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.     

Conditional Direction Dependence Analysis: Evaluating the Causal Direction of Effects in Linear Models with Interaction Terms

Abstract

Direction dependence analysis (DDA) makes use of higher than second moment information of variables (x and y) to detect potential confounding and to probe the causal direction of linear variable relations (i.e., whether x?→?y or y?→?x better approximates the underlying causal mechanism). The “true” predictor is assumed to be a continuous nonnormal exogenous variable. Existing methods compatible with DDA, however, are of limited use when the relation of a focal predictor and an outcome is affected by a moderator. This study presents a conditional direction dependence analysis (CDDA) framework which enables researchers to evaluate the causal direction of conditional regression effects. Monte–Carlo simulations were used to evaluate two different moderation scenarios: Study 1 evaluates the performance of CDDA tests when a moderator affects the strength of the causal effect x?→?y. Study 2 evaluates cases in which the causal direction itself (x?→?y vs y?→?x) depends on moderator values. Study 3 evaluates the robustness of DDA tests in the presence of functional model misspecifications. Results suggest that significance tests compatible with CDDA are suitable in both moderation scenarios, i.e., CDDA allows one to discern regions of a moderator in which the causal direction is uniquely identifiable. An empirical example is provided to illustrate the approach.     

Fungible Weights in Multiple Regression

Every set of alternate weights (i.e., nonleast squares weights) in a multiple regression analysis with three or more predictors is associated with an infinite class of weights. All members of a given class can be deemed fungiblebecause they yield identical SSE (sum of squared errors) and R ² values. Equations for generating fungible weights are reviewed and an example is given that illustrates how fungible weights can be profitably used to evaluate parameter sensitivity in multiple regression. The author wishes to thank Drs. Robyn Dawes, William Grove, Markus Keel, Leslie Yonce, Joe Rausch, the editor, and three anonymous reviewers for helpful comments on earlier versions of this article.     

Unstable Interaction in Multiple Criteria Decision Problems

In this paper, we present a decision‐aid method with interacting criteria. The fuzzy measures used to aggregate the criteria depend on the considered alternatives. Pairwise comparisons on the importance of criteria and some levels of veto (or favor) degrees, specified by the decision maker, are taken into consideration. For each alternative, we search for the fuzzy measure that makes it the best. The orness degrees of the resulting fuzzy measures are compared and the alternative associated with the minimum orness degree is selected. Copyright © 2014 John Wiley & Sons, Ltd.     

潜变量交互效应建模方法演变与简化

综述了近年来加入乘积指标的潜变量交互效应建模方法, 从产生乘积指标的策略、参数约束方法、均值结构与指标中心化的关系三个方面, 讨论了建模方法的简化进程。最后总结出同类方法中比较简洁又不失精确的潜变量交互效应建模方法—— 无需均值结构的无约束方法, 并给出了建模 步骤。     

选项具有诊断信息的多选题认知诊断测验编制

编制选项具有诊断信息的多选题是提高多选题认知诊断测验诊断效果的有效方法.研究从认知诊断的目标出发,根据认知诊断测验质量的评价标准,结合多选题的特点,探讨选项具有诊断信息的多选题认知诊断测验编制的原则.同时,结合多选题的特点和多选题采用称名计分方式的需要,对编制选项具有诊断信息的多选题提出两点要求.根据多选题认知诊断测验编制的原则和要求,给出具有可操作性的多选题认知诊断测验编制的步骤.模拟研究结果表明：根据所提出的原则和要求编制的多选题认知诊断测验具有较好的诊断效果,说明这些原则和要求合理、可行.由于这些原则、要求和步骤具有较强的可操作性,因此它对于编制多选题认知诊断测验具有一定的指导意义.     

