An individual differences model for multiple regression

A model for multiple regression was developed which allows individual differences to emerge empirically. The model encompasses as special cases several of the previous attempts to improve psychological prediction by deviating from the usual linear multiple regression model. The model is tested with both artificial and real data. The results indicate that the model effectively reduces the variance of the error of prediction, and that the weights obtained are stable over different samples, and, to some extent, over different sets of predictors.This article is based upon a thesis submitted in partial fulfillment of the requirements for the doctoral degree at the University of Illinois. The author thanks Professor Ledyard R Tucker who served as committee chairman and offered considerable support and assistance.     

An elicitation method for multiple linear regression models

This paper describes a method of quantifying subjective opinion about a normal linear regression model. Opinion about the regression coefficients and experimental error is elicited and modeled by a multivariate probability distribution (a Bayesian conjugate prior distribution). The distribution model is richly parameterized and various assessment tasks are used to estimate its parameters. These tasks include the revision of opinion in the light of hypothetical data, the assessment of credible intervals, and a task commonly performed in cue-weighting experiments. A new assessment task is also introduced. In addition, implementation of the method in an interactive computer program is described and the method is illustrated with a practical example.     

Norming clinical questionnaires with multiple regression: the Pain Cognition List

Questionnaires for measuring patients' feelings or beliefs are commonly used in clinical settings for diagnostic purposes, clinical decision making, or treatment evaluation. Raw scores of a patient can be evaluated by comparing them with norms based on a reference population. Using the Pain Cognition List (PCL-2003) as an example, this article shows how clinical questionnaires can be normed with multiple regression of raw scores on demographic and other patient variables. Compared with traditional norm tables for subgroups based on age or gender, this approach offers 2 advantages. First, multiple regression allows determination of which patient variables are relevant to the norming and which are not (validity). Second, by using information from the entire sample, multiple regression leads to continuous and more stable norms for any subgroup defined in terms of prognostic variables (reliability).     

Lasso回归：从解释到预测

传统的最小二乘回归法关注于对当前数据集的准确估计, 容易导致模型的过拟合, 影响模型结论的可重复性。随着方法学领域的发展, 涌现出的新兴统计工具可以弥补传统方法的局限, 从过度关注回归系数值的解释转向提升研究结果的预测能力也愈加成为心理学领域重要的发展趋势。Lasso方法通过在模型估计中引入惩罚项的方式, 可以获得更高的预测准确度和模型概化能力, 同时也可以有效地处理过拟合和多重共线性问题, 有助于心理学理论的构建和完善。     

An R package to compute commonality coefficients in the multiple regression case: An introduction to the package and a practical example

Multiple regression is a widely used technique for data analysis in social and behavioral research. The complexity of interpreting such results increases when correlated predictor variables are involved. Commonality analysis provides a method of determining the variance accounted for by respective predictor variables and is especially useful in the presence of correlated predictors. However, computing commonality coefficients is laborious. To make commonality analysis accessible to more researchers, a program was developed to automate the calculation of unique and common elements in commonality analysis, using the statistical package R. The program is described, and a heuristic example using data from the Holzinger and Swineford (1939) study, readily available in the MBESS R package, is presented.     

An approach to the problem of differential prediction

A procedure for maximizing selective efficiency is developed for application to situations in which it is desired to select from a single group of applicants for several possible assignments. The problem of comparable units for the several criteria whose values must be compared to each other for differential assignment purposes is discussed. It is demonstrated that, assuming linear regressions, maximal selection is obtained if individuals in any given assignment are differentiated from those rejected according to critical rejection scores on the multiple weighted sum of the predictors and from another possible assignment by critical difference scores which are merely the differences between the two critical rejection scores. Since the relationships just indicated give no way of determining the magnitude of the critical scores required to select the required number of persons for each assignment, a successive approximation procedure for accomplishing this purpose has been devised and a computational example is worked out.The opinions expressed are those of the author and are not to be construed as official or as those of the War Department.     

