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.     

A latent class distance association model for cross‐classified data with a categorical response variable

In this paper we propose a latent class distance association model for clustering in the predictor space of large contingency tables with a categorical response variable. The rows of such a table are characterized as profiles of a set of explanatory variables, while the columns represent a single outcome variable. In many cases such tables are sparse, with many zero entries, which makes traditional models problematic. By clustering the row profiles into a few specific classes and representing these together with the categories of the response variable in a low‐dimensional Euclidean space using a distance association model, a parsimonious prediction model can be obtained. A generalized EM algorithm is proposed to estimate the model parameters and the adjusted Bayesian information criterion statistic is employed to test the number of mixture components and the dimensionality of the representation. An empirical example highlighting the advantages of the new approach and comparing it with traditional approaches is presented.     

aPRIDIT Unsupervised Classification with Asymmetric Valuation of Variable Discriminatory Worth

Abstract

Sometimes one needs to classify individuals into groups, but there is no available grouping information due to social desirability bias in reporting behavior like unethical or dishonest intentions or unlawful actions. Assessing hard-to-detect behaviors is useful; however it is methodologically difficult because people are unlikely to self-disclose bad actions. This paper presents an unsupervised classification methodology utilizing ordinal categorical predictor variables. It allows for classification, individual respondent ranking, and grouping without access to a dependent group indicator variable. The methodology also measures predictor variable worth (for determining target behavior group membership) at a predictor variable category-by-category level, so different variable response categories can contain different amounts of information about classification. It is asymmetric in that a “0” on a binary predictor does not have a similar impact toward signaling “membership in the target group” as a “1” has for signaling “membership in the non-target group.” The methodology is illustrated by identifying Spanish consumers filing fraudulent insurance claims. A second illustration classifies Portuguese high school student’s propensity to alcohol abuse. Results show the methodology is useful when it is difficult to get dependent variable information, and is useful for deciding which predictor variables and categorical response options are most important.     

Model-based recursive partitioning of extended redundancy analysis with an application to nicotine dependence among US adults

Extended redundancy analysis (ERA) is used to reduce multiple sets of predictors to a smaller number of components and examine the effects of these components on a response variable. In various social and behavioural studies, auxiliary covariates (e.g., gender, ethnicity) can often lead to heterogeneous subgroups of observations, each of which involves distinctive relationships between predictor and response variables. ERA is currently unable to consider such covariate-dependent heterogeneity to examine whether the model parameters vary across subgroups differentiated by covariates. To address this issue, we combine ERA with model-based recursive partitioning in a single framework. This combined method, MOB-ERA, aims to partition observations into heterogeneous subgroups recursively based on a set of covariates while fitting a specified ERA model to data. Upon the completion of the partitioning procedure, one can easily examine the difference in the estimated ERA parameters across covariate-dependent subgroups. Moreover, it produces a tree diagram that aids in visualizing a hierarchy of partitioning covariates, as well as interpreting their interactions. In the analysis of public data concerning nicotine dependence among US adults, the method uncovered heterogeneous subgroups characterized by several sociodemographic covariates, each of which yielded different directional relationships between three predictor sets and nicotine dependence.     

One, two or three memories: some comments and new findings

Comments are presented on a paper by Tore Helstrup, ‘One, two or three memories? A problem-solving approach to memory for performed acts’ (Acta Psychologica, 1987, 66, 37–68). There he proposed that a monistic strategy-based explanation is sufficient to explain memory for performed acts and that a multi-code (e.g. Engelkamp and Zimmer 1985) is not necessary and raises a number of problems. We claim that his findings do not disconfirm our multi-code model. Using our model, we would predict the same results in nearly all of the experiments. Because there are some results which are contradictory to a strategy-free code redundancy model, and also further results which cannot be accounted for solely by a monistic model, we propose that a valuable approach would be to combine his assumption that subjects behave strategically with our multi-code approach.     

Showing that the race model inequality is not violated

When participants are asked to respond in the same way to stimuli from different sources (e.g., auditory and visual), responses are often observed to be substantially faster when both stimuli are presented simultaneously (redundancy gain). Different models account for this effect, the two most important being race models and coactivation models. Redundancy gains consistent with the race model have an upper limit, however, which is given by the well-known race model inequality (Miller, 1982). A number of statistical tests have been proposed for testing the race model inequality in single participants and groups of participants. All of these tests use the race model as the null hypothesis, and rejection of the null hypothesis is considered evidence in favor of coactivation. We introduce a statistical test in which the race model prediction is the alternative hypothesis. This test controls the Type I error if a theory predicts that the race model prediction holds in a given experimental condition.     

