A comparison of three predictor selection techniques in multiple regression

Three methods for selecting a few predictors from the many available are described and compared with respect to shrinkage in cross-validation. From 2 to 6 predictors were selected from the 15 available in 100 samples ranging in size from 25 to 200. An iterative method was found to select predictors with slightly, but consistently, higher cross-validities than the popularly used stepwise method. A gradient method was found to equal the performance of the stepwise method only in the larger samples and for the largest predictor subsets.     

Geometrical representation of two methods of linear least squares multiple correlation

Geometrical properties and relationships of the Doolittle and square root methods of multiple correlation, as represented in the variable subspace of an orthogonal person space, are shown. The method of representation is also useful for depicting zero-order and partial correlations, as well as for the more general problem of the combination of variables.     

An evaluation of exact methods for the multiple subset maximum cardinality selection problem

The maximum cardinality subset selection problem requires finding the largest possible subset from a set of objects, such that one or more conditions are satisfied. An important extension of this problem is to extract multiple subsets, where the addition of one more object to a larger subset would always be preferred to increases in the size of one or more smaller subsets. We refer to this as the multiple subset maximum cardinality selection problem (MSMCSP). A recently published branch‐and‐bound algorithm solves the MSMCSP as a partitioning problem. Unfortunately, the computational requirement associated with the algorithm is often enormous, thus rendering the method infeasible from a practical standpoint. In this paper, we present an alternative approach that successively solves a series of binary integer linear programs to obtain a globally optimal solution to the MSMCSP. Computational comparisons of the methods using published similarity data for 45 food items reveal that the proposed sequential method is computationally far more efficient than the branch‐and‐bound approach.     

Semantic distance as a predictor of metaphor selection

Empirical research on metaphor has focused on the interpretation and comprehension of figurative language, while ignoring the production or encoding of metaphors. This research presents a basic model that attempts to explain the encoding of metaphors in expressive communication. A basic premise of the model is that similarity in connotative meaning, measured as proximity in semantic space, leads to metaphor selection. Two experiments that tested the premise are described here. The first utilized a semantic differential based on Osgood's work, while the second utilized a specially developed instrument. Results of both experiments supported the hypothesis.     

Effects of predictor intercorrelations and reliabilities on moderated multiple regression

Results of Monte Carlo simulation suggest that detection of moderator effects in moderated multiple regression is hampered by poor reliability in either the independent variable, x, or the moderator variable, w. This finding was anticipated from the fact that reliability of a product term, xw, is determined in part by the product of the reliabilities of its constituents. An interesting finding was that the probability of detection of a product (interaction) term increases as the correlation between x and w increases; it is known that the reliability of a product term increases similarly. An unexpected finding was the inflated probabilities of Type I errors that occurred for direct effects of x or w when they were not directly related to the criterion in the underlying model. Detection of spurious direct effects was exacerbated by increased correlation between x and w. It is clear that moderated multiple regression is adversely affected by measurement error, but that the impact is complex. It is apparent that researchers in this area must strive to improve the reliabilities of predictor variables if they are to have a reasonable chance of discovering moderator effects.     

Multiple bi-serial and multiple point bi-serial correlation

Normal equations, using data in various forms, are presented for securing the regression weights for prediction of a dichotomized criterion, and a simplified equation for the estimation of the multiple bi-serial or multiple point bi-serial, depending upon the proper assumption as to the nature of the distribution of the criterion, on the basis of these maximal weights is given also. The weights, unaffected by the assumption as to the nature of the criterion, are identical (or proportional) to those found by the discriminant function approach based upon analysis of variance. The author holds that the present multiple correlation approach is both easier and more informative than the discriminant function (analysis of variance) approach and suggests that the discriminant function be abandoned in favor of multiple bi-serial and/or multiple point bi-serial correlation and regression.     

Some evidence about character and mate selection

The authors conducted four studies (total N = 292) about character and mate desirability. In Study 1, undergraduates judged stimuli for attractiveness-physically and as a casual or longterm date. The target was described as faithful, having cheated but stayed with mates, or having cheated and left. Contrary to the hypothesis, men and women were equally affected by both kinds of cheaters. Study 2 replicated Study 1 with nonstudent adults. In Study 3, undergraduates rated a stimulus on the same attractiveness variables. This target had $14 million from winning a lottery or selling a dot-com company. Women, but not men, found the dot-com creator to be more physically attractive than the lottery winner. In Study 4, undergraduates rated someone who sold a cookie-making company or profited from a lucky real estate transaction. Both men and women preferred the cookie-company seller on all three measures of attractiveness.     

Identifying criterion-related patterns of predictor scores using multiple regression

Along with examples involving vocational interests and mathematics achievement, the authors describe a multiple regression based, pattern recognition procedure that can be used to identify a pattern of predictor scores associated with high scores on a criterion variable. This pattern is called the criterion pattern. After the criterion pattern has been identified, a second regression procedure can be used to estimate the proportion of variation attributable to the criterion pattern. Cross-validation can then be used to estimate the variation attributable to a criterion pattern derived from regression weights estimated in another sample. Finally, issues of criterion pattern invariance and interpretation are discussed.     