Latent class regression analysis for describing cognitive developmental phenomena: An application to transitive reasoning

The aim of cognitive developmental research is to explain latent cognitive processes or structures by means of manifest variables such as age, cognitive behaviour, and environmental influences. In this paper the usefulness of the latent class regression model is discussed for studying cognitive developmental phenomena. Using this model, the relationships between latent and manifest variables can be explained by means of empirical data without the need of strong a priori assumptions made by a cognitive developmental theory. In the latent class regression model a number of classes are distinguished which may be characterized by particular cognitive behaviour. Environmental influences on cognitive behaviour may vary for different (developmental) classes. An application is given of the latent class regression model to transitive reasoning data. The results showed that a Five-Class model best fitted the data and that the latent classes differ with respect to age, strategy use (cognitive behaviour) and the influence of task characteristics (environmental influences) on the strategy use. The flexibility of the model in terms of mixed measurement levels and treatment of different cognitive variables offers a broad application to several cognitive developmental phenomena.     

The prediction of intelligence in preschool children using alternative models to regression

Statistical prediction of an outcome variable using multiple independent variables is a common practice in the social and behavioral sciences. For example, neuropsychologists are sometimes called upon to provide predictions of preinjury cognitive functioning for individuals who have suffered a traumatic brain injury. Typically, these predictions are made using standard multiple linear regression models with several demographic variables (e.g., gender, ethnicity, education level) as predictors. Prior research has shown conflicting evidence regarding the ability of such models to provide accurate predictions of outcome variables such as full-scale intelligence (FSIQ) test scores. The present study had two goals: (1) to demonstrate the utility of a set of alternative prediction methods that have been applied extensively in the natural sciences and business but have not been frequently explored in the social sciences and (2) to develop models that can be used to predict premorbid cognitive functioning in preschool children. Predictions of Stanford–Binet 5 FSIQ scores for preschool-aged children is used to compare the performance of a multiple regression model with several of these alternative methods. Results demonstrate that classification and regression treesprovided more accurate predictions of FSIQ scores than does the more traditional regression approach. Implications of these results are discussed.     

Comparing the predictive powers of alternative multiple regression models

Mean squared error of prediction is used as the criterion for determining which of two multiple regression models (not necessarily nested) is more predictive. We show that an unrestricted (or true) model witht parameters should be chosen over a restricted (or misspecified) model withm parameters if (P _t ² ?P _m ² )>(1?P _t ² )(t?m)/n, whereP _t ² andP _m ² are the population coefficients of determination of the unrestricted and restricted models, respectively, andn is the sample size. The left-hand side of the above inequality represents the squared bias in prediction by using the restricted model, and the right-hand side gives the reduction in variance of prediction error by using the restricted model. Thus, model choice amounts to the classical statistical tradeoff of bias against variance. In practical applications, we recommend thatP ² be estimated by adjustedR ² . Our recommendation is equivalent to performing theF-test for model comparison, and using a critical value of 2?(m/n); that is, ifF>2?(m/n), the unrestricted model is recommended; otherwise, the restricted model is recommended.     

Meehl's contribution to clinical versus statistical prediction

Paul E. Meehl's work on the clinical versus statistical prediction controversy is reviewed. His contributions included the following: putting the controversy center stage in applied psychology; clarifying concepts underpinning the debate (especially his crucial distinction between ways of gathering data and ways of combining them) as well as establishing that the controversy was real and not concocted, analyzing clinical inference from both theoretical and probabilistic points of view, and reviewing studies that compared the accuracy of these 2 methods of data combination. Meehl's (1954/1996) conclusion that statistical prediction consistently outperforms clinical judgment has stood up extremely well for half a century. His conceptual analyses have not been significantly improved since he published them in the 1950s and 1960s. His work in this area contains several citation classics, which are part of the working knowledge of all competent applied psychologists today.     

An empirical test of the problem solving model of depression and its application to the prediction of anxiety and anger

Building on research which has found positive but small correlations between stressful life events and negative psychological outcomes as well as studies which have demonstrated support for the problem solving model of depression, this study replicated the Problem Solving Model of Depression using instruments not previously used in this area. Additionally, this study tested the application and extension of the problem solving model to other emotions by assessing the efficacy of three variables, Negative Life Events, Current Problem, and Problem Solving as predictors of Depression, Anxiety, and Anger. To test this model, five assessment instruments were administered to 110 male and 178 female graduate students. Support was found for the application of this model to the prediction of Depression. While Current Problem and Problem Solving were related to Anxiety, Negative Life Events were not. In predicting Anger, some limited support was found for this model with females but no support was found with males.     