The occurrence of an increase in correlation with explicit selection

It is generally believed that correlations and standard deviations measured within an explicitly selected group must be smaller than those within an applicant population. A small data set is used to show that this is not always true, and that both validity and reliability estimates within a selected group can exceed those within the applicant population. The increase in correlation within the explicitly selected group is tied to an increase in standard deviation of the predictor in the selected group. This conclusion extends Levin's (1972) result for the case of incidental selection, selection on an unmeasured third variable. If possible, theoretical derivations should not be limited to the case where the predictor standard deviation in the applicant population exceeds that in the selected group. When such a situation occurs in observed data, it cannot be immediately dismissed as an artifact.The author would like to thank Mark L. Davison and other reviewers for their comments on earlier drafts of the paper. An anonymous reviewer provided a better example than the original one, resulting in a more general conclusion.This work was supported in part by a Dissertation Fellowship from the University of Minnesota.     

Testing Manifest Monotonicity Using Order-Constrained Statistical Inference

Most dichotomous item response models share the assumption of latent monotonicity, which states that the probability of a positive response to an item is a nondecreasing function of a latent variable intended to be measured. Latent monotonicity cannot be evaluated directly, but it implies manifest monotonicity across a variety of observed scores, such as the restscore, a single item score, and in some cases the total score. In this study, we show that manifest monotonicity can be tested by means of the order-constrained statistical inference framework. We propose a procedure that uses this framework to determine whether manifest monotonicity should be rejected for specific items. This approach provides a likelihood ratio test for which the p-value can be approximated through simulation. A simulation study is presented that evaluates the Type I error rate and power of the test, and the procedure is applied to empirical data.     

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 bigram trough hypothesis and the syllable number effect in lexical decision

There has been an increasing volume of evidence supporting the role of the syllable in various word processing tasks. It has, however, been suggested that syllable effects may be caused by orthographic redundancy. In particular, it has been proposed that the presence of bigram troughs at syllable boundaries cause what are seen as syllable effects. We investigated the bigram trough hypothesis as an explanation of the number of syllables effect for lexical decision in five-letter words and nonwords from the British Lexicon Project. The number of syllables made a significant contribution to prediction of lexical decision times along with word frequency and orthographic similarity. The presence of a bigram trough did not. For nonwords, the number of syllables made a significant contribution to prediction of lexical decision times only for nonwords with relatively long decision times. The presence of a bigram trough made no contribution. The evidence presented suggests that the bigram trough cannot be an explanation of the syllable number effect in lexical decision. A comparison of the results from words and nonwords is interpreted as providing some support for dual-route models of reading.     

问卷数据建模的前传

问卷法是一种常见的实证研究方法。问卷数据建模的前期工作,就像是一栋大楼的奠基工程,基础是否扎实,影响后续的工程质量。本文专门讨论统计模型建立之前要做的事情（重点是量表评价）,内容包括：处理缺失值、评价量表的结构效度和题目删除的适当性、多维量表需要合成总分时检验同质性并计算合成信度、检验共同方法偏差和评价（变量）区分效度、题目打包、检验自变量的多重共线性,最后也涉及建模理据和无关变量控制等。     

脑成像在心理学研究领域的价值

现在普遍使用的脑成像技术给心理学研究增加了新的数据和资料。和任何新的方法一样,我们需要决定如何以适当的方式应用这项技术。这项技术如何以现有的方法所不能的方式帮助回答理论问题？这项技术最好是作为因变量还是作为预测变量来使用？它如何与其它感兴趣的心理变量相关？这种新的成像技术有助于我们了解大脑的运作及其与心理学的关系。研究人员需要弄清楚如何利用这项技术提供的信息加深对心理现象的理解。     

Comparison of optimal cutoff points for single and multiple tests in personnel selection

This paper compares the determination of optimal cutoff points for single and multiple tests in the field of personnel selection. Decisional skills of predictor tests composing the multiple test are assumed to be endogenous variables that depend on the cutting points to be set. It is shown how the predictor cutoffs and the collective decision rule are determined dependently by maximizing the multiple test's common expected utility. Our main result specifies the condition that determines the relationship between the optimal cutoff points for single and multiple tests, given the number of predictor tests, the collective decision rule (aggregation procedure of predictor tests' recommendations) and the function relating the tests' decisional skills to the predictor cutoff points. The proposed dichotomous decision-making method is illustrated by an empirical example of selecting trainees by means of the Assessment Center method.     

What Can Austin Tell Us about Truth?

In recent discussions of the problem of truth, Austin's views have been largely overlooked. This is unfortunate, since many of his criticisms aimed at Strawson's redundancy theory carry over to more recent incarnations of deflationism. And unlike contemporary versions of the correspondence theory of truth, Austin's manages properly to situate truth in its conceptual neighbourhood wherein it belongs to “a whole dimension of different appraisals which have something or other to do with the relation between what we say and the facts.” A proper analysis of truth cannot be given apart from a broader study of speech acts.     

