bluuebunny/crossref_metadata_2025_split huggingface dataset:
Current Misuse of the Factorial Methods
Authors: Thurstone L. L. 
Published: January 2006

Papers involving factorial methods appearing in current literature often misuse factorial methods. These meaningless results are reached because of neglect of certain conditions basic to factor theory. The conditions are:
(1) The number of basic factors must be smaller than the number of tests.(2) The diagonals of the correlation matrix must be regarded as unknown.(3) The axes must be rotated into a simple configuration.(4) Each factor must be overdetermined by appearance in several tests.(5) Tests should have simple factorial composition.
Finite Markov Processes in Psychology
Authors: Miller George A. 
Published: January 2006

Finite Markov processes are reviewed and considered for their usefulness in the description of behavioral data. The various alternative responses in an experimental situation define a vector space, and changes in the probabilities of these alternatives are represented by movements in this space. Methods of fitting the theory to experimental data are considered.The simplest process, with a constant matrix of transitional probabilities that is applied repeatedly to represent the effect of successive trials, seems inadequate for most learning data. A matrix function that may be useful for learning theory is presented.
A Superior Rotational Method in Factor Analysis or Psychometricians in Government Service
Authors: Adkins Dorothy C. 
Published: January 2006

The topic that I have chosen, “A Superior Rotational Method in Factor Analysis or Psychometricians in Government Service,” may puzzle you at first. But there is an explanation. A study in progress at the University of North Carolina requires the interpretation of 16 factors obtained from a centroid analysis of 66 variables. The task that was approached with greatest apprehension was the location of a meaningful reference frame. With so many vectors protruding into a space of such a large number of dimensions, the problem appeared practically insoluble. Hence we sought a rotational method that would obviate the necessity for the numerous graphs and the matrix multiplication associated with the commonly accepted techniques.Perhaps some of you have had the experience of solving a difficult mathematical problem in a state of sleep and later being able to transcribe the complete solution immediately. A relatively painless approach to mathematics, it is the one which enabled me to pass a course in Mathematical Probability years ago. I scarcely dared presume that I could evoke it in the present emergency. To my astonishment, however, it worked. One day the project staff had had a particularly trying session during which we tried in vain to stretch the available funds to cover the rotational work. Upon falling asleep in my office chair, I dreamed a solution so simple that an ordinary statistical clerk, upon mere inspection of the score matrix, could visualize the most interpretable reference frame in up to an infinite number of dimensions. This was beyond our most extravagant hopes, for it rendered obsolete both the correlation matrix and the centroid solution.
Remarks on the Method of Paired Comparisons: III. A Test of Significance for Paired Comparisons when Equal Standard Deviations and Equal Correlations are Assumed
Authors: Mosteller Frederick 
Published: January 2006

A test of goodness of fit is developed for Thurstone's method of paired comparisons, Case V.The test involves the computation of \documentclass[12pt]{minimal}
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$$\chi ^2 = n\Sigma(\theta '' - \theta ')^2 /821,$$
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On Oblique Procrustes Rotation
Authors: Browne Michael W. 
Published: January 2006

The equations involved in the rotation of an arbitrary factor matrix to a least squares fit to a specified factor structure have been known for many years. These equations, in general, cannot be solved by purely algebraic means, and an approximate solution has previously been used in practical applications.In this paper an effective iterative method for obtaining the exact solution is developed. By algebraic manipulation the set of equations is expressed in the form of one polynomial equation in one unknown. Newton's method is suggested for solving this equation. Practical applications of the procedure indicate that convergence within small tolerance limits is generally attained after few iterations.
A Strong True-Score Theory, with Applications
Authors: Lord Frederic M. 
Published: January 2006

A “strong” mathematical model for the relation between observed scores and true scores is developed. This model can be used
1. To estimate the frequency distribution of observed scores that will result when a given test is lengthened.2. To equate true scores on two tests by the equipercentile method.3. To estimate the frequencies in the scatterplot between two parallel (nonparallel) tests of the same psychological trait, using only the information in a (the) marginal distribution(s).4. To estimate the frequency distribution of a test for a group that has taken only a short form of the test (this is useful for obtaining norms).5. To estimate the effects of selecting individuals on a fallible measure.6. To effect matching of groups with respect to true score when only a fallible measure is available.7. To investigate whether two tests really measure the same psychological function when they have a nonlinear relationship.8. To describe and evaluate the properties of a specific test considered as a measuring instrument.The model has been tested empirically, using it to estimate bivariate distributions from univariate distributions, with good results, as checked by chi-square tests.
The Computer Revolution in Psychometrics
Authors: Green Bert F. 
Published: January 2006

