Direction of Effects in Multiple Linear Regression Models

Previous studies analyzed asymmetric properties of the Pearson correlation coefficient using higher than second order moments. These asymmetric properties can be used to determine the direction of dependence in a linear regression setting (i.e., establish which of two variables is more likely to be on the outcome side) within the framework of cross-sectional observational data. Extant approaches are restricted to the bivariate regression case. The present contribution extends the direction of dependence methodology to a multiple linear regression setting by analyzing distributional properties of residuals of competing multiple regression models. It is shown that, under certain conditions, the third central moments of estimated regression residuals can be used to decide upon direction of effects. In addition, three different approaches for statistical inference are discussed: a combined D’Agostino normality test, a skewness difference test, and a bootstrap difference test. Type I error and power of the procedures are assessed using Monte Carlo simulations, and an empirical example is provided for illustrative purposes. In the discussion, issues concerning the quality of psychological data, possible extensions of the proposed methods to the fourth central moment of regression residuals, and potential applications are addressed.     

PROGRESS IN PSYCHOMETRICS: CAN INDUSTRIAL AND ORGANIZATIONAL PSYCHOLOGY CATCH UP?

Murphy and DeShon (2000) show that interrater correlations do not provide reasonable estimates of the reliability of job performance ratings, and suggest that better estimates can be obtained by applying the methods of generalizability theory. Schmidt, Viswesvaran, and Ones (2000) criticize our suggestions as radical, and argue that: (a) the reliability of ratings should be evaluated using the parallel test model rather than the more general and more realistic generalizability model, (b) reliability and validity are distinct concepts that should not be confused, and (c) measurement models have little to do with substantive models of the processes that generate scores on a test or measure. All three of these ideas were once part of the psychometric mainstream, but progress in psychometrics over the last 3 decades has moved the field well beyond these assumptions and approaches. Modern psychometric theory calls for close linkages between measurement models and substantive models of the phenomena being measured.     

回归混合模型：方法进展与软件实现

近来以个体为分析对象的方法日益受到研究者的重视, 其中潜类别和潜剖面模型最为流行。研究者在潜类别和潜剖面模型建模时往往需要进一步探讨协变量与潜分组之间的关系(即带有协变量的潜类别模型)。例如, 哪些变量预测个体类别归属, 以及个体的类别归属对结果变量的预测。本文对近年来研究者提出的各种方法进行了回顾和比较。包括当结果变量是分类变量的LTB法; 当结果变量是连续变量时的BCH和稳健三步法。在此基础上, 文章为应用研究者提供了Mplus软件示例, 并在最后对当前研究存在的问题和未来研究趋势进行了简要评价。     

Evidence for a Higher-Order ESEM Structure of ADHD in a Sample of Chinese Children

Exploratory structural equation modeling (ESEM) solutions have been proposed to represent the factor structures of attention-deficit/hyperactivity disorder (ADHD) in recent literature, yet no studies have assessed those structures in Chinese children. The primary aim of this study was to comprehensively examine the factor structures of the Chinese version of the ADHD Rating Scale-IV (ADHD RS-IV): Home Version. Data on 458 Chinese children aged 3–8 years (boys: 246; 54%) were used to test and compare eleven factor models: confirmatory factor analysis (CFA) models (one-factor, two-factor and three-factor), second-order CFA model, bifactor CFA models (two and three specific factors), ESEM models (two-factor and three-factor), second-order ESEM model, and bifactor ESEM models (two and three specific factors). The results showed that, overall, ESEM models displayed better fit than CFA models. Specifically, the second-order ESEM model with three first-order factors best represented of the ADHD factor structure in our sample. In addition, measurement invariance testing results showed that scalar invariance was established across gender, age and informant groups. Implications for future research are discussed.

     

A simple and powerful test for autocorrelated errors in OLS intervention models

The important assumption of independent errors should be evaluated routinely in the application of interrupted time-series regression models. The two most frequently recommended tests of this assumption [Mood's runs test and the Durbin-Watson (D-W) bounds test] have several weaknesses. The former has poor small sample Type I error performance and the latter has the bothersome property that results are often declared to be "inconclusive." The test proposed in this article is simple to compute (special software is not required), there is no inconclusive region, an exact p-value is provided, and it has good Type I error and power properties relative to competing procedures. It is shown that these desirable properties hold when design matrices of a specified form are used to model the response variable. A Monte Carlo evaluation of the method, including comparisons with other tests (viz., runs, D-W bounds, and D-W beta), and examples of application are provided.     

