Test selection and suppressor variables

A theoretical discussion of the factor pattern of predictor tests and criterion shows that ordinary test selection methods break down under certain circumstances. It is shown that maximal resultsmay not occur if suppressor variables are present among the predictors. Suggested solutions to the problem include: (1) prior item analysis of tests against the criterion, (2) selection of several trial batteries including some with suppressor variables on the basis of a factor analysis of tests and criterion, (3) modification of the usual test selection procedures to include separate solutions based upon each of several starting variables, or (4) the cumbersome and tedious solution of all possible combinations of predictors. The solutions are recommended in the order named above. Although all of the suggested solutions involve added labor and may not be necessary, the test or battery constructor should at least be aware of the problem.     

Exploratory regression analysis: A tool for selecting models and determining predictor importance

Linear regression analysis is one of the most important tools in a researcher’s toolbox for creating and testing predictive models. Although linear regression analysis indicates how strongly a set of predictor variables, taken together, will predict a relevant criterion (i.e., the multiple R), the analysis cannot indicate which predictors are the most important. Although there is no definitive or unambiguous method for establishing predictor variable importance, there are several accepted methods. This article reviews those methods for establishing predictor importance and provides a program (in Excel) for implementing them (available for direct download at . The program investigates all 2 ^p – 1 submodels and produces several indices of predictor importance. This exploratory approach to linear regression, similar to other exploratory data analysis techniques, has the potential to yield both theoretical and practical benefits.     

The effect of affine transformation on redundancy analysis

Canonical redundancy analysis provides an estimate of the amount of shared variance between two sets of variables and provides an alternative to canonical correlation. The proof that the total redundancy is equal to the average squared multiple correlation coefficient obtained by regressing each variable in the criterion set on all variables in the predictor set is generalized to the case in which there are a larger number of criterion than predictor variables. It is then shown that the redundancy for the criterion set of variables is invariant under affine transformation of the predictor variables, but not invariant under transformation of the criterion variables.     

The Appreciation of Humor in Captioned Cartoons

Humor appreciation for captioned cartoons was studied as a function of cartoon category and eight predictor variables: complexity, difficulty, fit, depth, visual humor, artwork, vulgarity, and originality. Preference and funniness proved to be virtually identical as criterion variables and were combined as appreciation for further analysis. A nonmetric factor analysis of appreciation ratings yielded four dimensions: (a) Sexual, (b) Incongruity, (c) Social Issues, and (d) Marriage-Family. Sexual and Marriage-Family were the most appreciated categories, Social Issues the least appreciated. Fit and originality were the only predictor variables with significant relationships to appreciation independent of the category effect. Cartoons judged to have the most originality and the best fit between drawing and caption were most appreciated. The results suggest that the kinds of cognitive processes involved in cartoon-humor appreciation are very similar to those involved in environmental preference.     

A criterion for selecting variables in a regression analysis

Methods are given for deciding whether to use some or no predictor variables in a regression analysis. Previously obtained results on the more general problem, whether to usek ork — r predictor variables are reviewed with emphasis on applications.     

Personality and Cognitive Ability as Predictors of Typical and Maximum Managerial Performance

Despite long-established distinctions between typical and maximum performance variables on both the predictor and criterion side, little previous research has directly addressed the extent to which these distinctions translate into differential predictor-criterion relationships. Using a sample of candidates for managerial positions, we examined relations of predictors conceptually linked to typical (i.e., broad, narrow, and compound personality traits) and maximum (i.e., broad and narrow cognitive abilities) performance with corresponding criterion measures (N = 84–873). Supervisory ratings of managerial performance served as the typical performance criterion, whereas maximum performance was assessed via an assessment center. Confirmatory factor analyses supported the distinction between typical and maximum performance. Results also confirmed our hypothesis that cognitive abilities are more strongly correlated with maximum performance than with typical performance and largely supported the expectation of the opposite pattern with personality traits as predictors.     

