)-paths of its first-order subgraphs. The result is exploited to give an algorithm for computing the matrix of n-paths. The algorithm is illustrated with a 6 × 6 matrix.
Notes on Factorial Invariance
Authors: Meredith William
Published: January 2006

Lawley's selection theorem is applied to subpopulations derived from a parent in which the classical factor model holds for a specified set of variables. The results show that there exists an invariant factor pattern matrix that describes the regression of observed on factor variables in every subpopulation derivable by selection from the parent, given that selection does not occur directly on the observable variables and does not reduce the rank of the system. However, such a factor pattern matrix is not unique, which in turn implies that if a simple structure factor pattern matrix can be satisfactorily determined in one such subpopulation the same simple structure can be found in any subpopulation derivable by selection. The implications of these results for “parallel proportional profiles” and “factor matching” techniques are discussed.
A Double Law of Comparative Judgment for the Analysis of Preferential Choice and Similarities Data
Authors: Coombs C. H. , Greenberg M. , Zinnes J.
Published: January 2006

By virtue of certain modifications in the Law of Comparative Judgment, equations are developed which (i) permit the construction of a joint scale of individuals and items, as in the case of attitude measurement, directly from their pair-comparison preferences, and (ii) take into account the variable of laterality which is significant for the construction of group preference scales.
Some Asymptotic Properties of Luce's Beta Learning Model
Authors: Lamperti John , Suppes Patrick
Published: January 2006

This paper studies asymptotic properties of Luce's beta model. Asymptotic results are given for the two-operator and four-operator cases of contingent and noncontingent reinforcement.
On the Wilson Tests
Authors: Ylvisaker N. Donald
Published: January 2006

A general critical analysis of the median tests proposed by Wilson for certain analysis of variance hypotheses is presented. Specifically, discrepancies between the purported and actual approximate distributions of some of the test statistics are noted. Validity and power of the resulting tests are discussed.
Use of True-Score Theory to Predict Moments of Univariate and Bivariate Observed-Score Distributions
Authors: Lord Frederic M.
Published: January 2006

Formulas are derived for using the available item statistics and score statistics on a test to estimate the moments of the score distribution of a lengthened (or shortened) form of the same test. Other formulas are derived for estimating the bivariate moments of the scatterplot between two parallel test forms using only the data available on either form alone. An empirical study is made showing in each case satisfactory agreement between the theoretical values predicted from the formulas and the values actually observed. These results suggest the utility of the true-score model used in deriving the formulas.
A Rational Origin Obtained by the Method of Contingent Paired Comparisons
Authors: Shuford Emir H. , Jones Lyle V. , Bock R. Darrell
Published: January 2006

A new paired comparison method, based upon choices between lotteries, is developed for the measurement of utilities of objects with respect to the utility of receiving nothing, i.e., the status quo. The method is used to estimate the utilities of four birthday gifts. These objects had also been studied in an earlier experiment which used choices between single objects and pairs of objects to determine a rational origin. A comparison of the results of the two experiments indicates that both methods scale objects with respect to the same rational origin and unit of measurement.
On the Number of Significant Findings to be Expected by Chance
Authors: Block Jack
Published: January 2006

When multiple significance tests are computed, a certain number of “significant” findings will emerge simply because of chance fluctuations. In the present paper, some factors affecting the number of nominally significant results are elaborated and a general method is suggested which permits unbiased inference as to the significance of a set of findings, as a set. The method advocated employs a high speed computer to generate empirically a sampling distribution tailormade to a particular data matrix. The method is illustrated in the case of dichotomous response to inventory items, where it is found that the statistical model still often used as a basis for estimation is overly conservative. Some problems in the application of the method are discussed.
Point Biserial Correlation Coefficient and its Generalization
Authors: Gupta S. Das
Published: January 2006