What Will the Neighbors Think? The Effect of Moral Communities on Cohabitation

In this study, we analyze the relationship between county-level religious adherence rates and county-level cohabitation rates in the year 2000. Based on the concept of moral communities, we test hypotheses that higher rates of affiliation with certain religious traditions and lower levels of religious heterogeneity will correlate with lower rates of cohabitation. The analysis consists of data from two sources: the 2000 U.S. Census and the 2000 Religious Congregations and Membership Study. In well-controlled models, spatial regression analysis indicates significant negative relationships between evangelical adherence rates and percent cohabiting. Our results also show that, although rates of adherence and heterogeneity also matter outside the South, the effects are consistently stronger in the South and among Christian denominations. This study advances research on cohabitation by conducting a county-level examination of the impact of religion and moral communities on the increasingly high levels of cohabitation that we are seeing in the United States.     

Gender-specific movement strategies using a computer-pointing task

Females typically demonstrate a movement time advantage for tasks requiring high levels of manual dexterity, whereas males are notably better at targeting activities. According to D. Kimura (2000), the hunter-gatherer hypothesis primarily accounts for those performance advantages; that dichotomy fails, however, when one makes movement outcome predictions for tasks that are not clearly fine-motor or interceptive in nature. Investigators have recently proposed that time constraints (M. Peters, 2005) and gender-specific response style differences (M. Peters & P. Campagnaro, 1996; L. E. Rohr, 2006) affect motor performance. Here, the author used a computer-pointing task measuring both movement error and movement time in 16 participants to further investigate response style differences. Kinematic and linear regression analyses between resultant error and both movement time and task difficulty reinforced the notion that gender-specific movement biases emphasize speed and accuracy, respectively, for men and women.     

Gender-Specific Movement Strategies Using a Computer-Pointing Task

Females typically demonstrate a movement time advantage for tasks requiring high levels of manual dexterity, whereas males are notably better at targeting activities. According to D. Kimura (2000), the hunter-gatherer hypothesis primarily accounts for those performance advantages; that dichotomy fails, however, when one makes movement outcome predictions for tasks that are not clearly fine-motor or interceptive in nature. Investigators have recently proposed that time constraints (M. Peters, 2005) and gender-specific response style differences (M. Peters & P. Campagnaro, 1996; L. E. Rohr, 2006) affect motor performance. Here, the author used a computer-pointing task measuring both movement error and movement time in 16 participants to further investigate response style differences. Kinematic and linear regression analyses between resultant error and both movement time and task difficulty reinforced the notion that gender-specific movement biases emphasize speed and accuracy, respectively, for men and women.     

The Experiences in Close Relationships-Relationship Structures questionnaire: a method for assessing attachment orientations across relationships

Most research on adult attachment is based on the assumption that working models are relatively general and trait-like. Recent research, however, suggests that people develop attachment representations that are relationship-specific, leading people to hold distinct working models in different relationships. The authors report a measure, the Relationship Structures questionnaire of the Experiences in Close Relationships-Revised (ECR-RS; R. C. Fraley, N. G. Waller, & K. A. Brennan, 2000), that is designed to assess attachment dimensions in multiple contexts. Based on a sample of over 21,000 individuals studied online, it is shown that ECR-RS scores are reliable and have a structure similar to those produced by other measures. In Study 2 (N = 388), it is shown that relationship-specific measures of attachment generally predict intra- and interpersonal outcomes better than broader attachment measures but that broader measures predict personality traits better than relationship-specific measures. Moreover, it is demonstrated that differentiation in working models is not related to psychological outcomes independently of mean levels of security.     

Effects of pair collaboration and word-frequency in recognition memory: a study with the remember-know procedure

The present study investigated the effects of pair collaboration and word-frequency on recognition memory, using the "remember-know" procedure. The aim was to test the predictions of the information-exchange hypothesis (Clark, Hori, Putnam & Martin, 2000), which states that collaborative facilitation occurs when participants are able to share their recollective memories with other members of the group. Results showed that recognition performance was significantly better in the collaborative than in the individual condition, and better for low-frequency than for high-frequency words. The advantage of collaborating dyads was produced by an increase of correct hits, coupled with a significant reduction of false alarms. Furthermore, the analysis of the "remember" (R) and "know" (K) responses indicated that the effects of both pair collaboration and word-frequency were larger on recollection than on familiarity processes. It is concluded that, in a collaborative condition, arguments based on the retrieval of the contextual details associated with the target words are more effective than those based on familiarity in increasing the proportions of correct hits. In addition, it is proposed that collaboration may lead to a reduction of the probability to accept new items on the basis of familiarity (K) responses.     

