Showing papers in "Psychometrika in 1968"

Estimation of latent ability using a response pattern of graded scores

Abstract: Estimation of latent ability using the entire response pattern of free-response items is discussed, first in the general case and then in the case where the items are scored in a graded way, especially when the thinking process required for solving each item is assumed to be homogeneous. The maximum likelihood estimator, the Bayes modal estimator, and the Bayes estimator obtained by using the mean-square error multiplied by the density function of the latent variate as the loss function are taken as our estimators. Sufficient conditions for the existence of a unique maximum likelihood estimator and a unique Bayes modal estimator are formulated with respect to an individual item rather than with respect to a whole set of items, which are useful especially in the situation where we are free to choose optimal items for a particular examinee out of the item library in which a sufficient number of items are stored with reliable quality controls. Advantages of the present methods are investigated by comparing them with those which make use of conventional dichotomous items or test scores, theoretically as well as empirically, in terms of the amounts of information, the standard errors of estimators, and the mean-square errors of estimators. The utility of the Bayes modal estimator as a computational compromise for the Bayes estimator is also discussed and observed. The relationship between the formula for the item characteristic function and the philosophy of scoring is observed with respect to dichotomous items.

A general nonmetric technique for finding the smallest coordinate space for a configuration of points

Abstract: LetA 1,A 2, ...,A n be anyn objects, such as variables, categories, people, social groups, ideas, physical objects, or any other. The empirical data to be analyzed are coefficients of similarity or distance within pairs (A i,A i ), such as correlation coefficients, conditional probabilities or likelihoods, psychological choice or confusion, etc. It is desired to represent these data parsimoniously in a coordinate space, by calculatingm coordinates {x ia } for eachA i for a semi-metricd of preassigned formd ij =d(|x i1 -x j1 |, |x i2 -x j2|, ..., |x im -x jm |). The dimensionalitym is sought to be as small as possible, yet satisfy the monotonicity condition thatd ij

A statistical model which combines features of factor analytic and analysis of variance techniques

Abstract: This paper describes a method of matrix decomposition which retains the ability of factor analytic techniques to summarize data in terms of a relatively low number of coordinates; but at the same time, does not sacrifice the useful analysis of variance heuristic of partitioning data matrices into independent sources of variation which are relatively simple to interpret. The basic model is essentially a two-way analysis of variance model which requires that the matrix of interaction parameters be decomposed by using factor analytic techniques. Problems of judging statistical significance are discussed; and an illustrative example is presented.

A comparison of factor analytic techniques

Abstract: Statistical properties of several methods for obtaining estimates of factor loadings and procedures for estimating the number of factors are compared by means of random sampling experiments. The effect of increasing the ratio of the number of observed variables to the number of factors, and of increasing sample size, is examined. A description is given of a procedure which makes use of the Bartlett decomposition of a Wishart matrix to generate random correlation matrices.

Some test theory for tailored testing

Abstract: In a tailored test, each item is selected for administration on the basis of the examinee's responses to previous items, with a view towards optimum measurement of this particular examinee. Various simple rules for 1) selecting the items to be administered and 2) scoring the examinee's responses are compared and evaluated. Some fundamental ideas emerge that will serve as guides in the future design of tailored testing programs.

Maximum likelihood estimation of parameters of signal detection theory--a direct solution.

Abstract: Ogilvie and Creelman have recently attempted to develop maximum likelihood estimates of the parameters of signal-detection theory from the data of yes-no ROC curves. Their method involved the assumption of a logistic distribution rather than the normal distribution in order to make the mathematics more tractable. The present paper presents a method of obtaining maximum likelihood estimates of these parameters using the assumption of underlying normal distributions.

Alpha-maximized factor analysis (alphamax): its relation to alpha and canonical factor analysis.