Linear dependence in multiple correlation work

The problem in multiple correlation work of nonsense results attributable to linear dependence of variables, which has been discussed by Ragnar Frisch in relation to economic data, is presented from the standpoint of its significance in psychological research. It is shown that a symmetric correlation determinant with unity in the diagonal cells can vanish only when there is a first-order or partial correlation of unity between one pair of the variables. On the basis of this result, it is argued that the problem should be expected to cause less difficulty in the field of psychology than in economics and that psychologists should be able to avoid the pitfall by bringing to bear their knowledge of the variables with which they are working.     

Methodological and computational considerations for multiple correlation analysis

The squared multiple correlation coefficient has been widely employed to assess the goodness-of-fit of linear regression models in many applications. Although there are numerous published sources that present inferential issues and computing algorithms for multinormal correlation models, the statistical procedure for testing substantive significance by specifying the nonzero-effect null hypothesis has received little attention. This article emphasizes the importance of determining whether the squared multiple correlation coefficient is small or large in comparison with some prescribed standard and develops corresponding Excel worksheets that facilitate the implementation of various aspects of the suggested significance tests. In view of the extensive accessibility of Microsoft Excel software and the ultimate convenience of general-purpose statistical packages, the associated computer routines for interval estimation, power calculation, a nd samplesize determination are alsoprovided for completeness. The statistical methods and available programs of multiple correlation analysis described in this article purport to enhance pedagogical presentation in academic curricula and practical application in psychological research.     

Some local models for correlation experiments

This paper constructs two classes of models for the quantum correlation experiments used to test the Bell-type inequalities, synchronization models and prism models. Both classes employ deterministic hidden variables, satisfy the causal requirements of physical locality, and yield precisely the quantum mechanical statistics. In the synchronization models, the joint probabilities, for each emission, do not factor in the manner of stochastic independence, showing that such factorizability is not required for locality. In the prism models the observables are not random variables over a common space; hence these models throw into question the entire random variables idiom of the literature. Both classes of models appear to be testable.Work on this paper was supported, in part, by National Science Foundation Grant SES 79-25917.     

The contribution of an orthogonal multiple factor solution to multiple correlation

A method is indicated by which multiple factor analysis may be used in determining a number,r, and then in selectingr predicting variables out ofn variables so that each of the remainingn-r variables may be predicted almost as well from ther variables as it could be predicted from all then—1 variables.     

Some effects of correlation between response-contingent shock and reinforcement

Rats responded on a two-component chain schedule in which a response-contingent electric shock at the end of the first component was either positively correlated, negatively correlated, or uncorrelated with reinforcement availability in the second component. With 0.4-ma shocks, rate in the first component depended on the shock-reinforcement correlation: when shock and reinforcement availability were positively correlated, after extended exposure to the contingencies, rates exceeded those in the absence of shock; when shock and reinforcement availability were negatively correlated, responding was generally suppressed throughout. The discriminative control of shock over responding in the second component, in which reinforcement was available 50% of the time, also depended somewhat on correlation. However, rate change in the first component was not specifically related to discrimination in the second component. With 0.8-ma shocks, responding was substantially suppressed in the first component at all three values of shock-reinforcement correlations.     

A note on correlation clusters and cluster search methods

Four methods of determining the clusters in a correlation matrix are described and compared. The choice of method has to be made according to the size of the matrix and the type of cluster sought. The relativity of clusters is emphasized and a distinction is drawn between phenomenal clusters and nuclear clusters. The relative utility of clusters and factors is briefly commented upon.     

Item selection methods for increasing test homogeneity

A number of methods for increasing test homogeneity by item selection are discussed. Exact selection conditions which will maximize obtained homogeneity as measured by KR - 20 and KR - 21 are derived, and an application is given. Since they require only item count data, the selection conditions are economical to apply.     

A further simplification of the multiple and partial correlation process

Formulas are derived for simplified computation of partial and multiple correlation coefficients, and generalized ton variables. Time required for computation is compared with other methods.     

Inhibitory mechanisms in selection among multiple object names

Many objects have multiple names. Nonlinguistic context may help to constrain object-name selection to a single alternative for use in speaking tasks. Children at three ages (5, 7, and 9 years old) named objects with multiple names in two contexts. In the neutral context, the intended object could be designated unambiguously with any of its alternative names. In the biased context, the intended referent could be clearly designated only with a name from a subset of possible alternatives. Children selected names in accord with nonlinguistic constraints, but at the cost of longer naming times. Both name selection success and associated cost were more evident in older than in younger children. The results are consistent with the hypotheses that name selection involves inhibition of competing alternative names and that efficient use of these inhibitory processes develops gradually.