The problem of measuring the association between two characters, one quantitative and the other qualitative, is discussed. The formula for the large sample standard error of the point biserial correlation coefficient under general conditions is derived. The point multiserial correlation coefficient is introduced and some of its properties are examined. Tests of different hypotheses appropriate to these types of problems are formulated.
Statistical Inferences About True Scores
Authors: Lord Frederic M.
Published: January 2006

Formulas are derived for unbiased sample estimators of any raw or central moment of the frequency distribution of true scores. A general method is developed for obtaining from each examinee's observed score a least squares estimate of his true score.
Simple Statistical Methods for Scalogram Analysis
Authors: Goodman† Leo A.
Published: January 2006

Simple statistical methods are developed to test whether coefficients of reproducibility, of homogeneity, or of consistency differ significantly from what can be expected if responses to different items are statistically independent. Simple methods are also developed for estimating the variance of coefficients of reproducibility when it is not assumed that responses to different items are independent. These estimates are used to test whether a coefficient differs significantly from any prescribed value, and also to obtain confidence intervals for these coefficients. The rationale for the measurement of reproducibility is also discussed.
Note on ϕ/ϕmax
Authors: Cureton Edward E.
Published: January 2006

Formulas are given for a descriptive statistic related to the fourfold-point correlation but having always-attainable limits ±1.
An Empirical Study of the Factor Analysis Stability Hypothesis
Authors: Bechtoldt Harold P.
Published: January 2006

Note is taken of four related sources of confusion as to the usefulness of Thurstone's factor analysis model and of their resolutions. One resolution uses Tucker's distinction between exploratory and confirmatory analyses. Eight analyses of two sets of data demonstrate the procedures and results of a confirmatory study with statistical tests of some, but not all, relevant hypotheses in an investigation of the stability (invariance) hypothesis. The empirical results provide estimates, as substitutes for unavailable sampling formulations, of effects of variation in diagonal values, in method of factoring, and in samples of cases. Implications of these results are discussed.
The Mystery of the Missing Corpus
Authors: Mosteller Frederick
Published: January 2006

Until recently, two happy vices stole a good share of my time. Of those burglars, the first was the reading of science-fiction stories, a source of entertainment that I discovered at the age of eight, but kept manfully in check because I never stumbled upon a continuous supply. Of late, however, real life has mocked this branch of fiction so closely that I now miss in it the elements of fantasy and escape that used to delight. You might say that, being crowded out by the real thing, we armchair spacemen face technological obsolescence.

My second time-stealer has been “Murder for Pleasure,” as Howard Haycraft calls the detective story. Fortunately, I did not discover its existence until my twenties, so I had a little time for study before then. The great value of the detective story, quite apart from its educational aspects– after all, where else can one gather so much data about useful everyday questions such as tasteless poisons, homicidal law, and criminal psychology–is the fine training one gets in applied psychology and in the logic of everyday life.
A Markov Model for Discrimination Learning
Authors: Atkinson Richard C.
Published: January 2006

A theory for discrimination learning which incorporates the concept of an observing response is presented. The theory is developed in detail for experimental procedures in which two stimuli are employed and two responses are available to the subject. Applications of the model to cases involving probabilistic and nonprobabilistic schedules of reinforcement are considered; some predictions are derived and compared with experimental results.
A Comparison of the Precision of Three Experimental Designs Employing a Concomitant Variable
Authors: Feldt Leonard S.
Published: January 2006

Three techniques are commonly employed to capitalize on a concomitant variate and improve the precision of treatment comparisons: (1) stratification of the experimental samples and use of a factorial design, (2) analysis of covariance, and (3) analysis of variance of difference scores. The purpose of this paper is to compare the effectiveness of these alternatives in improving experimental precision, to identify the most precise design and the conditions under which its advantage holds, and to derive, in the case of the factorial approach, recommendations as to the optimal numbers of levels.
Application of a Model to Paired-Associate Learning
Authors: Bower Gordon H.
Published: January 2006