Abstract: An alpha-O coefficient of internal consistency is defined for an observed score composite. Maximizing alpha-O leads to a system of psychometric (vs. statistical) factor analysis in which successive factors describe dimensions of successively less internal-consistency. Factoring stops when alpha-O is zero or less. In contrast to Kaiser-Caffrey's alpha-C analysis, when the factored matrix is rank 1, alpha-O does not reach unity; it can approach unity only as the number of variables reach infinity. The relative usefulness and domains of generalization of alpha-C and alpha-O are compared. Basically, alpha-C analysis is concerned with the representativeness of factors while alpha-O analysis is concerned with the assessibility of factors. Consequently, either system of factoring can and should be summarized by both the alpha-C and alpha-O coefficients. Not surprisingly, alpha-O analysis is computationally analogous to Rao's canonical factor analysis.

Individual differences in multidimensional scaling

Abstract: Applications of Tucker and Messick's model of individual differences in multidimensional scaling have suggested the occasional appropriateness of a refinement of that model. The refinement is to consider just one multidimensional stimulus space for all persons (or sets of persons) and with each person having a “weight” for each axis. This paper presents a formal description of this model and a least squares solution for its parameters. The solution has yet to be tested empirically.

Statistical adjustments when comparing preexisting groups

Abstract: An illustration is given showing why the analysis of covariance usually does not provide the appropriate adjustment to compensate for preexisting differences between nonexperimental groups.

Identifiability and statistical properties of two-stage learning with no successes in the initial stage

Abstract: A model is considered for learning where there is an initial stage with only errors, an intermediate state with errors and correct responses, and an absorbing state with only correct responses. A model with observable states is constructed, and sufficient identifiable parameters are given for the original model. Distribution statistics and other properties of data are derived as functions of the identifiable parameters. Informal estimates and sufficient statistics are given for the identifiable parameters. A number of testable hypotheses about the theoretical parameters are described. Some identifying restrictions for the model are given, along with the estimates for the unrestricted free parameters which follow. An application is made to data from a pairedassociate learning experiment.

The influence of communality andN on the sampling distributions of factor loadings

Abstract: The effects ofN and communality on the variability of zero and nonzero factor loadings were assessed using a Monte Carlo approach. It was found that increasingN or communality resulted in decreased sampling error of individual factor loadings, but for zero loadingsN was found to have the greatest influence. It was also found that distributions of factor loadings become relatively elongated as communality increases.

On two-sided orthogonal Procrustes problems.

Abstract: A least squares method for approximating a given symmetric matrixB by another matrixB which is orthogonally similar to a second given matrixA is derived and then generalized to nonsymmetric (but square)A andB A possible application to ordering problems is discussed

A unified treatment of the weighting problem.

Abstract: A general procedure is described for obtaining weighted linear combinations of variables. This includes as special cases, multiple regression weights, canonical variate analysis, principal components, maximizing composite reliability, canonical factor analysis, and certain other well-known methods. The general procedure is shown to yield certain desirable invariance properties, with respect to transformations of the variables.

A note on invariance in three-mode factor analysis.

Abstract: Previous results of the application of Lawley's selection theorem to the common factor analysis model are extended to a revision of Tucker's three-mode principal components model. If the regression of the three-mode manifest variates on variates used to select subpopulations is both linear and homoscedastic, the two factor pattern matrices, the core matrix, and the residual variance-covariance matrix in the three-mode model can all be assumed to be invariant across subpopulations. The implication of this finding for simple structure is discussed.

Play behavior in the year‐old infant: early sex differences1

Abstract: Thirty-two boys and 32 girls, 13 months old, were observed with their mothers in a standardized free play situation. There were striking sex differences in the infants' behavior toward their mothers and in their play. Earlier observation of the mothers' behavior toward the infants at six months indicates that some of these sex differences were related to the mothers' behavior toward the infants. It was suggested that parents behave differently toward girls and boys, even as infants, reinforcing sex appropriate behavior. This study emphasizes the importance of observing the freely emitted behavior of the very young child.

The "idealized individual" interpretation of individual differences in multidimensional scaling.

