Some problems in the nonorthogonal analysis of variance.

Contends that nonorthogonal analysis of variance has been much misunderstood by psychologists, and as a result there has been considerable controversy as to the appropriate methods of analysis. These problems traditionally associated with the nonorthogonal multifactor analysis of variance are rather easily resolved by viewing the analysis of variance (either orthogonal or nonorthogonal) as a series of model comparisons. From this point of view, the analysis of highly confounded designs is seen to yield results that correspond to those that a purely logical analysis would suggest. A logical flow of comparisons and decisions is developed for both the 2- and 3-factor designs that, although more complicated than procedures previously proposed, seems necessary for drawing proper inferences. It is further shown that there is no logical difference between orthogonal and nonorthogonal analysis of variance. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Rules for coding dummy variables in multiple regression.

Describes how an apparent contradiction between the methods of coding dummy variables proposed by J. Cohen (see record 1969-06106-001) and those by J. Overall and D. Spiegel (see record 1970-01534-001) led to the discovery of a general formula for such coding, based on demonstrating a theoretical connection between multiple comparison and dummy multiple regression. Examples are given for various cases of orthogonal and nonorthogonal designs, which explicitly include assumptions about sample size. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Multivariate analysis of variance by multiple regression methods.

Discusses multivariate analysis of variance as a general case of familiar multiple regression analysis. A consequence of this approach is a unified treatment of multivariate analysis of variance which can be used by psychologists who are generally familiar with multiple regression approaches to univariate analysis of variance. It is suggested that the generality of the approach permits solutions consistent with any of the several available strategies for dealing with problems of unequal and disproportionate cell frequencies. Inherent in the multiple regression formulation is the otherwise not so obvious fact that univariate analysis of variance results are an integral part of the multivariate solution and that both are important for understanding complex data. Methods of interpreting multivariate analysis of variance results in complex factorial experimental designs are discussed. (32 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Parametric statistics and levels of measurement: Factorial designs and multiple regression.

Let Y be a continuous, ordinal measure of a latent variable Θ. In general, for factorial designs, an analysis of variance of the observed variable Y cannot be used to draw inferences about main effects and interactions on the latent variable Θ even when the standard normality and equality of variance assumptions hold. If Y is a continuous, ordinal measure of a latent variable Θ; X?,…, Xn are continuous, ordinal measures of latent variables Φ?,…, Φn; and the observed measures have a multivariate normal distribution, then a multiple regression analysis of the observed criterion measure Y and predictors X?,…, Xn can be used to test hypotheses about multivariate associations among the latent variables. Furthermore, the predicted values Y′ are unbiased estimates of quantities that are monotonically related to predicted values on the latent criterion variable Θ. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Orthogonality of patterns does not predict their discriminability.

The Lie algebra of continuous transformation groups proposes a theoretical basis for predicting the discriminability of patterns. Three pairs of orthogonal patterns generated by 1st-order Lie operators were used to test the predictions that (1) pair mates that are orthogonal would be more discriminable than nonorthogonal pair mates and (2) the ease of discrimination for the 3 pairs of orthogonal patterns would be predictable from the relative complexity of the Lie operators that generate them. 18 Mongolian gerbils (Meriones unguiculatus) were trained in a jumping stand to discriminate 3 successive pairs of patterns; training continued to a criterion of 2 consecutive days at 90% correct or better. The 1st prediction was not confirmed, and the 2nd was only partially confirmed. Discriminations, using a grating as the positive or negative stimulus or both, were learned significantly faster than those in which no grating appeared. Results offer no strong support for a model of pattern analysis based on the theory of Lie operators. It is concluded that simple orientation of linear contours, rather than contour orthogonality, is the most salient feature of simple patterns. (French abstract) (20 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Note on nonorthogonal analysis of variance.

Criticizes J. E. Overall and D. K. Spiegel's article (see record 1970-01534-001) discussing 3 methods for performing nonorthogonal analysis of variance (ANOVA). It is observed that the statistics obtained do not provide exact tests for main effects when one is assuming an interaction model. An alternative method is presented for treating nonorthogonal ANOVA which uses an existing general linear model program. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Reorganization of variables in analysis of variance and multidimensional contingency tables.

Appropriate reorganization of variables in some analysis of variance designs may make the obtained results more easily interpretable and may also expand the range of experimental designs that can easily be analyzed by standard procedures. A rule is given for determining equivalences of effects in terms of original and reorganized variables, and an example illustrates the usefulness for theoretical purposes of such restructuring. The potential of reorganization for broadening the range of readily applicable experimental designs, and the implications of the possibility of reorganization for nonorthogonal analysis of variance, are explored. Applications of restructuring in multidimensional contingency table analysis are noted. (19 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Cognitive and motivational variables as predictors of academic performance among disadvantaged college students.