The proposal is made to consider a paired-associate item as becoming conditioned to its correct response in all-or-none fashion, and that prior to this conditioning event the subject guesses responses at random to an unlearned item. These simple assumptions enable the derivation of an extensive number of predictions about paired-associate learning. The predictions compare very favorably with the results of an experiment discussed below.
The Use of Extreme Groups to Test for the Presence of a Relationship
Authors: Feldt Leonard S.
Published: January 2006

Experimenters in psychology frequently investigate the relationship between two variables by selecting extreme groups on the first measure and comparing their mean scores on the second. This paper considers the efficacy of this procedure from the criterion of the power of the statistical tests. Optimal cutting points for the extreme groups are defined, and the power of the difference approach is compared to that of significance tests for the productmoment correlation coefficient.
A Note on a Class of Probability Matching Models
Authors: Feldman Julian , Newell Allen
Published: January 2006

Probability matching is shown to be a property of a broad class of models of binary choice behavior.
An Approach to Mental Test Theory
Authors: Lord Frederic M.
Published: January 2006

It currently seems to me that the heart of mental test theory is the concept of true score.

The trouble starts as soon as it is realized that the actual test score obtained by a particular individual might just as well have been some numerical value other than the one actually observed. The individual examinee might have guessed differently, might have been less nervous, or might have slept better the night before. The testing conditions might have been different–lighting, facilities for use of paper and pencil, presence or absence of distraction. Finally, any one of many different but equally appropriate psychological tests might have been constructed and administered.

Mental test theory must deal with all these kinds of disturbing influences. However, we are not really interested in each of the different test scores that an examinee might obtain under all sorts of conditions. We are interested in something approximated by these scores. This something may be called the true score on the test.
Theoretical Models of Choice and Strategy Behavior: Stable State Behavior in the Two-Choice Uncertain Outcome Situation
Authors: Siegel Sidney
Published: January 2006

A theoretical approach to the understanding of human behavior in uncertain outcome situations is suggested, an approach which draws upon utility theory, decision-making theory, and statistical association theory. Experimental evidence supporting this approach as opposed to alternative approaches is summarized. Three different formalizations are presented, and a variety of experimental tests is suggested.
A Note on the Use of Mood's Likelihood Ratio Test for item Analyses Involving 2 × 2 Tables with Small Samples
Authors: Weiner Irving B.
Published: January 2006

Mood's likelihood ratio test is generally considered an unreliable x2 approximation in 2 × 2 contingency tables containing expected cell frequencies less than five. Probability values were computed for 60 such tables as part of an item analysis for two 30-item alternate forms of a measure. The rank orders of the items, from best to worst differentiators, as determined separately by Mood's test and by Fisher's exact test correlated .97 for one form and .96 for the other.
On Methods in the Analysis of Profile Data
Authors: Greenhouse Samuel W. , Geisser Seymour
Published: January 2006

This paper is concerned with methods for analyzing quantitative, non-categorical profile data, e.g., a battery of tests given to individuals in one or more groups. It is assumed that the variables have a multinormal distribution with an arbitrary variance-covariance matrix. Approximate procedures based on classical analysis of variance are presented, including an adjustment to the degrees of freedom resulting in conservative F tests. These can be applied to the case where the variance-covariance matrices differ from group to group. In addition, exact generalized multivariate analysis methods are discussed. Examples are given illustrating both techniques.
An Augmented Model for Spontaneous Regression and Recovery
Authors: McConnell David
Published: January 2006

The Estes model for spontaneous recovery and regression is modified by relaxing the assumption that within-experiment stimulus fluctuation can be treated as negligible in the general case. The augmented model allows description of stimulus fluctuation both between and within experimental periods. Application of the model to mock experimental situations illustrates some of its properties.
Item Selection Procedures for Item Variables with a Known Factor Structure
Authors: Elfving G. , Sitgreaves R. , Solomon H.
Published: January 2006