SummaryWe have said that psychometric methods involving algorithms are completely objective—at least they are if the algorithm is in the form of a program for a digital computer. These objective procedures need Monte Carlo and other computer runs to determine their properties, but so do many equation-oriented techniques. The objective algorithms are flexible but not flaccid. They offer a way of dealing with complexities that formerly seemed beyond our grasp. As the computer revolution continues in psychometrics, we can expect objective algorithmic methods to become the rule rather than the exception.
The Prediction of Averages
Authors: Meredith William 
Published: January 2006

Criterion measures are frequently obtained by averaging ratings, but the number and kind of ratings available may differ from individual to individual. This raises issues as to the appropriateness of any single regression equation, about the relation of variance about regression to number and kind of criterion observations, and about the preferred estimate of regression parameters. It is shown that if criterion ratings all have the same true score the regression equation for predicting the average is independent of the number and kind of criterion scores averaged.Two cases are distinguished, one where criterion measures are assumed to have the same true score, and the other where criterion measures have the same magnitude of error of measurement as well. It is further shown that the variance about regression is a function of the number and kind of criterion ratings averaged, generally decreasing as the number of measures averaged increases. Maximum likelihood estimates for the regression parameters are derived for the two cases, assuming a joint normal distribution for predictors and criterion average within each subpopulation of persons for whom the same type of criterion average is available.
Psychological Measurement a Hundred and Twenty-Five Years Later
Authors: Guilford J. P. 
Published: January 2006

When writing this paper as well as during our commemorative luncheon, I could not help going back in memory to two experiences. One of these occurred during the fall semester of 1935 while I was visiting professor at Northwestern University and took advantage of the opportunity and had the rare privilege of attending Thurstone’s seminar. The atmosphere at the University of Chicago at that time clearly reflected the birth and early infancy of both the Psychometric Society and its Journal Psychometrika.The other experience comes back in the form of an image of our first annual dinner in the Inn at Dartmouth College in September 1936. The banquet had an unexpectedly large and enthusiastic attendance. Thurstone provided one of his memorable addresses, which was later published in Science, entitled “Psychology as a quantitative rational science” [35]. The address is well worth rereading.I might spend the time alloted to me in declaiming the merits of quantitative psychology and what it has done for the progress of psychology in general. But in this group I shall take our substantial contribution for granted and try instead to help measurement psychologists look at themselves and their own progress and some of their own problems.
A Graph Theoretic Approach to Similarity Relations
Authors: Harary Frank 
Published: January 2006

SummaryA similarity relation is reflexive and symmetric. A graph may be regarded as a geometric representation of an irreflexive symmetric relation; an r-graph then coincides with a similarity relation. For the realization of psychophysical phenomena, the points of a graph stand for the stimuli and a line for indistinguishability of a stimulus pair. Not all graphs, however, are likely to arise as similarity relations in a real situation. A special class of graphs, called interval graphs, does have this realistic property. These graphs are described and characterized.
Investigations of the Simplex
Authors: Humphreys Lloyd G. 
Published: January 2006

I am honored to be able to speak on the 25th anniversary of the founding of the Psychometric Society. It would be appropriate for your president on this occasion to review the 25-year history of our society and of mathematical methods in psychology. Fortunately our committee headed by Charles Wrigley has taken care of this need, and speakers better qualified than I will speak to these issues. I shall turn to a less demanding problem.In limiting my topic I was faced with certain constraints arising from my training, background, and interests. One constraint arises from a misspent youth during which too many years were spent studying disciplines other than mathematics. A second constraint, which probably stems from my training in experimental psychology, is a tendency to be more interested in data than theory. Finally, there is the Air Force personnel research experience which developed in me an abiding interest in applied prediction problems. If you consider this combination to be an odd one for the President of the Psychometric Society, don't blame me. You elected me!
The Error
Authors: Winer B. J. 
Published: January 2006

