Lyle F. Schoenfeldt

DACAR: A Fortran Program for Fitting Linear and Distance Models of Preference

DACAR is an algorithm (Davison, 1976 a, b) for fitting a broad class of linear models, distance models, and mixed linear-distance models in a multidimensional external analysis of preference data. Submodels of this general class include Tucker’s (1960) vector model, Coombs’ (1964) unfolding model, and Carroll’s (1972) weighted distance model. Using the algorithm, model parameters can be estimated, various models can be compared on the basis of their fit to the data, and expected subject preferences for various assumed models can be estimated. The algorithm can perform either a metric or a nonmetric analysis, and it can be applied to either pairwise preference data or single stimulus preference data. Using the approach described by Davi-

3-Mode-MDS: A Computer Program to Execute Tucker's Three-Mode Multidimensional Scaling

Tucker (1972) proposes a very general individual differences model for multidimensional scaling. The model assumes that all individuals share a common stimulus space and that individual differences in perceptions of stimulus relationships arise from (1) diffeïentiâi weighting of the stimulus dimensions and (2) individual differences in perceived relationships among the stimulus dimensions. Basic components of the model consist of (1) the stimulus space matrix; (2) the person space matrix; and (3) the core matrix, which specifies how each person dimension is related to perception of the stimulus dimensions. Tucker (1972) shows how the information in the person space and core matrix can be combined to produce weights and cosines of angles between stimulus dimensions for each individual.

GAPID: A Program for Generalizability Analyses with Single-Facet Designs: Robert L. Brennan, American College Testing Program

GAPID is a practitioner-oriented computer program for generalizability analyses (Cronbach, Gleser, Nanda, & Rajaratnam, 1972) with single-facet designs. The following input/output features, among others, are incorporated in GAPID: (1) input consists of a set of control cards and usually an input data matrix; (2) output is provided that is relevant for G studies and D studies involving either norm-referenced or domain-referenced score interpretations (see Brennan, 1980); (3) multiple D studies can be performed using the results for a single G study; and (4) multiple runs can be processed in the same job. This last feature of GAPID also enables it to provide some types of multiple-matrix sampling output. Although GAPID is principally intended for single-facet designs, it can be used (somewhat indirectly) to obtain sums of squares for many balanced and unbalanced designs. GAPID is primarily intended for use by practitioners in different applied settings. Consequently, consideration has been given to making GAPID easy to use, relatively fast, and suitable for implementation at different computer installations. Among the characteristics of GAPID that bear upon these issues are the following: (1) it is coded entirely in ANSI FORTRAN IV; (2) core storage requirements are unaffected by the number of rows (e.g., persons) of an input data matrix; (3) total core requirements are minimal (e.g., approximately 21K 60-bit words of core storage on a CDC CYBER 70/71 computer, and approximately 58K bytes on an IBM 370/168 computer); and (4) except for a very large input data matrix (say, over 150,000 observations), GAPID should take less than 1 minute of CPU time.

Interrelationships among interests, life-history, and educational criteria.

The relationship between measures of vocational interest, life history data, and two major educa tional criteria—performance and number of courses taken by area—was explored in a university sample of 1,900 students. Canonical correlation analysis was used to uncover and to describe the major rela tionships between the variable sets. The largest and most important dimension emerging was a general academic achievement dimension. Indices of vari ance overlap suggested that background data, rather than vocational interests, exhibited a stronger relationship with the educational criteria.

Book Reviews : R. B. Cattell and P. Kline. The Scientific Analysis of Personality and Motivation. New York: Academic Press, 1977. Pp. xii + 385.

concern explorations in the factor analytic approach to developing measures of personality, motivation, traits, moods, and states. Also examined in the text are the relationships of the resulting factors to other measures of personality and to outside criteria. As such, the book constitutes one of the most extensive and elaborate published efforts at documenting the methodology and results associated with the development and construct validation of a related series of objective and non-cognitive questionnaires, that is, the various versions of the 16 PF and related tests indelibly linked to R. B. Cattell.

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POLYCHR calculates a matrix of polychoric correlation coefficients from trichotomous data. The polychoric correlation, like the tetrachoric correlation, estimates the correlation between two continuous variables underlying categorical observations. POLYCHR should be particularly useful in analyses of interest measurement data, although it is applicable to any set of variables of trichotomous form for which an underlying bivariate normal relationship can be assumed. POLYCHR is based on the polychoric series algorithm suggested by Lancaster and Hamdan (1964). The polychoric series is an extension of the tetrachoric series concept. Although the algorithm suggested is useful for variables with any number of categories, POLYCHR is limited to variables with three categories. The original algorithm assumed the correlation was positive and gave a positive result regardless of the direction of the correlation. POLYCHR calculates the determinant of the joint frequency matrix and uses its sign as an indicator of the sign of the correlation. Input and output capabilities of POLYCHR are limited and simple. Data must be coded 1, 2, or 3 and must be complete. Output consists of the lower diagonal of the correlation matrix written to a logical unit. Enhanced input/output features may be easily added internally or externally, however.

POLYCHR: A Computer Program to Calculate Polychoric Correlation Coefficients from Trichotomous Data

Davison and his coworkers (Davison, 1979; Davison, in press; Davison, King, Kitchener, & Parker, in press; Davison & Thoma, 1979) have described and illustrated loglinear models for examining a priori hypotheses about (1) learning hierarchies in dichotomous test data; (2) patterns in rank order preference data; (3) patterns in test score profiles; and (4) duster structures in co-occurrence or oonfusion data. CONSCAL utilizes an iterative proportional fitting algorithm to fit the above models to the appropriate contingency table data. The algorithm can also be used to examine associations between outcome variables and test score profiles. Input consists of a program card, contingency table cell frequencies, a list of the number of cells associated with each parameter in the loglinear model, and a list of cells associated with each parameter. The table can have up to 124 cells, 7 ways, and 10 levels in a way. The program handles all complete tables and some incomplete ones. Output contains expected cell frequencies under the model, Pearson chi-square and likelihood ratio fit statistics, and estimates of the model parameters.

Computer Program Exchange: CONSCAL: Program for Testing Structural Hypotheses

AXMTEST is a computer-based algorithm that parallels the ADDIMOD program (cf. Nygren, 1978) for testing violations of Axioms 3 to 6 of The Additive Difference Model for dissimilarities data (Beals, Krantz, & Tversky, 1968). Whereas ADDIMOD is designed to test for violations of these axioms in an individual’s set of dissimilarity judgments, AXMTEST is based on an error theory that provides a basis for comparing observed proportions of violations of the axioms with the proportions that would be expected by chance for random data. The AXMTEST program can be particularly useful to researchers employing multidimensional scaling models (e.g., INDSCAL, ALSCAL, TORSCA), since the program can be used to derive the probabilities or, equivalently, the expected proportion of times that Axioms 3 to 6 and the triangular inequality property will be satisfied by chance in a set of