This paper discusses the item selection problem when the item responses follow a linear multiple factor model. Because of this restrictive assumption, not too unrealistic in situations such as mental testing, it is possible to select optimal sets of items without going through all possible combinations. A method proposed by Elfving to accomplish this is analyzed and then demonstrated through the use of two illustrations. The common and often used procedure of observing the magnitude of the correlation coefficient as an index in item selection is shown to have some merit in the single-factor case.
Maximum Likelihood Estimates of Item Parameters using the Logistic Function
Authors: Maxwell A. E.
Published: January 2006

The logistic function is proposed as an alternative to the integrated normal function when estimating parameters of test items. The logistic curve is described; an iterative method for finding maximum likelihood estimates of its parameters is given, and an example of its use is presented.
Three Multivariate Models: Factor Analysis, Latent Structure Analysis, and Latent Profile Analysis
Authors: Gibson W. A.
Published: January 2006

The factor analysis model and Lazarsfeld's latent structure scheme for analyzing dichotomous attributes are derived to show how the latter model avoids three knotty problems in factor analysis: communality estimation, rotation, and curvilinearity. Then the latent structure model is generalized into latent profile analysis for the study of interrelations among quantitative measures. Four latent profile examples are presented and discussed in terms of their limitations and the problems of latent metric and dimensionality thereby raised. The possibility of treating higher order empirical relations in a manner paralleling their various uses in the latent structure model is indicated.
A Note on Tryon's Measure of Reliability
Authors: Edwards Allen L.
Published: January 2006

Two alternative formulas, based upon the analysis of variance, are given for Tryon's general form for the reliability coefficient.
A Note on the Tryon-Kaiser Solution for the Communalities
Authors: Kaiser Henry F.
Published: January 2006

The Tryon-Kaiser solution for the communalities is reviewed. Numerical investigation suggests that the procedure is applicable if and only if the correlation matrix has unique minimum rank communalities. This implies that this approach to the communality problem is not general enough to be of practical use.
A Generalized Expression for the Reliability of Measures
Authors: Horst Paul
Published: January 2006

In certain situations it is important to obtain as many measures as possible, all presumably measuring the same function, for each of a group of persons. In general the number and source of the measures may vary from one member of the group to another. We take the mean of the measures for each person as the best estimate of the function for that person. The conventional formulas can not be used to determine the reliability of a set of means so obtained. A formula is developed which provides a unique estimate of the reliability of such a set of means. The formula is more general than some of the well-known reliability formulas, so that these formulas are shown to be special cases of the more general formula.
A Factorial Approach to Job Families
Authors: Coombs Clyde H. , Satter George A.
Published: January 2006

This is an experimental study of the application of factor analysis to a new domain—the formation of job families. Correlations between jobs are computed from the formula based on the number of common elements between two variables and the job analyses provide the basic data on the presence or absence of the elements. A first-order general factor and four common factors are obtained in a small sample of twenty occupations. Tentative interpretations are made and implications for job analysis and the formation of job families are pointed out.
A Statistical Critique of the Usafi Tests of General Educational Development
Authors: Findley Warren G. , Andregg Neal B.
Published: January 2006

Data resulting from the administration of the USAFI Tests of General Educational Development to more than 1000 junior Air Force officers have been statistically analyzed to indicate the reliability of these tests, their correlation with school achievement, the comparability of their intercorrelations with intercorrelations among grades in school subjects, their capacity for differential diagnosis, their factorial composition, and their average item-test correlations. In the light of these findings and the finding that there is a low gradient between achievement on these tests and amount of formal education among these officers, the tests have been evaluated as possessing the practical validity suggested by their face validity for selection of young Air Force officers for assignment to study at civilian colleges and universities.
Note on the Computation of Product-Moment Correlation Coefficients
Authors: Adkins Dorothy C.
Published: January 2006