On Insensitivity of the Chi-Square Model Test to Nonlinear Misspecification in Structural Equation Models

In this paper, we show that for some structural equation models (SEM), the classical chi-square goodness-of-fit test is unable to detect the presence of nonlinear terms in the model. As an example, we consider a regression model with latent variables and interactions terms. Not only the model test has zero power against that type of misspecifications, but even the theoretical (chi-square) distribution of the test is not distorted when severe interaction term misspecification is present in the postulated model. We explain this phenomenon by exploiting results on asymptotic robustness in structural equation models. The importance of this paper is to warn against the conclusion that if a proposed linear model fits the data well according to the chi-quare goodness-of-fit test, then the underlying model is linear indeed; it will be shown that the underlying model may, in fact, be severely nonlinear. In addition, the present paper shows that such insensitivity to nonlinear terms is only a particular instance of a more general problem, namely, the incapacity of the classical chi-square goodness-of-fit test to detect deviations from zero correlation among exogenous regressors (either being them observable, or latent) when the structural part of the model is just saturated.     

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.     

运用基因表达式编程的自陈量表数据建模

探讨基因表达式编程对自陈量表测量数据的建模方法。运用威廉斯创造力测验和认知需求量表获得400位中学生的测量分数,通过数据清洗,保留383个被试的分数作为建模的数据集。运用哈曼单因素检验方法没有发现共同方法偏差。采用均匀设计方法对基因表达式编程中的5个参数进行优化配置,在测试拟合度最大的试验条件下,找到了测试误差最小的模型。比较基因表达式编程和BP神经网络、支持向量回归机、多元线性回归、二次多项式回归所建模型的预测精度。研究表明,基因表达式编程能用于自陈量表测量数据的建模,该模型比传统方法所建的模型具有更高的预测精度,而且模型是稳健的。     

A Unified Approach to Power Calculation and Sample Size Determination for Random Regression Models

The underlying statistical models for multiple regression analysis are typically attributed to two types of modeling: fixed and random. The procedures for calculating power and sample size under the fixed regression models are well known. However, the literature on random regression models is limited and has been confined to the case of all variables having a joint multivariate normal distribution. This paper presents a unified approach to determining power and sample size for random regression models with arbitrary distribution configurations for explanatory variables. Numerical examples are provided to illustrate the usefulness of the proposed method and Monte Carlo simulation studies are also conducted to assess the accuracy. The results show that the proposed method performs well for various model specifications and explanatory variable distributions. The author would like to thank the editor, the associate editor, and the referees for drawing attention to pertinent references that led to improved presentation. This research was partially supported by National Science Council grant NSC-94-2118-M-009-004.     

用层级相合性指标探测反应数据中噪音大小

不同的认知诊断模型（CDM）对反应数据中噪音的抗干扰能力不同,在评估CDM性能的模拟实验中,反应数据中所含噪音的大小是十分重要的实验条件。由于噪音的内隐性,为应用中选用相应的CDM带来困难。本文在认知模型已知条件下,欲使用MHCI和NHCI指标评估认知诊断测验的反应数据（0, 1评分）中噪音的大小。模拟实验表明,两指标与噪音存在明显的统计规律。尤其是以NHCI为主要自变量对噪音进行预测的回归方程中,回归模型解释率均接近90%;以此实现对噪音的有效预测,从而为选择CDM提供一个参考。     

A better lemon squeezer? Maximum-likelihood regression with beta-distributed dependent variables

Uncorrectable skew and heteroscedasticity are among the "lemons" of psychological data, yet many important variables naturally exhibit these properties. For scales with a lower and upper bound, a suitable candidate for models is the beta distribution, which is very flexible and models skew quite well. The authors present maximum-likelihood regression models assuming that the dependent variable is conditionally beta distributed rather than Gaussian. The approach models both means (location) and variances (dispersion) with their own distinct sets of predictors (continuous and/or categorical), thereby modeling heteroscedasticity. The location sub-model link function is the logit and thereby analogous to logistic regression, whereas the dispersion sub-model is log linear. Real examples show that these models handle the independent observations case readily. The article discusses comparisons between beta regression and alternative techniques, model selection and interpretation, practical estimation, and software.     

