John H. Wolfe

PATTERN CLUSTERING BY MULTIVARIATE MIXTURE ANALYSIS

Cluster analysis is reformulated as a problem of estimating the para- meters of a mixture of multivariate distributions. The maximum-likelihood theory and numerical solution techniques are developed for a fairly general class of distributions. The theory is applied to mixtures of multivariate nor- mals (NORMIX) and mixtures of multivariate Bernoulli distributions (Latent Classes). The feasibility of the procedures is demonstrated by two examples of computer solutions for normal mixture models of the Fisher Iris data and of artifjcially generated clusters with unequal covariance matrices.

Automatic question generation from text - an aid to independent study

This report describes an experimental computer-based educational system called automatic question generation (AUTOQUEST) for assisting independent study of written text. Studies of reading comprehension have shown that retention of material is enhanced if the student is periodically required to answer questions about what he has read (Anderson & Biddle, 1975; Anderson et al., 1974; Alessi et al., 1974; Anderson et al., 1975a, 1975b). This principle has been employed in computer-managed instruction, but it requires considerable human effort to prepare the questions.

Comparative Cluster Analysis Of Patterns Of Vocational Interest.

Published data on the Strong Vocational Interest Blank profiles of 113 occupational groups are analyzed by three different clustering procedures: (a) Hierarchical grouping of standard scores, (b) Hierarchical grouping of orthonormal factor scores and, (c) NORMIX analysis assuming equal covariance matrices for each group. It is shown that the NORMIX solution differs from the other solutions in a psychologically meaningful way.

Validity results for g from an expanded test base

Abstract When vocational aptitude batteries are expanded by adding new tests, the most common way to measure validity gains is to regress various criteria onto the subtest scores from the old and new batteries and contrast the results. A rarely tried approach that may be of equal value, however, is to examine “accidental” validity gains for a recalculated general intelligence (or g ) score based on the new battery, because many psychologists have argued that the majority of test validity comes from g rather than specific abilities. In this article, we examine validity differences for a g score calculated on the Armed Services Vocational Aptitude Battery (ASVAB) alone versus the ASVAB plus nine diverse experimental tests selected for their potential importance and uniqueness from the ASVAB. Although no validity gain for expanded g was observed for final school grade criteria, a 6% validity gain was obtained for hands-on performance measures. A gain of this size is of practical importance in the armed forces.

Optimal item difficulty for the three-parameter normal ogive response model

In tailored testing, it is important to determine the optimal difficulty of the next item to present to the examinee. This paper shows that the difference that maximizes information for the three-parameter normal ogive response model is approximately 1.7 times the optimal differenceθ −b for the three-parameter logistic model. Under the normal model, calculation of the optimal difficulty for minimizing the Bayes risk is equivalent to maximizing an associated information function.

Standard Errors of Multivariate Range-Corrected Validities

The multivariate rather than the univariate range correction is used for estimating unrestricted applicant population validities in many military test validity studies but not uniformly. A Monte Carlo approach compared the standard errors of range-corrected validities under various experimental conditions adhering to the assumptions underlying correction accuracy. The multivariate corrected validities had smaller standard errors than both the univariate-corrected validities and the unrestricted validities. We conclude that using the univariate correction could fail to reveal the most valid selection instrument and that the multivariate correction should be used when scores for relevant predictors are available for the unrestricted population.

Chapter IV: Regression and Correlation

A large class of models descriptive of natural and behavioral phenomena can be characterized by an equation of the form y=F[x,ß] +e, where y is the dependent variable of particular interest, F[x,ß] is a function of some variables x and parameters ß, and e is an error component. The model can be particularized in a bewildering number of ways by specifying various kinds of statistical properties of y, x, and e, and forms for F[x,ß]. For example, y and x may be random or fixed variables, and F[x,ß] may be a linear or nonlinear function (in the usual algebraic sense) of the ß. If the F[x,ß] is ß-nonlinear, then statistical literature terms the model nonlinear, whereas if F[x,ß] is #-nonlinear, the model is called curvilinear. Semantically, this distinction is not too clear, and it consequently has led to confusion. Nevertheless, it is very important. The equation y = ßiΛ;i + ß2#2 + e is both ß-linear and #-linear; whereas y = ß±x±+ ß2x2+ß3X1X2+ e is ß-linear and #-nonlinear because of the term x±x2. The equation y = ß1x1-\(ß±) (ß2)#2 + e is ß-nonlinear and #-linear, but y — ßιXι-\ ̄ {ß2) {ß3)x2 ̄\ ̄e is ß-nonlinear and #-nonlinear. We have made these distinctions at some length because we find this classification system convenient for part of this review. If y = F[x,ß] +e is looked at as a prediction model, it is usual to assume that y, x, and e are random variables and that F[x9ß] is ß-linear. Also, in this case, if a particular set of values for x = X is given with X and e uncorrelated, and if the elements of e have expected values of zero and if they are independently distributed with constant common variance, then the model is known as one of multiple regression. Particular care needs to be taken to select a proper regression model. Guidance in this matter is difficult to obtain; experience and professional training are the best aids. A much-needed general discussion of model

Regression and Correlation

A large class of models descriptive of natural and behavioral phenomena can be characterized by an equation of the form y=F[x,/,] +e, where y is the dependent variable of particular interest, F[x,3] is a function of some variables x and parameters f/, and e is an error component. The model can be particularized in a bewildering number of ways by specifying various kinds of statistical properties of y, x, and e, and forms for F[x,/3]. For example, y and x may be random or fixed variables, and F[x,/8] may be a linear or nonlinear function (in the usual algebraic sense) of the /f. If the F[x,3] is /-nonlinear, then statistical literature terms the model nonlinear, whereas if F[x,/,] is x-nonlinear, the model is called curvilinear. Semantically, this distinction is not too clear, and it consequently has led to confusion. Nevertheless, it is very important. The equation y = i1x + /2x2+e is both /3-linear and x-linear; whereas y = /1x + f2x2 + 33x1x2+ e is /f-linear and x-nonlinear because of the term xlx2. The equation y=lx,1 +(381) (/2)x2+e is /8-nonlinear and x-linear, but y= B1X12 + (/2) (/83) 2 + e is /8-nonlinear and x-nonlinear. We have made these distinctions at some length because we find this classification system convenient for part of this review. If y= F[x,,] + e is looked at as a prediction model, it is usual to assume that y, x, and e are random variables and that F[x,,3] is 8-linear. Also, in this case, if a particular set of values for x=X is given with X and e uncorrelated, and if the elements of e have expected values of zero and if they are independently distributed with constant common variance, then the model is known as one of multiple regression. Particular care needs to be taken to select a proper regression model. Guidance in this matter is difficult to obtain; experience and professional training are the best aids. A much-needed general discussion of model