This paper describes a systematic plan for computing all of the product-moment correlation coefficients among a number of variables that has been taught by Professor Toops for many years. It offers several advantages over a scheme presented by Kossack in a recent issue of this journal.
An Asymptotic Likelihood Ratio Test for a Markov Chain with Bernoullian or Contingent Input
Authors: Bogartz Richard S.
Published: January 2006

A Markov chain with transition probabilities pij(θ) that are functions of a parameter vector θ is defined. One of t input values is delivered to the chain on each trial. Under the hypothesis H0 the parameter vector is independent of the input; under the hypothesis H1 the vector is in general different for each different input. A likelihood ratio test for a single observation on a chain of great length is given for testing H0 against H1, given that the distribution of the inputs depends at most on the previous input and the present state of the chain. The test is therefore one of stationarity of the transition probabilities against a specific alternative form of nonstationarity. Application of the approach to a statistical test of lumpability of the states of a chain is indicated. Tests for other related hypotheses are suggested. Application of the test to “within-subject effects” for individual subjects is considered. Finally, some applications of the results in psychophysical contexts are suggested.
A Probabilistic Formulation and Statistical Analysis of Guttman Scaling
Authors: Proctor C. H.
Published: January 2006

By proposing that the latent or true nature of subjects is identified with a limited number of response patterns (the Guttman scale patterns), the probability of an observed response pattern can be written as the sum of products of the probability of the true type multiplied by the chance of sufficient response error to cause the observed pattern to appear. This model contains the proportions of the true types as parameters plus some misclassification probabilities as parameters. Maximum likelihood methods are used to make estimates and test the fit for some examples.
The Estimation of True Score Variance and Error Variance in the Classical Test Theory Model
Authors: Jackson Paul H.
Published: January 2006

The use of one-way analysis of variance tables for obtaining unbiased estimates of true score variance and error score variance in the classical test theory model is discussed. Attention is paid to both balanced (equal numbers of observations on each person) and unbalanced designs, and estimates provided for both homoscedastic (common error variance for all persons) and heteroscedastic cases.

It is noted that optimality properties (minimum variance) can be claimed for estimates derived from analysis of variance tables only in the balanced, homoscedastic case, and that there they are essentially a reflection of the symmetry inherent in the situation. Estimates which might be preferable in other cases are discussed. An example is given where a natural analysis of variance table leads to estimates which cannot be derived from the set of statistics which is sufficient under normality assumptions. Reference is made to Bayesian studies which shed light on the difficulties encountered.
A Comment on Birnbaum’s Three-Parameter Logistic Model in the Latent Trait Theory
Authors: Samejima Fumiko
Published: January 2006

Birnbaum's three-parameter logistic model for the multiple-choice item in the latent trait theory is considered with respect to the item response information function and the unique maximum condition. It is clarified that with models of knowledge or random guessing nature, which include the three-parameter logistic model, the unique maximum condition is not satisfied for the correct answer, and the item response information function is negative for the interval (− ∞, θg). It is suggested that we should use θg as a criterion in selecting optimal items for a specified group of examinees, so that we can practically avoid the possibility of non-unique maxima of the likelihood function on the response pattern given by an examinee in the group.
A Rank Test for Two Group Concordance
Authors: Schucany W. R. , Frawley W. H.
Published: January 2006

A test statistic is introduced which allows one to test the hypothesis of agreement of several judges on the ranking of items within each of two groups and between the two groups. The groups of judges may be unequal in size. A normal approximation for the test statistic is developed. The relationship to existing techniques given by Kendall, Friedman, Page, Spearman, and Lyerly is discussed. A generalization of the coefficient of concordance is presented and the extension of the method to multi-group problems is suggested.
Estimation of J Scales for Unidimensional Unfolding
Authors: Hettmansperger Thomas P. , Thomas Hoben
Published: January 2006