After I had started to put some of my thoughts into a first draft for this talk, I selected “The Error” as a title. This selection gave me a great deal of flexibility since, no matter how I went wrong, I was still well within the limits of the title. After additional deliberation, I had more than a slight feeling that the title was more appropriate for a potential best-seller in the field of popular fiction than it was for a potential presidential address to this society. I have, on occasion, thought that I could write–in fact, I started my academic life in a School of Journalism. At least at the academic level, the journalistic style of writing rather quickly suppressed my interest therein as a means of making a livelihood.Errors, random and otherwise, are often the heart of some rather undercover plots and subplots in best-sellers. But just as in the case of novels, in experimental designs errors also play a dominant role–unfortunately the experimental units, which are the players, often do not understand their roles as set forth in the design script. The latter is usually in the form of a mathematical model. A question might be raised in some instances as to whether it is more difficult to teach the experimental units what the model calls for, or to teach the designer what types of designs are potentially appropriate for expressing the behavior of experimental units, under specified experimental conditions.
Retrospective Anticipation
Authors: Harman Harry H. 
Published: January 2006

The objectives of the Psychometric Society are coincident with those of its journal, namely, “the development of psychology as a quantitative rational science.” This general theme has frequently been referred to by the past presidents in their annual addresses. They did so by employing several different approaches: some by proposing directions of future research of the Society; some by making critical-instructive appraisals of past research; some by presenting reports of their own ongoing research; and some by viewing the present scene from an historical or philosophical perspective. Furthermore, the tone of these addresses has run the gamut from the frivolous to the profoundly scholarly.A brief analysis of the previous addresses disclosed some interesting items. First, there have been eight instances, in our 34 year history, when the address was skipped entirely, beginning with Thurstone’s [1937] published in Science rather than in Psychometrika. Of the addresses that subsequently appeared in Psychometrika, the average was 13 pages (including references) with a range from 5 to 26 pages. (Hopefully, the longer ones were not read in their entirety.) More than half the papers were expository in nature. Although 12 were reports on serious research problems, only four contained heavy mathematical developments. Five addresses could be characterized as facetious or humorous, but nonetheless carried a moral for the Society. In general, suggestions were made in 13 instances for future research or directions of emphasis for the Society, and 9 addressed themselves explicitly to its aims. There was also a sprinkling of criticism, philosophy, and history relating to the Society or to specific psychometric methods. Of course, the foregoing classifications were not mutually exclusive, and merely constitute one man’s opinions.
Simultaneous Factor Analysis in Several Populations
Authors: Jöreskog K. G. 
Published: January 2006

This paper is concerned with the study of similarities and differences in factor structures between different groups. A common situation occurs when a battery of tests has been administered to samples of examinees from several populations.A very general model is presented, in which any parameter in the factor analysis models (factor loadings, factor variances, factor covariances, and unique variances) for the different groups may be assigned an arbitrary value or constrained to be equal to some other parameter. Given such a specification, the model is estimated by the maximum likelihood method yielding a large sample x2 of goodness of fit. By computing several solutions under different specifications one can test various hypotheses.The method is capable of dealing with any degree of invariance, from the one extreme, where nothing is invariant, to the other extreme, where everything is invariant. Neither the number of tests nor the number of common factors need to be the same for all groups, but to be at all interesting, it is assumed that there is a common core of tests in each battery that is the same or at least content-wise comparable.
A Monte Carlo Evaluation of Interactive Multidimensional Scaling
Authors: Girard Roger A. , Cliff Norman 
Published: January 2006

Interactive Scaling with Individual Subjects (ISIS) developed by Young & Cliff [1972], is a method involving interaction between subject and computer in real time to determine which judgments made by the subject are critical to the definition of a dimensional structure. The procedure is based on the mathematical fact that it is possible to define a space of R dimensions in terms of only the interpoint distances between all stimuli being scaled and a subset of (R +1) of these stimuli. For errorless judgments, any subset of (R + 1) stimuli is appropriate. However, fallible data require that the subset consist of stimuli that are maximally dissimilar, and the ISIS procedure is designed to obtain such an optimum subset (a “basis”).This research evaluates a modified version of ISIS with respect to (a) a metric MDS analysis based on all possible pairs of the stimuli, and (b) a metric MDS analysis based on a subset of one-third of the possible pairs, or about the same number as that required by ISIS. Results show that the ISIS method achieves better fit than (b) at low error levels, and may also achieve better fit than (b) at higher error levels if the size of the basis is increased. The more stimuli in the basis the more indices of fit approach those of (a).A new method of introducing error in MDS studies is used in the evaluation.
Nonmetric Individual Differences Multidimensional Scaling: An Alternating Least Squares Method with Optimal Scaling Features
Authors: Takane Yoshio , Young Forrest W. , de Leeuw Jan 
Published: January 2006