Abstract: It is shown that several variants of the Tucker-Messick points of view procedure are interpretable in terms of their “idealized individual” concepts. It is contended that the main function of the method is that it allows the computation ofseveral vectors of mean judgments instead of only one and that each of these may be used to stand for the actual judgments of a subgroup of subjects. Vectors that do not correspond to the judgments of any subjects are to be avoided. It is alleged that Ross's interpretation of “points of view” is quite different from that intended by Tucker and Messick.

Children's social sensitivity and the relationship to interpersonal competence, intrapersonal comfort and intellectual level

Abstract: A method of measuring children's social sensitivity is described and the relationship between social sensitivity and certain variables hypothesized as important in its development is investigated. Using a series of four tape recordings depicting two adults in happy, angry, anxious, and sad interactions, social sensitivity was assessed in third and fifth grade children. Age, intellectual ability and interpersonal adjustment contributed most to the development of accurate social perceptions. Surprisingly, there were no significant effects on social sensitivity due to sex, ordinal position, or size of family.

Development of native language skills beyond the early years

Abstract: This chapter, prepared for a volume on Language Learning to be published by the National Council of Teachers of English, is a review of the development of language competence and performance skills beyond the years of primary language acquisition, i.e., from about the first grade on. First, development of specific skills relating to phonology, syntax, and vocabulary is reviewed, and then attention shifts to the development of “integrated skills”: listening, speaking, reading, and writing. Emphasis is put on identifying dimensions of individual differences in rates of growth and development. Although a substantial degree of basic competence in the rules of the native language is attained by the normal child at school entry age, development is by no means complete at that time. In many aspects of language skill, development continues throughout the years of schooling and to a lesser extent throughout adult life In adult populations, there are enormous individual differences in nearly all aspects of language skill. Gaps in our knowledge of factors in development are pointed out

Rate and uniqueness in children's creative responding1

Abstract: Three ideational fluency measures were administered to 34 seven- and eight-year-old boys. Response rate and uncommonness were compared with results from published studies using college student Ss. In agreement with earlier findings, response rate decreased, and average uncommonness of responses increased, over time; Ss who eventually produced more ideas gave them at a higher rate. Creative children (those having high response fluency) did not differ from uncreative ones either in their proportion of uncommon responses throughout the task or in the rate at which their successive responses became less stereotyped. The possibility was raised that children identified as creative differ from others solely in personality and motivational, rather than ability, characteristics.

Personality development and concepts of structure

Abstract: It is proposed that many concepts of personality structure and structural development are of primary relevance to one of three general orientations, here called the “classical,” “differential,” and “ipsative” views. Certain theoretical and methodological features of each approach are reviewed. The discussion emphasizes differences and similarities among the views and points out some implications for research.

The development and evaluation of several programmed testing methods

Abstract: Seven programmed test procedures were developed and investigated using existing data on 190 verbal-type items for 4,885 students. Tests were scored as if the student had taken items in the order implied by the test. Shortened conventional tests were also scored for comparative purposes. The criteria against which these procedures were evaluated were the 190-item total test score and four outside criterion tests. Against the criterion of reproducing the 190-item total test score in the cross-validation sample the programmed tests were found to he only slightly superior to the shortened conventional tests. However, the programmed tests had correlations with the outside criterion tests that were substantially higher than the corresponding shortened conventional tests. It was estimated that a test which was parallel to the 190-item total test would have to be 3.36 times as long as the best programmed test to have an equal median correlation with the outside criterion tests.

Estimating item characteristic curves without knowledge of their mathematical form

Abstract: A method is outlined for estimating item characteristic curves without knowledge of their mathematical form. For illustrative purposes, the method is applied to five items from a regular test administration. Previously, curves had been estimated for these same items on the assumption that all were of logistic form. Surprising agreement was found between the results obtained from the two unrelated methods.