Analyzed, via multiple regression, the validity of selected cognitive and affective variables as predictors of academic success among 106 disadvantaged minority college students. Positive zero-order correlations with the criterion variable (grade point index after 1 yr) were highest for reading, vocabulary, mathematics, intellectual achievement responsibility, and attitudes toward authority, with significant negative correlations for dogmatism, alienation, and internality-externality (selected items). Multiple regression analysis yielded an R of .62, accounting for approximately 40% of the variance in grades. The best combination of predictors was reading, attitude toward authority, internality-externality (selected items), and dogmatism, which together accounted for approximately 35% of the total variance. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Comments on the Overall and Spiegel Paper.

Responds to the comments by J. F. Overall and D. K. Spiegel (see record 1973-20070-001) on the current author's original article "Note on nonorthogonal analysis of variance" (see record 1972-26084-001). The purpose of this note is the clarification of certain erroneous interpretations concerning the nonorthogonal analysis of variance which appear in the comment by Overall and Spiegel. This note demonstrates that the method proposed by Overall and Spiegel and the method proposed by the current author are not equivalent. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Identification and prediction of two training criterion factors.

12 examination scores from 6 courses given as part of the Naval Pre-Flight Training Program were factored into two interpretable criterion factors. The intercorrelations of 10 predictor (standard test) variables were then added to the correlation matrix, and loadings for them on the criterion factors were obtained. Using the factor loadings of the predictors as validity coefficients, regression weights were found for them on each of the two criterion factors, using a modified Doolittle method. "The principal advantage… derived from the initial factor analysis of the criterion variables is that the obtained criterion factors may be isolated free from the influence of the variance of the predictor variables." (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Robustness properties of nonorthogonal analysis of variance.

Nonorthogonal analysis of variance (ANOVA) is defined as a factorial ANOVA with differing numbers of subjects in the cells. Despite the volume of literature in the psychological journals dealing with the problems of nonorthogonal ANOVA, little attention has been focused on the robustness properties of the corresponding hypothesis tests. Monte Carlo results are presented for the two-way ANOVA design indicating that all of the standard computational routines for the unequal cell size case are nonrobust. This occurs when the assumptions of homogeneity of variance or normality are violated. The user is cautioned against collecting such data. If such data must be analyzed, then alternative or supplemental analysis strategies should be used. Alternative approaches would include simulation, rank transformation, modified ANOVA procedures, and alternative developments in linear models, such as nonparametric factorial ANOVA. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Effect of personal characteristics on relationships between attitudes and job performance.

Using 376 airmen, Whitlock and Cureton (see 35: 7252) collected attitude score and biographical data, which is reanalysed in the present study, using multiple regression techniques. "… much of the criterion variance associated with attitude measures is also related to more easily obtained biographical characteristics of workers and biographical variables should be considered when relating attitudes to productivity." (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

五元精炼渣系熔化温度的研究

利用正交实验的方法对CaO-Al₂O₃-SiO₂-MgO-CaF₂精炼渣的熔点进行了研究。经过方差分析和显著性检验,得出该五元精炼渣系的最佳组成为:25%Al₂O₃、12%CaF₂、7%MgO、R2(CaO/SiO₂)=2.5。并用SPSS软件回归出了可信度高的组分与精炼渣熔化温度之间的数学关系式:T_m=1 451.3-6.25CaF₂-7.36R₂。     

Prediction of advanced level aviation performance criteria from early training and selection variables.

Considers the prediction problem in the case of designated aviators who are not successful in the replacement air group (RAG), or postgraduate, phase of instruction. The sample group consisted of 592 naval jet aviators assigned to RAG training in East and West Coast squadrons. Employing multiple correlation analysis to examine RAG completion as a remote criterion variable, undergraduate training grades significantly predicted RAG completion. Had the obtained regression weights been employed, the attrition rate of a cross-validation sample would have been reduced by 33.8%. Those skills in undergraduate training that were "mission oriented" as opposed to academic or flight skills contributed the most to the explained criterion variance. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Can decision criteria interchange locations? Some positive evidence.