A new procedure is discussed which fits either the weighted or simple Euclidian model to data that may (a) be defined at either the nominal, ordinal, interval or ratio levels of measurement; (b) have missing observations; (c) be symmetric or asymmetric; (d) be conditional or unconditional; (e) be replicated or unreplicated; and (f) be continuous or discrete. Various special cases of the procedure include the most commonly used individual differences multidimensional scaling models, the familiar nonmetric multidimensional scaling model, and several other previously undiscussed variants.The procedure optimizes the fit of the model directly to the data (not to scalar products determined from the data) by an alternating least squares procedure which is convergent, very quick, and relatively free from local minimum problems.The procedure is evaluated via both Monte Carlo and empirical data. It is found to be robust in the face of measurement error, capable of recovering the true underlying configuration in the Monte Carlo situation, and capable of obtaining structures equivalent to those obtained by other less general procedures in the empirical situation.
Three Technical Word Processors
Authors: Cudeck Robert , McGuire Dennis P. 
Published: January 2006

If Gutenberg had been a psychometrician, the invention of movable type would have occured much later than the year 1456. As anyone who has ever approached the problem knows, the requirements for automating technical writing are much greater than those for standard prose. A writer of technical documents needs all standard Roman letters, plus the full array of Greek characters, mathematical symbols, and the ability to freely half space for superscripts and subscripts. It is not known when the first scientific or technical manuscript was produced with movable type, but one can be sure that it came decades after Gutenberg's Bible.In our time it has taken substantially longer for word processing software that is used in conjunction with a microcomputer to be developed for the technical writer than for the writer of standard prose.
Nominal Scale Agreement Among Observers
Authors: Schouten Hubert J. A. 
Published: January 2006

Experiments are considered where each of a sample of subjects is assigned to one of C categories separately by each of a fixed or varying group of observers. Building on earlier publications, general procedures are proposed to analyze agreements and disagreements among observers. In the case of a varying group of observers, it is shown that it is not necessary to demand a constant number of observers per subject. In the case of a fixed group of observers, the problem of missing data is considered.The procedures are illustrated within the context of two clinical diagnosis examples. In the first example it is investigated which categories are relatively hard to distinguish from one another; a new theorem is applied that shows a useful property of the statistic kappa. In the second example it is investigated if a subgroup of observers can be found with a significantly higher degree of interobserver agreement.
Two-Group Classification in Latent Trait Theory: Scores with Monotone Likelihood Ratio
Authors: Grayson D. A. 
Published: January 2006

This paper deals with two-group classification when a unidimensional latent trait, θ, is appropriate for explaining the data, X. It is shown that if X has monotone likelihood ratio then optimal allocation rules can be based on its magnitude when allocation must be made to one of two groups related to θ. These groups may relate to θ probabilistically via a non-decreasing function p(θ), or may be defined by all subjects above or below a selected value on θ.In the case where the data arise from dichotomous items, then only the assumption that the items have nondecreasing item characteristic functions is enough to ensure that the unweighted sum of responses (the number-right score or raw score) possesses this fundamental monotone likelihood ratio property.
Structural Analysis of Subjective Categorical Data
Authors: Klauer Karl Christoph , Batchelder William H. 
Published: January 2006

A general approach to the analysis of subjective categorical data is considered, in which agreement matrices of two or more raters are directly expressed in terms of error and agreement parameters. The method provides focused analyses of ratings from several raters for whom ratings have measurement error distributions that may induce bias in the evaluation of substantive questions of interest. Each rater's judgment process is modeled as a mixture of two components: an error variable that is unique for the rater in question as well as an agreement variable that operationalizes the “true” values of the units of observation. The statistical problems of identification, estimation, and testing of such measurement models are discussed.The general model is applied in several special cases. The most simple situation is that underlying Cohen's Kappa, where two raters place units into unordered categories. The model provides a generalization and systematization of the Kappa-idea to correct for agreement by chance. In applications with typical research designs, including a between-subjects design and a mixed within-subjects, between-subjects design, the model is shown to disentangle structural and measurement components of the observations, thereby controlling for possible confounding effects of systematic rater bias. Situations considered include the case of more than two raters as well as the case of ordered categories. The different analyses are illustrated by means of real data sets.