Dealing with Multiple Solutions in Structural Vector Autoregressive Models

Structural vector autoregressive models (VARs) hold great potential for psychological science, particularly for time series data analysis. They capture the magnitude, direction of influence, and temporal (lagged and contemporaneous) nature of relations among variables. Unified structural equation modeling (uSEM) is an optimal structural VAR instantiation, according to large-scale simulation studies, and it is implemented within an SEM framework. However, little is known about the uniqueness of uSEM results. Thus, the goal of this study was to investigate whether multiple solutions result from uSEM analysis and, if so, to demonstrate ways to select an optimal solution. This was accomplished with two simulated data sets, an empirical data set concerning children's dyadic play, and modifications to the group iterative multiple model estimation (GIMME) program, which implements uSEMs with group- and individual-level relations in a data-driven manner. Results revealed multiple solutions when there were large contemporaneous relations among variables. Results also verified several ways to select the correct solution when the complete solution set was generated, such as the use of cross-validation, maximum standardized residuals, and information criteria. This work has immediate and direct implications for the analysis of time series data and for the inferences drawn from those data concerning human behavior.     

Bayesian Extended Redundancy Analysis: A Bayesian Approach to Component-based Regression with Dimension Reduction

Abstract

Extended redundancy analysis (ERA) combines linear regression with dimension reduction to explore the directional relationships between multiple sets of predictors and outcome variables in a parsimonious manner. It aims to extract a component from each set of predictors in such a way that it accounts for the maximum variance of outcome variables. In this article, we extend ERA into the Bayesian framework, called Bayesian ERA (BERA). The advantages of BERA are threefold. First, BERA enables to make statistical inferences based on samples drawn from the joint posterior distribution of parameters obtained from a Markov chain Monte Carlo algorithm. As such, it does not necessitate any resampling method, which is on the other hand required for (frequentist’s) ordinary ERA to test the statistical significance of parameter estimates. Second, it formally incorporates relevant information obtained from previous research into analyses by specifying informative power prior distributions. Third, BERA handles missing data by implementing multiple imputation using a Markov Chain Monte Carlo algorithm, avoiding the potential bias of parameter estimates due to missing data. We assess the performance of BERA through simulation studies and apply BERA to real data regarding academic achievement.     

Heteroscedasticity as a Basis of Direction Dependence in Reversible Linear Regression Models

Heteroscedasticity is a well-known issue in linear regression modeling. When heteroscedasticity is observed, researchers are advised to remedy possible model misspecification of the explanatory part of the model (e.g., considering alternative functional forms and/or omitted variables). The present contribution discusses another source of heteroscedasticity in observational data: Directional model misspecifications in the case of nonnormal variables. Directional misspecification refers to situations where alternative models are equally likely to explain the data-generating process (e.g., x → y versus y → x). It is shown that the homoscedasticity assumption is likely to be violated in models that erroneously treat true nonnormal predictors as response variables. Recently, Direction Dependence Analysis (DDA) has been proposed as a framework to empirically evaluate the direction of effects in linear models. The present study links the phenomenon of heteroscedasticity with DDA and describes visual diagnostics and nine homoscedasticity tests that can be used to make decisions concerning the direction of effects in linear models. Results of a Monte Carlo simulation that demonstrate the adequacy of the approach are presented. An empirical example is provided, and applicability of the methodology in cases of violated assumptions is discussed.     

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.     

纳入式分类分析法在潜在剖面模型的后续多元回归中的应用

纳入式分类分析法能克服传统的分类分析法对后续一元回归模型参数的低估,发挥潜在类别模型的后续分析简化变量间交互作用的功能。本文进一步将纳入式分类分析法拓展至潜在剖面模型后续的多元统计分析中。通过蒙特卡洛模拟实验,比较各种纳入变量的方法思路与后续分析模型在四种常见的多元回归模型中参数估计的表现。结果发现,纳入式分类分析法所需纳入的变量取决于后续分析中与因变量、潜类别变量的关系,且后续分析使用含交互作用的模型更为稳健。     