In its simplest form, signal detection theory posits a single, invariant criterion for the yes/no detection task. But if paradigms with multiple criteria, such as the rating procedure, admit criterion variance, a new problem arises. If there are 2 or more response criteria on the decision axis and if these are each subject to random variation, the question arises as to whether a pair of criteria is constrained to maintain its nominal order at all times, or cause 2 criteria to change places. The theory of criterion setting developed by the 1st author and T. C. Williams (see record 1984-08523-001) is described, and it is shown that criterion-setting processes may produce criterion variance that is at least partly uncorrelated. Two alternative models for the organization of criteria in the rating procedure, the standard model and the distributed criterion model, are discussed. A prediction is derived that allows a test between the hypotheses that criteria are constrained to maintain a fixed order or that they may interchange locations on the decision axis. The results of 2 experiments, with 7 22–34 yr old observers (including the 2nd author), support the hypothesis that decision criteria may change places with one another. Alternative explanations are also considered. (20 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Refinements in the assessment of dementia-related behaviors: Factor structure of the memory and behavior problem checklist.

This study explored the factor structure of the Memory and Behavior Problem Checklist (MBPC) of S. H. Zarit et al (1980), a 29-item inventory that samples negative behavior changes associated with dementia (e.g., incontinence and destroying property). Family caregivers for 185 progressive-dementia patients provided information on their affected relatives. A principal-components factor analysis with an oblique (nonorthogonal) rotation produced an 8-factor solution that accounted for 62.9% of the variance. A second-order factor analysis of the first 5 factors produced a 3-factor solution that accounted for 74.7% of the variance. The 3 factors were (a) self-care and self-maintenance functions, (b) memory problems and psychiatric symptoms associated with dementia, and (c) communication problems and agitation. Correlations between MBPC frequency scores and measures of adaptive ability and level of dementia were high and positive. Potential clinical and research applications of the scale in other related populations are discussed. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

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. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Cancellous bone architecture: advantages of nonorthogonal trabecular alignment under multidirectional joint loading

Wolff proposed that trabeculae align at 90 degrees angles (orthogonal). However, nonorthogonal alignment of trabeculae has been observed near many joints, including the proximal femur. We propose that nonorthogonal alignment is an adaptation to multidirectional joint loads. When the loading direction does not correspond with the trabecular alignment, warping or shear coupling occurs leading to large shear strains within the cancellous structure. Using a simplified continuum model for trabecular bone, we demonstrate that shear coupling caused by multidirectional joint loads is reduced 33-75% when trabeculae are aligned 60 degrees from one another (as is observed in regions of the proximal femur), as opposed to 90 degrees from one another (as was predicted by Wolff). The results suggest that an optimal cancellous structure may appear differently under multidirectional joint loads than the 'trajectorial' organization proposed by Wolff, which was based upon assumptions drawn from unidirectional loading.     

Tukey tests for pair-wise contrasts following the analysis of variance: Is there a type IV error?

Following a significant analysis of variance F test with a Tukey multiple comparison statistic for pair-wise contrasts is a popular testing sequence. J. R. Levin and L. A. Marascuilo (1972) maintain that by adopting this sequence the E may be committing a Type IV error, since the Tukey test could detect differences not judged significant by an analysis of variance. P. A. Games (1971), however, believes that the analysis of variance-Tukey sequence is legitimate and consequently maintains that one therefore could not commit a Type IV error. Data from the present investigation indicate that the likelihood of committing a Type IV error, even if it is a theoretically valid concept for the above testing sequence, is extremely small. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Regression models for multiple outcomes in large epidemiologic studies

In situations in which one cannot specify a single primary outcome, epidemiologic analyses often examine multiple associations between outcomes and explanatory covariates or risk factors. To compare alternative approaches to the analysis of multiple outcomes in regression models, I used generalized estimating equations (GEE) models, a multivariate extension of generalized linear models, to incorporate the dependence among the outcomes from the same subject and to provide robust variance estimates of the regression coefficients. I applied the methods in a hospital-population-based study of complications of surgical anaesthesia, using GEE model fitting and quasi-likelihood score and Wald tests. In one GEE model specification, I allowed the associations between each of the outcomes and a covariate to differ, yielding a regression coefficient for each of the outcome and covariate combinations; I obtained the covariances among the set of outcome-specific regression coefficients for each covariate from the robust 'sandwich' variance estimator. To address the problem of multiple inference, I used simultaneous methods that make adjustments to the test statistic p-values and the confidence interval widths, to control type I error and simultaneous coverage, respectively. In a second model specification, for each of the covariates I assumed a common association between the outcomes and the covariate, which eliminates the problem of multiplicity by use of a global test of association. In an alternative approach to multiplicity, I used empirical Bayes methods to shrink the outcome-specific coefficients toward a pooled mean that is similar to the common effect coefficient. GEE regression models can provide a flexible framework for estimation and testing of multiple outcomes.