In Coombs' unidimensional unfolding theory each individual ranks all stimuli, often in terms of preference judgments. These ranks, called I scales, are used to infer the latent continuum called a J scale which is presumed to have generated the I scale rankings. A major problem concerns the inference of the J scale given a set of I scales because an I scale is not unique to any one J scale. This paper presents a procedure for estimating J scale probabilities given a set of I scales. Models for three and four or more stimuli are presented. Results of computer tests are reported.
Pairwise Nonmetric Multidimensional Scaling
Authors: Johnson Richard M.
Published: January 2006

A method of nonmetric multidimensional scaling is described which minimizes pairwise departures from monotonicity. The procedure is relatively simple, both conceptually and computationally. Experience to date suggests that it produces solutions comparable to those of other methods.
Monotone Invariant Clustering Procedures
Authors: Hubert Lawrence
Published: January 2006

A major justification for the hierarchical clustering methods proposed by Johnson is based upon their invariance with respect to monotone increasing transformations of the original similarity measures. Several alternative procedures are presented in this paper that also share in the same property of invariance. One of these techniques constructs a hierarchy of partitions by sequentially minimizing a monotone invariant goodness-of-fit statistic; the other techniques construct a hierarchy of partitions by successively subdividing the complete set of objects until one partition class is defined for each individual member in the set. A numerical example comparing these alternative procedures with Johnson's two methods is discussed in terms of a simplified computational scheme for obtaining the necessary hierarchies.
Min and Max Hierarchical Clustering using Asymmetric Similarity Measures
Authors: Hubert Lawrence
Published: January 2006

The min and the max hierarchical clustering methods discussed by Johnson are extended to include the use of asymmetric similarity values. The first part of the paper presents the basic min and max procedures but in the context of graph theory; this description is then generalized to directed graphs as a way of introducing the less restrictive characterization of the original clustering techniques.
A Test of Inclusion which allows for Errors of Measurement
Authors: White Richard T. , Clark R. Malcolm
Published: January 2006

A test which allows for errors of measurement is derived for the hypothesis that all the members of a population who possess a certain skill are a sub-set of the members who possess another skill. Formulae are given for one particular case when two questions are used for each skill, and for when three questions are used for each skill. An illustrative example is given for the two-question case.
Beyond Structure: In Search of Functional Models of Psychological Process
Authors: Messick Samuel
Published: January 2006

Silvan Tomldns [1962] once remarked that it seemed to him that human personality was “organized as a language is organized, with elements of varying degrees of complexity–from letters, words, phrases, and sentences to styles–and with a set of rules of combination which enable the generation of both endless novelty and the very high order of redundancy which we call style.” He went on to note that “if we had to be blind about one or the other of these types of components, we should sacrifice the elements for the rules,” although “factor analysis appears to have made the opposite decision. It would tell what letters, or words, or phrases, or even styles were invariant and characteristic of a personality or of a number of personalities,” but by itself it does not and cannot “generate the rules of combination which together with the elements constitute personality” [Tomkins, 1962, p. 287].
The Relation between Hierarchical and Euclidean Models for Psychological Distances
Authors: Holman Eric W.
Published: January 2006

In one well-known model for psychological distances, objects such as stimuli are placed in a hierarchy of clusters like a phylogenetic tree; in another common model, objects are represented as points in a multidimensional Euclidean space. These models are shown theoretically to be mutually exclusive and exhaustive in the following sense. The distances among a set of n objects will be strictly monotonically related either to the distances in a hierarchical clustering system, or else to the distances in a Euclidean space of less than n − 1 dimensions, but not to both. Consequently, a lower bound on the number of Euclidean dimensions necessary to represent a set of objects is one less than the size of the largest subset of objects whose distances satisfy the ultrametric inequality, which characterizes the hierarchical model.
Alternative Approaches to Factorial Invariance
Authors: Bloxom Bruce
Published: January 2006