Quality of Life and Multiple Sclerosis: Comparison Between People with Multiple Sclerosis and People from the General Population

This paper evaluated the quality of life (QOL) of people with multiple sclerosis (MS) and people from the general population. Gender differences between the 2 groups of respondents and the influence of coping style on adjustment were also evaluated. The participants were 381 (144 males, 237 females) people with MS, and 291 (101 males, 190 females) people from the general population. The results demonstrated that people with MS experienced lower levels of QOL than people from the general population for both the objective and subjective dimensions of all domains (physical health, psychological adjustment, social relationships, environmental adjustment). All coping strategies (problem-focused, focusing on the positive, detachment, wishful thinking, seeking social support) were important predictors of QOL for both males and females with MS, with wishful thinking being the strongest predictor of poor QOL. These results are discussed in terms of the various factors that impact on QOL among people with MS, and the types of coping strategies that are most adaptive in improving the QOL of people with this illness.     

人机交互中认知负荷变化预测模型的构建

设计模拟的人机交互实验, 分析持续作业过程中认知负荷在评估指标上的变化; 采用Elman神经网络和BP神经网络二种建模方法, 探索人机交互过程中认知负荷变化预测建模的构建方法。结果显示：持续作业中认知负荷在主任务反应时、主任务正确率、注视时间、注视次数4个评估指标上变化显著; 在心理努力、任务主观难度2个评估指标上变化不显著; Elman神经网络和BP神经网络两种预测模型可以对不同作业时间段认知负荷在评估指标上发生的变化进行预测; 再结合认知负荷的综合评估模型, 可实现对不同作业时间段个体认知负荷水平等级进行分析。     

有限理性的"占优启发式"和"齐当别"决策模型的作为——当Allais悖论杠杆撬动了期望效用理论

人们在做决策时常常要受到时间或知识的限制,有时还要受到其双重限制。关于人们是如何进行风险决策,早期有期望效用理论对其加以解释,但Allais悖论对其标准化地位提出了挑战。Simon的“有限理性”观点提出后,一些研究者开始致力于开发决策的“有限理性”模型。文章讨论并比较了无限理性的期望效用理论被Allais悖论杠杆撬动之后,有限理性的“占优启发式”和“齐当别”决策模型所能做的和所不能做的。两种模型的决策标准、计算策略以及未来研究的展望也一并作了讨论。     

有限理性的“占优启发式”和“齐当别”决策模型的作为 ——当Allais悖论杠杆撬动了期望效用理论

人们在做决策时常常要受到时间或知识的限制,有时还要受到其双重限制。关于人们是如何进行风险决策,早期有期望效用理论对其加以解释,但Allais悖论对其标准化地位提出了挑战。Simon的“有限理性”观点提出后,一些研究者开始致力于开发决策的“有限理性”模型。文章讨论并比较了无限理性的期望效用理论被Allais悖论杠杆撬动之后,有限理性的“占优启发式”和“齐当别”决策模型所能做的和所不能做的。两种模型的决策标准、计算策略以及未来研究的展望也一并作了讨论     

Assessment of Multiple Membership Multilevel Models: An Application to Interviewer Effects on Nonresponse

Multilevel multiple membership models account for situations where lower level units are nested within multiple higher level units from the same classification. Not accounting correctly for such multiple membership structures leads to biased results. The use of a multiple membership model requires selection of weights reflecting the hypothesized contribution of each level two unit and their relationship to the level one outcome. The Deviance Information Criterion (DIC) has been proposed to identify such weights. For the case of logistic regression, this study assesses, through simulation, the model identification rates of the DIC to detect the correct multiple membership weights, and the properties of model variance estimators for different weight specifications across a range of scenarios. The study is motivated by analyzing interviewer effects across waves in a longitudinal study. Interviewers can substantially influence the behavior of sample survey respondents, including their decision to participate in the survey. In the case of a longitudinal survey several interviewers may contact sample members to participate across different waves. Multilevel multiple membership models are suitable to account for the inclusion of higher-level random effects for interviewers at various waves, and to assess, for example, the relative importance of previous and current wave interviewers on current wave nonresponse. To illustrate the application, multiple membership models are applied to the UK Family and Children Survey to identify interviewer effects in a longitudinal study. The paper takes a critical view on the substantive interpretation of the model weights and provides practical guidance to statistical modelers. The main recommendation is that it is best to specify the weights in a multiple membership model by exploring different weight specifications based on the DIC, rather than prespecifying the weights.     