A square root method of selecting a minimum set of variables in multiple regression: I. The method

An extension of Dwyer's “square root” method has been made to the problem of selecting a minimum set of variables in a multiple regression problem. The square root method of selection differs from the Wherry-Doolittle method primarily in that (1) the computations required are more compact, (2) anF ratio criterion is used which leads to the selection of fewer variables. The method provides solutions for the problems of test selection, item analysis, analysis of variance with disproportionate frequencies, and other problems requiring the rejection of superfluous variables. In a subsequent article a worked example will be given, and the square root and Wherry-Doolittle methods compared.     

The relationships between contact,status and prejudice: An integrated threat theory analysis of Hindu–Muslim relations in India

In the context of Hindu–Muslim relations in India, the present study (N = 87) utilized Integrated Threat Theory (Stephan & Stephan, 2000 ) to examine the mediating roles of intergroup anxiety, realistic and symbolic threats and the moderating role of group membership (Hindu vs. Muslim) in the relationships between cross‐community contact, relative in‐group status and prejudice. Overall, intergroup anxiety and realistic, but not symbolic, threat emerged as proximal predictors of prejudice and partial mediators between the predictor and criterion variables. But these findings were qualified by majority (Hindu) versus minority (Muslim) group membership. As predicted, while symbolic threat was a predictor of prejudice for Hindus, realistic threat was a paramount predictor for Muslims. In‐group status was as a significant predictor for low‐status minority group only. The results are discussed with reference to their potential implications for future research and interventions aimed at improving intergroup relations. Copyright © 2008 John Wiley & Sons, Ltd.     

Retrieving relevant factors with exploratory SEM and principal-covariate regression: A comparison

Behavioral researchers often linearly regress a criterion on multiple predictors, aiming to gain insight into the relations between the criterion and predictors. Obtaining this insight from the ordinary least squares (OLS) regression solution may be troublesome, because OLS regression weights show only the effect of a predictor on top of the effects of other predictors. Moreover, when the number of predictors grows larger, it becomes likely that the predictors will be highly collinear, which makes the regression weights’ estimates unstable (i.e., the “bouncing beta” problem). Among other procedures, dimension-reduction-based methods have been proposed for dealing with these problems. These methods yield insight into the data by reducing the predictors to a smaller number of summarizing variables and regressing the criterion on these summarizing variables. Two promising methods are principal-covariate regression (PCovR) and exploratory structural equation modeling (ESEM). Both simultaneously optimize reduction and prediction, but they are based on different frameworks. The resulting solutions have not yet been compared; it is thus unclear what the strengths and weaknesses are of both methods. In this article, we focus on the extents to which PCovR and ESEM are able to extract the factors that truly underlie the predictor scores and can predict a single criterion. The results of two simulation studies showed that for a typical behavioral dataset, ESEM (using the BIC for model selection) in this regard is successful more often than PCovR. Yet, in 93% of the datasets PCovR performed equally well, and in the case of 48 predictors, 100 observations, and large differences in the strengths of the factors, PCovR even outperformed ESEM.     

On the Misconception of Multicollinearity in Detection of Moderating Effects: Multicollinearity Is Not Always Detrimental

Due to its extensive applicability and computational ease, moderated multiple regression (MMR) has been widely employed to analyze interaction effects between 2 continuous predictor variables. Accordingly, considerable attention has been drawn toward the supposed multicollinearity problem between predictor variables and their cross-product term. This article attempts to clarify the misconception of multicollinearity in MMR studies. The counterintuitive yet beneficial effects of multicollinearity on the ability to detect moderator relationships are explored. Comprehensive treatments and numerical investigations are presented for the simplest interaction model and more complex three-predictor setting. The results provide critical insight that both helps avoid misleading interpretations and yields better understanding for the impact of intercorrelation among predictor variables in MMR analyses.     

External Single-Set Components Analysis Of Multiple Criterion/Multiple Predictor Variables

Although much progress has been made in clarifying the properties of canonical correlation analysis in order to enhance its applicability, there are several remaining problems. Canonical variates do not always represent the observed variables even though the canonical correlation is high. In addition, canonical solutions are often difficult to interpret.