Comments on “markovian processes with identifiable states: General considerations and applications to all-or-none learning”

Abstract: When knowledge of the response sequence permits one to specify the sequence of theoretical states that occurred, we propose to say that the theory has observable states. Our earlier usage of “identifiable” conflicts with established usage in econometrics. We also present a revised definition of implication between theories that avoids a technical flaw in the earlier definition, and we correct a mistake in an example in our earlier paper.

Some origins of concern for others1

Abstract: This paper summarizes a series of naturalistic and experimental investigations into the nature of personal commitment and prosocial behavior. An intensive naturalistic study of Civil Rights workers distinguished those who were fully committed (i.e., had actively participated in Civil Rights activities for more than a year) from those who were partially committed (i.e., had gone on one or two Freedom Rides) on the basis of the kinds of models to which they were exposed as children. The parent of the fully committed was a behavioral altruist, fully committed to a social cause. Moreover, he maintained a strong positive relationship with the child. The parent of the partially committed, on the other hand, was described as having often failed to practice what he preached, and maintained a negative or ambivalent relationship with the child. These observations were examined in a variety of experiments that were predicated on social learning theory. In one, adolescents who observed a model rebel against authority for prosocial reasons tended themselves subsequently to rebel more than their peers who had observed an obedient model. In another, children who observed a model contribute to charity tended also to contribute, even in the absence of adult surveillance. However, these findings, while statistically significant, were nevertheless quite weak. Additional experiments provided strong evidence that while observation of a model was helpful, internalization of prosocial norms was more strongly facilitated by the opportunity to rehearse prosocial behavior voluntarily with the model. In a series of developmental studies it was found that internalization of prosocial norms occurred rarely with five-year-old children, but quite commonly with eight- and nine-year-old ones. This finding was puzzling since the required behaviors were neither physically nor psychologically taxing. It was proposed that the internalization of prosocial behavior on the basis of observation of others may require a predisposing cognitive and affective matrix, the elements of which are briefly elaborated.

A principal components analysis of models and men

Abstract: : One consequence of stimulus sampling theory is the prediction of probability matching as the asymptotic response probability. That is, subjects tend to choose each alternative with the frequency of its reinforcement. This prediction has been tested in many experiments and the boundaries within which it holds have been delineated. However, the experiments which find probability matching have been criticized for doing one or more of several inappropriate things. It should be noted that probability matching is not a 'rational' solution, in the sense that the behavior which maximizes gain would be always to choose the more frequently reinforced response. Some investigators have found it possible to devise experimental situations in which the subjects do come closer to maximizing behavior. This study attempts to differentiate the conditions which lead to 'matching' behavior from those which lead to 'maximizing' and to develop a mathematical model for this behavior. (Author)

Organizational climates and administrative performance

Abstract: : The aim of the study is to answer three kinds of questions: What are the effects of organizational climates (1) on the factorial structure of measures of administrative performance, (2) on the correlations between measures of administrative performance and various predictors of such performance, (3) and on the means of various measures of administrative performance. Data were collected at a two-day 'Research Institute' at which 260 executives employed by the State of California served as subjects. Each served as Chief of the Field Services Division of a fictitious department of the state, using an elaborate situational test that simulated an administrative position by requiring the examinee to respond to items in his in-basket as though he were actually on the job. Subjects also took a variety of ability tests and inventories and provided biographical information. (Author)

Factorial rotation to simple structure and maximum similarity

Abstract: When the regression of factored variates on variates defining subpopulations (or experimental groups) is (a) nonlinear or (b) heteroscedastic, an existing solution to the problem of factorial invariance does not apply. This paper presents an approach which can be used in place of the existing solution and derives a method for obtaining maximally similar orthogonal simple structure factor pattern matrices across subpopulations. The method is applied to data from three experimental groups.

Probabilistic foundations for coefficients of generalizability.

Abstract: This paper explores certain problems which arise within the context of the theory of generalizability put forward by Cornbach, Rajaratnam, and Gleser. In particular, a formal explication of their theory for the single observation is given, and the various coefflcients of generalizability which they define are related to the estimation of universe scores.