Quantile Mediation Models: A Comparison of Methods for Assessing Mediation Across the Outcome Distribution

Recent introduction of quantile regression methods to analysis of epidemiologic data suggests that traditional mean regression approaches may not suffice for some health outcomes such as Body Mass Index (BMI). In the same vein, the traditional mean-based approach to mediation modeling may not be sufficient to capture the potentially different mediating effects of behavioral interventions across the outcome distribution. By combining methods for estimating conditional quantiles with traditional mediation modeling techniques, mediation effects can be estimated for any quantile of the outcome distribution (so-called quantile mediation effects). Estimation and inference techniques for quantile mediation effects are compared through simulation studies, and recommendations are given. The quantile mediation methods are further compared with the traditional mean-based regression approaches to mediation analysis through analysis of data from Healthy Places, a trial that is examining the effects of the community–built environment on resident obesity risk. We found the magnitudes of indirect (mediating) effects of walkability on BMI and waist circumference were substantially larger for the upper quantiles compared with the median or mean. Results suggest that restricting the examination of mediation to the mean of the outcome distribution provides an incomplete picture of proposed mediating mechanisms and in some cases may miss important mediational relationships to outcomes.     

A Comparison of Two-Stage Approaches for Fitting Nonlinear Ordinary Differential Equation Models with Mixed Effects

Several approaches exist for estimating the derivatives of observed data for model exploration purposes, including functional data analysis (FDA; Ramsay &; Silverman, 2005 Ramsay, J. O., &; Silverman, B. W. (2005). Functional data analysis (2nd ed.). New York, NY: Springer-Verlag. [Google Scholar]), generalized local linear approximation (GLLA; Boker, Deboeck, Edler, &; Peel, 2010 Boker, S. M., Deboeck, P. R., Edler, C., &; Peel, P. K. (2010). Generalized local linear approximation of derivatives from time series. In S. Chow, E. Ferrer, &; F. Hsieh (Eds.), Statistical methods for modeling human dynamics: An interdisciplinary dialogue (pp. 161–178). New York, NY: Taylor &; Francis. [Google Scholar]), and generalized orthogonal local derivative approximation (GOLD; Deboeck, 2010 Deboeck, P. R. (2010). Estimating dynamical systms: Derivative estimation hints from Sir Ronald A. Fisher. Multivariate Behavioral Research, 45, 725–745. doi:10.1080/00273171.2010.498294[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]). These derivative estimation procedures can be used in a two-stage process to fit mixed effects ordinary differential equation (ODE) models. While the performance and utility of these routines for estimating linear ODEs have been established, they have not yet been evaluated in the context of nonlinear ODEs with mixed effects. We compared properties of the GLLA and GOLD to an FDA-based two-stage approach denoted herein as functional ordinary differential equation with mixed effects (FODEmixed) in a Monte Carlo (MC) study using a nonlinear coupled oscillators model with mixed effects. Simulation results showed that overall, the FODEmixed outperformed both the GLLA and GOLD across all the embedding dimensions considered, but a novel use of a fourth-order GLLA approach combined with very high embedding dimensions yielded estimation results that almost paralleled those from the FODEmixed. We discuss the strengths and limitations of each approach and demonstrate how output from each stage of FODEmixed may be used to inform empirical modeling of young children’s self-regulation.