This paper presents a method designed to deal with these two problems. Instead of maximizing the correlation between unobserved variates, the sum of squared inter-set loadings is maximized. Contrary to the canonical correlation solution, this method ensures that the shared variance between predictor variates and criterion variables is maximal. Instead of extracting variates from both criterion and predictor variables, only one set of components (from the predictor variables) is constructed. Without loss of common variance, an orthogonal rotation is applied to the resulting loadings in order to simplify structure.     

Simple and multiple P‐splines regression with shape constraints

In many research areas, especially within social and behavioural sciences, the relationship between predictor and criterion variables is often assumed to have a particular shape, such as monotone, single‐peaked or U‐shaped. Such assumptions can be transformed into (local or global) constraints on the sign of the nth‐order derivative of the functional form. To check for such assumptions, we present a non‐parametric regression method, P‐splines regression, with additional asymmetric discrete penalties enforcing the constraints. We show that the corresponding loss function is convex and present a Newton–Raphson algorithm to optimize. Constrained P‐splines are illustrated with an application on monotonicity‐constrained regression with both one and two predictor variables, using data from research on the cognitive development of children.     

Organizational identification and leader evaluation in a global workplace: Interaction of self-uncertainty,self-construal,and organizational culture

Past studies in social psychology, and in organizational psychology, have incorporated social identity theory but have not specifically examined the effects of self-construal and self-uncertainty on an individual's organizational identification. Through two social psychology experiments, the present research advances the literature by studying the effects of three predictor variables (self-construal, self-uncertainty, and organizational culture) on the criterion variables of identification with the organization, commitment to the organization, extra-role behaviors (Study 1), and leader evaluations (Study 2). Study 1 (N = 256) found that participants evaluated a self-inclusive organization more favorably when it possessed a relational (as opposed to nonrelational) organizational culture. This effect was, as predicted, moderated by self-uncertainty such that it was significantly stronger under high rather than low self-uncertainty. Study 2 (N = 336) examined the same criterion variables as the previous study but with the addition of leader evaluation. It was found that interdependent participants identified with and were more committed to their organization. Participants with an interdependent self-construal and high levels of self-uncertainty rated their leader more favorably when in a relational (as opposed to nonrelational) organization. Additionally, a significant three-way interaction between the predictors was explored. Future research directions and wider implications for strengthening employee identification and leader evaluations in organizations are discussed.     

A Multivariate Analysis of Psychographic Variables

This study examined the relationship between demographic and personality variables through the use of a multivariate technique, canonical analysis. The principal advantage of such a technique lies in its ability to simultaneously consider sets of variables rather than focusing narrowly in a single predictor or criterion variable. The four demographic variables examined, sex, age, education, and marital status, produced four statistically significant relationships with personality traits measured by the Edwards Personal Preference Schedule. These relations were examined and suggestions made as to how the results might be used to indicate areas for further research.     

On a test of dimensionality in redundancy analysis

Lazraq and Cléroux (Psychometrika, 2002, 411–419) proposed a test for identifying the number of significant components in redundancy analysis. This test, however, is ill-conceived. A major problem is that it regards each redundancy component as if it were a single observed predictor variable, which cannot be justified except for the rare situations in which there is only one predictor variable. Consequently, the proposed test leads to drastically biased results, particularly when the number of predictor variables is large, and it cannot be recommended for use. This is shown both theoretically and by Monte Carlo studies.The work reported in this paper was supported by Grant A6394 to the first author from the Natural Sciences and Engineering Research Council of Canada.     

Parent involvement in school: English speaking versus Spanish speaking families

The purpose of the present study was to explore the relationships between three predictor variables (attitude toward school, parent-child communication, and school commitment action) and the criterion variable (parent involvement) in a representative sample and to examine if these relationships were consistent across three groups (English speaking Caucasian family, English speaking Latino family, and Spanish speaking Latino families). Using a national database (N = 9.841), multi-group SEM analyses were conducted to investigate the relationship between three predictor variables and the criterion variable in three family groups. While all three predictor variables significantly predicted parent involvement in English speaking Caucasian and Latino families, only two variables (parent-child communication and school commitment actions), significantly predicted parent involvement in Spanish speaking Latino families. The results of this study suggest that when administrators, teachers and counselors in school strive to share specific school-related information with Latino families, Spanish speaking families are more likely to become involved with schools.     