Probing three-way interactions in moderated multiple regression: development and application of a slope difference test

Researchers often use 3-way interactions in moderated multiple regression analysis to test the joint effect of 3 independent variables on a dependent variable. However, further probing of significant interaction terms varies considerably and is sometimes error prone. The authors developed a significance test for slope differences in 3-way interactions and illustrate its importance for testing psychological hypotheses. Monte Carlo simulations revealed that sample size, magnitude of the slope difference, and data reliability affected test power. Application of the test to published data yielded detection of some slope differences that were undetected by alternative probing techniques and led to changes of results and conclusions. The authors conclude by discussing the test's applicability for psychological research.     

Computing aspects of power for multiple regression

Rules of thumb for power in multiple regression research abound. Most such rules dictate the necessary sample size, but they are based only upon the number of predictor variables, usually ignoring other critical factors necessary to compute power accurately. Other guides to power in multiple regression typically use approximate rather than precise equations for the underlying distribution; entail complex preparatory computations; require interpolation with tabular presentation formats; run only under software such as Mathmatica or SAS that may not be immediately available to the user; or are sold to the user as parts of power computation packages. In contrast, the program we offer herein is immediately downloadable at no charge, runs under Windows, is interactive, self-explanatory, flexible to fit the user’s own regression problems, and is as accurate as single precision computation ordinarily permits.     

The principle of additivity and its relation to clinical decision making

Clients (N = 178) with varying degrees of organic indicators were administered a psychological battery including the Memory for Designs Test (MFD; Graham & Kendall, 1960) to assess the extent to which joint presence of organic indicators affected the sensitivity of the MFD in identifying organicity. Joint presence failed to add to the discriminability of the MFD, although individual instruments such as the PIAT (Arithmetic) and WAIS-R (PIQ less than VIQ) clearly discriminated across the MFD.     

Computing aspects of power for multiple regression.

Rules of thumb for power in multiple regression research abound. Most such rules dictate the necessary sample size, but they are based only upon the number of predictor variables, usually ignoring other critical factors necessary to compute power accurately. Other guides to power in multiple regression typically use approximate rather than precise equations for the underlying distribution; entail complex preparatory computations; require interpolation with tabular presentation formats; run only under software such as Mathmatica or SAS that may not be immediately available to the user; or are sold to the user as parts of power computation packages. In contrast, the program we offer herein is immediately downloadable at no charge, runs under Windows, is interactive, self-explanatory, flexible to fit the user's own regression problems, and is as accurate as single precision computation ordinarily permits.     

Challenging the bioethical application of the autonomy principle within multicultural societies

This article critically re-examines the application of the principle of patient autonomy within bioethics. In complex societies such as those found in North America and Europe health care professionals are increasingly confronted by patients from diverse ethnic, cultural, and religious backgrounds. This affects the relationship between clinicians and patients to the extent that patients' deliberations upon the proposed courses of treatment can, in various ways and to varying extents, be influenced by their ethnic, cultural, and religious commitments. The principle of patient autonomy is the main normative constraint imposed upon medical treatment. Bioethicists typically appeal to the principle of patient autonomy as a means for generally attempting to resolve conflict between patients and clinicians. In recent years a number of bioethicists have responded to the condition of multiculturalism by arguing that the autonomy principle provides the basis for a common moral discourse capable of regulating the relationship between clinicians and patients in those situations where patients' beliefs and commitments do or may contradict the ethos of biomedicine. This article challenges that claim. I argue that the precise manner in which the autonomy principle is philosophically formulated within such accounts prohibits bioethicists' deployment of autonomy as a core ideal for a common moral discourse within multicultural societies. The formulation of autonomy underlying such accounts cannot be extended to simply assimilate individuals' most fundamental religious and cultural commitments and affiliations per se. I challenge the assumption that respecting prospective patients' fundamental religious and cultural commitments is necessarily always compatible with respecting their autonomy. I argue that the character of some peoples' relationship with their cultural or religious community acts to significantly constrain the possibilities for acting autonomously. The implication is clear. The autonomy principle may be presently invalidly applied in certain circumstances because the conditions for the exercise of autonomy have not been fully or even adequately satisfied. This is a controversial claim. The precise terms of my argument, while addressing the specific application of the autonomy principle within bioethics, will resonate beyond this sphere and raises questions for attempts to establish a common moral discourse upon the ideal of personal autonomy within multicultural societies generally.     

The application of multiple factorial methods to the study of motor abilities

A battery of thirteen tests of motor abilities are analyzed by means of the Thurstone factor methods. Interpretations of the nature of the six factors extracted are offered, with reservations. The high degree of specificity of motor abilities results in very narrow group factors.