Two efficient selection methods for high-dimensional CD-CAT utilizing max-marginals factor from MAP query and ensemble learning approach

Computerized adaptive testing for cognitive diagnosis (CD-CAT) needs to be efficient and responsive in real time to meet practical applications' requirements. For high-dimensional data, the number of categories to be recognized in a test grows exponentially as the number of attributes increases, which can easily cause system reaction time to be too long such that it adversely affects the examinees and thus seriously impacts the measurement efficiency. More importantly, the long-time CPU operations and memory usage of item selection in CD-CAT due to intensive computation are impractical and cannot wholly meet practice needs. This paper proposed two new efficient selection strategies (HIA and CEL) for high-dimensional CD-CAT to address this issue by incorporating the max-marginals from the maximum a posteriori query and integrating the ensemble learning approach into the previous efficient selection methods, respectively. The performance of the proposed selection method was compared with the conventional selection method using simulated and real item pools. The results showed that the proposed methods could significantly improve the measurement efficiency with about 1/2–1/200 of the conventional methods' computation time while retaining similar measurement accuracy. With increasing number of attributes and size of the item pool, the computation time advantage of the proposed methods becomes more significant.     

Abstract: Genome-Wide Complex Trait Analysis of Shared Genetic Effects Between Brain Electrophysiology Measures and Alcohol Dependence

Multilevel analysis is an appropriate tool for the analysis of hierarchically structured data. There may, however, be reasons to ignore one of the levels of nesting in the data analysis. In this article a three level model with one predictor variable is used as a reference model and the top or intermediate level is ignored in the data analysis. Analytical results show that this has an effect on the estimated variance components and that standard errors of regression coefficients estimators may be overestimated, leading to a lower power of the test of the effect of the predictor variable. The magnitude of these results depends on the ignored level and the level at which the predictor variable varies, and on the values of the variance components and the sample sizes.     

The usefulness of human figure drawings as an index of overall adjustment

This study investigates the relation between global ratings of human figure drawings and psychological adjustment. The sample was comprised of a group of Vietnamese refugees who were evaluated at their entry into a residential education program. Adjustment was defined as the number of foster-care placements experienced by these clients during the 5 years following the program. Results showed that ratings of overall artistic quality, figure bizarreness, and estimated client adjustment all varied linearly as a function of number of foster-care placements. A fourth predictor variable, number of Koppitz emotional indicators, did not produce this result. All four predictor variables were found to be related, and it was shown that ratings of figure bizarreness alone adequately predicted the criterion. Implications of these results are discussed, and results suggest that projective drawings could provide a useful index of overall adjustment when better sources of information are not available.     

The Usefulness of Human Figure Drawings as an Index of Overall Adjustment

This study investigates the relation between global ratings of human figure drawings and psychological adjustment. The sample was comprised of a group of Vietnamese refugees who were evaluated at their entry into a residential education program. Adjustment was defined as the number of foster-care placements experienced by these clients during the 5 years following the program. Results showed that ratings of overall artistic quality, figure bizarreness, and estimated client adjustment all varied linearly as a function of number of foster-care placements. A fourth predictor variable, number of Koppitz emotional indicators, did not produce this result. All four predictor variables were found to be related, and it was shown that rating of figure bizarreness alone adequately predicted the criterion. implications of these results are discussed, and results suggest that projective drawings could provide a useful index of overall adjustment when better sources of information are not available.     

Notes and shorter communications: Psychoticism and unemployment

The Eysenck Personality Questionnaire (EPQ) was given to male skilled and semi-skilled workers facing redundancy, in an attempt to ascertain whether any of the factors measured contributed towards a predispositional tendency for unemployment. Psychoticism was found to be a sound predictor of future work status for the school group, whilst no differences of merit were noted for any variable for the redundant group. The results are discussed in relation to other findings with regard to EPQ trait factors, and in particular to Psychoticism.     

Simultaneous nonlinear prediction

A previous article was concerned with simultaneous linear prediction [1]. There one was given a set of predictor tests or items and one predicted a set of predictands (also tests or items, or perhaps criteria.) We proposed asimultaneous prediction which was a certain weighted sum of the predictors. In the present article the constraint that the prediction be a weighted sum is relaxed. We seek a general function of the predictors which will maximize the quantity chosen for measuring prediction efficiency. This quantity is the same as the one used in linear prediction and we justify this approach by showing it is the appropriate one when there is only one predictand. In order to solve the problem we restrict consideration to a vector of predictors having only a finite number of possible values, i.e., it possesses discrete probability distribution weights. This can be applied in the case of dichotomous items for instance. It may also be used in continuous distributions as an approximation, by first dividing the original range of values into a finite number of intervals. Then one attributes to the interval the weight corresponding to the probability mass it underlies in the original distribution.This work was initiated at Stanford University under contract 2-10-065 with U. S. Office of Education and was partly revised at the Université de Montréal.I wish to express my gratitude to Professor Herbert Solomon, Stanford University, for his unfailing assistance at all stages of my work and specially for bringing to my attention the problem of nonlinear prediction in the present context.