Fisher transformations for correlations corrected for selection and missing data

The validity of a test is often estimated in a nonrandom sample of selected individuals. To accurately estimate the relation between the predictor and the criterion we correct this correlation for range restriction. Unfortunately, this corrected correlation cannot be transformed using Fisher'sZ transformation, and asymptotic tests of hypotheses based on small or moderate samples are not accurate. We developed a Fisherr toZ transformation for the corrected correlation for each of two conditions: (a) the criterion data were missing due to selection on the predictor (the missing data were MAR); and (b) the criterion was missing at random, not due to selection (the missing data were MCAR). The twoZ transformations were evaluated in a computer simulation. The transformations were accurate, and tests of hypotheses and confidence intervals based on the transformations were superior to those that were not based on the transformations.     

Complex problem solving: another test case?

Attacks on classic complex problem solving focus on both their ecological validity and the difficulty to analyze such a complex interplay of system variables. But we argue that the domain of travel planning is in some sense a much more “natural” domain and at least partially able to deal with this kind of criticism. We first review the main existing scenarios and paradigms like Lohhausen, Tailorshop, and Moro and compare them to what we call the TRAVELPLAN problem. This problem contains a number of computationally well-investigated problems, which are worked out and can be described by so-called constrained satisfaction problems. The formal investigations have led to the development of a computational architecture which is able to deal with these kinds of subproblems simultaneously. More important, however, is that it serves as a basis for developing experiments and particularly to determine aspects of the computational complexity of the main problem. This in turn allows us to specify and to formulate experimental ideas. Finally, the status quo of ongoing experiments is briefly presented.     

Analysis of Interactions and Nonlinear Effects with Missing Data: A Factored Regression Modeling Approach Using Maximum Likelihood Estimation

Abstract

When estimating multiple regression models with incomplete predictor variables, it is necessary to specify a joint distribution for the predictor variables. A convenient assumption is that this distribution is a multivariate normal distribution, which is also the default in many statistical software packages. This distribution will in general be misspecified if predictors with missing data have nonlinear effects (e.g., x²) or are included in interaction terms (e.g., x·z). In the present article, we introduce a factored regression modeling approach for estimating regression models with missing data that is based on maximum likelihood estimation. In this approach, the model likelihood is factorized into a part that is due to the model of interest and a part that is due to the model for the incomplete predictors. In three simulation studies, we showed that the factored regression modeling approach produced valid estimates of interaction and nonlinear effects in regression models with missing values on categorical or continuous predictor variables under a broad range of conditions. We developed the R package mdmb, which facilitates a user-friendly application of the factored regression modeling approach, and present a real-data example that illustrates the flexibility of the software.     

Role stress reexamined: An investigation of role stress predictors

R. L. Kahn, R. P. Wolfe, R. P. Quinn, J. D. Snock, and R. A. Rosenthal (1964, Organizational Stress: Studies in Role Conflict and Ambiguity, New York: Wiley) distinguished three different types of predictor of role stress; personal, interpersonal, and organizational. Based on a sample of young professional engineers this investigation studied the relationship betwen these three types of predictor and four forms of role stress (role conflict, role ambiguity, quantitative role overload, qualitative role underload). The relationship was studied both within each predictor set and between each predictor set. Employing bivariate and multiple regression analyses, variables were identified within each predictor set which were significantly predictive of role stress. In addition, comparison was made between the sets of predictor variables selected and between each of the four role stresses that were studied. The results support the relevance of personal, interpersonal, and organizational predictors to role stress, as well as suggesting that role stress researchers should pay more attention to differentiating between varying forms of role Stress.