Hostility patterns and health implications: correlates of Cook-Medley Hostility Scale scores in a national survey

Correlated Cook-Medley Hostility Scale (Ho) scores with sociodemographic variables in a national survey of 2,536 adults. Multiple regression models revealed that Ho scores were associated with race (p less than .0001), years of education (p less than .001), sex (p less than .001), occupation (p = .0002), and income (p = .0025). Higher scores were found in non-Whites, men, and those of lower socioeconomic status. There was a Race x Income interaction (p less than .005), such that the greatest Ho score differences between the races occurred among those with the lowest incomes. Age was related to Ho scores in a curvilinear fashion: higher scores in the youngest and oldest age groups than in the middle-aged groups (p = .025). Marital status was unrelated to Ho scores. These patterns of hostility are similar to the patterns of health indicators in the population. Because hostility has been found to be associated with adverse health outcomes, hostility may account for some of the demographic variations in health status. However, it is argued that research must first establish the generality of the hostility-health relationship across subgroups of the population.     

MODELING PROBABIUSTIC CATEGORIZATION DATA:

Abstract— In probabilistic categorization tasks, the correct category is determined only probabilistically by the stimulus pattern Data from such experiments have been successfully accounted for by a simple network model, but have posed difficulties for exemplar models In the present article, we consider an exemplar model, CLEM (concept learning by exemplar memorization), which differs from previously tested exemplar models in that exemplar traces are assumed to be stored only when the subject has guessed or made a classification error Fits of CLEM to both learning and test data were comparable to those of the network model, and better than those obtained for a version of CLEM in which encoding was independent of the subject's response The implications of these results for the processes underlying classification decisions are discussed.     

Statistical inference for multiple choice tests

Finite sample inference procedures are considered for analyzing the observed scores on a multiple choice test with several items, where, for example, the items are dissimilar, or the item responses are correlated. A discrete p-parameter exponential family model leads to a generalized linear model framework and, in a special case, a convenient regression of true score upon observed score. Techniques based upon the likelihood function, Akaike's information criteria (AIC), an approximate Bayesian marginalization procedure based on conditional maximization (BCM), and simulations for exact posterior densities (importance sampling) are used to facilitate finite sample investigations of the average true score, individual true scores, and various probabilities of interest. A simulation study suggests that, when the examinees come from two different populations, the exponential family can adequately generalize Duncan's beta-binomial model. Extensions to regression models, the classical test theory model, and empirical Bayes estimation problems are mentioned. The Duncan, Keats, and Matsumura data sets are used to illustrate potential advantages and flexibility of the exponential family model, and the BCM technique.The authors wish to thank Ella Mae Matsumura for her data set and helpful comments, Frank Baker for his advice on item response theory, Hirotugu Akaike and Taskin Atilgan, for helpful discussions regarding AIC, Graham Wood for his advice concerning the class of all binomial mixture models, Yiu Ming Chiu for providing useful references and information on tetrachoric models, and the Editor and two referees for suggesting several references and alternative approaches.     

Detection of aberrant responding on a personality scale in a military sample: an application of evaluating person fit with two-level logistic regression

Person-fit assessment is used to identify persons who respond aberrantly to a test or questionnaire. In this study, S. P. Reise's (2000) method for evaluating person fit using 2-level logistic regression was applied to 13 personality scales of the Schedule for Nonadaptive and Adaptive Personality (SNAP; L. Clark, 1996) that had been administered to military recruits (N = 2,026). Results revealed significant person-fit heterogeneity and indicated that for 5 SNAP scales (Disinhibition, Entitlement, Exhibitionism, Negative Temperament, and Workaholism), the scale was more discriminating for some people than for others. Possible causes of aberrant responding were explored with several covariates. On all 5 scales, severe pathology emerged as a key influence on responses, and there was evidence of differential test functioning with respect to gender, ethnicity, or both. Other potential sources of aberrancy were carelessness, haphazard responding, or uncooperativeness. Social desirability was not as influential as expected.