Special cases of the factor analysis model are developed for four selection situations. Methods are suggested whereby parameters in each case can be estimated using a maximum likelihood procedure recently developed by Jöreskog. Also, a numerical illustration is presented for each case.
An Algebraic Solution for a Class of Subjective Metrics Models
Authors: Schönemann Peter H.
Published: January 2006

It is shown that an obvious generalization of the subjective metrics model by Bloxom, Horan, Carroll and Chang has a very simple algebraic solution which was previously considered by Meredith in a different context. This solution is readily adapted to the special case treated by Bloxom, Horan, Carroll and Chang. In addition to being very simple, this algebraic solution also permits testing the constraints of these models explicitly. A numerical example is given.
Presolution Performance Functions for Markov Models
Authors: Polson Peter G.
Published: January 2006

Performance measures, conditionalized on the last error and other events, have been of central concern in the development of absorbing Markov-chain models for learning and problem solving. Expressions for response probabilities and expected latencies conditional on the occurrence of the last error and other events are derived using matrix methods.
A Monte Carlo Evaluation of Three Nonmetric Multidimensional Scaling Algorithms
Authors: Spence Ian
Published: January 2006

As a consequence of the complexity of the iterative optimum seeking procedures used by practical nonmetric multidimensional scaling algorithms, many of their computational properties have not been well understood. In particular, the following questions are of interest: (a) from the user’s point of view, are there significant differences between alternative available programs, (b) are suboptimal solutions frequently encountered, and how does this depend on the characteristics of the algorithm? Using Monte Carlo techniques to generate dissimilarity matrices with known underlying configurations, Kruskal’s M-D-SCAL, Guttman-Lingoes’ SSA-I, and Young-Torgerson’s TORSCA-9 programs were compared. It was found: (a) that differences between the solutions obtained by the algorithms were typically so small as to be of little practical importance, (b) deviant solutions were occasionally produced by each of the algorithms, but most often by M-D-SCAL, and furthermore, most frequently in one dimension. The likelihood of being trapped in a nonoptimal position is reduced by a good choice of initial configuration, and also possibly by constructing the iterative process to favor the possibility of stepping over small local depressions when far from the location of the optimum. The conclusions of this study are based on a total of 2160 scaling solutions.
Estimating the Reliability of Interview Data
Authors: Fleiss Joseph L.
Published: January 2006

A model for a score based on an interview is presented which identifies the effect due to the subject, to the manner in which the interviewer tends to conduct his interviews, to the criteria he tends to use in scoring subjects' responses, to the compromises he tends to adopt between the demands of interviewing and those of scoring, and to chance errors. A suggested experimental design calls for each of K investigators to interview a different sample of N subjects, but for all investigators to score each subject. The drawing of inferences when interest is only in the K participants in the reliability study is considered, and a numerical example is given.
Fitting a Response Model for n Dichotomously Scored Items
Authors: Bock R. Darrell , Lieberman Marcus
Published: January 2006

A method of estimating the parameters of the normal ogive model for dichotomously scored item-responses by maximum likelihood is demonstrated. Although the procedure requires numerical integration in order to evaluate the likelihood equations, a computer implemented Newton-Raphson solution is shown to be straightforward in other respects. Empirical tests of the procedure show that the resulting estimates are very similar to those based on a conventional analysis of item “difficulties” and first factor loadings obtained from the matrix of tetrachoric correlation coefficients. Problems of testing the fit of the model, and of obtaining invariant parameters are discussed.
A “Halo”-Model for Multidimensional Ratio Scaling
Authors: Micko H. C.
Published: January 2006

A model for direct multidimensional ratio scaling is presented, based on the concepts “common” and “difference” of the “halos” of two percepts. Measures of halos and their differences are proportional to lengths of corresponding percept vectors and their distance in subjective space. Ekman type scaling judgements are assumed to reflect the ratio measure of the common/measure of the standard's halo. The model is supposed to yield results that are in line with the results of distance models of multidimensional ratio scaling since negative scalar products of percept vectors are admitted.