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.     

权力感对拟人化产品购买意愿的影响

从信息加工流畅性视角切入,探讨消费者权力感对不同类型拟人化产品购买意愿的影响及其作用机理。168名本科生参与分组实验。结果表明,对于高权力感的人来说,与热情型拟人化产品相比,他们对能力型拟人化产品的购买意愿更高;对于低权力感的人来说,与能力型拟人化产品相比,他们对热情型拟人化产品的购买意愿更高。信息加工流畅性在权力感与拟人化类型交互影响拟人化产品购买意愿关系中起完全中介作用。     

Rasch's multiplicative poisson model with covariates

As a multivariate model of the number of events, Rasch's multiplicative Poisson model is extended such that the parameters for individuals in the prior gamma distribution have continuous covariates. The parameters for individuals are integrated out and the hyperparameters in the prior distribution are estimated by a numerical method separately from difficulty parameters that are treated as fixed parameters or random variables. In addition, a method is presented for estimating parameters in Rasch's model with missing values. The author is now affiliated with the Otara University of Commerce. The author is grateful to Yoshio Takane, Haruo Yanai, Eiji Muraki, the editor and referees for their careful readings and helpful suggestions on earlier versions of this paper. Part of this work was presented at the third European Congress of Psychology at Tampere, Finland in 1993.     

基于多元回归的调节效应分析

在心理学和其他社科研究领域,大量实证研究建立调节模型,以分析自变量对因变量关系的影响机制,但在基于多元回归的调节效应分析实践中仍存在不足。我们回顾了均值中心化在基于多元回归的调节效应分析中的作用,均值中心化不影响乘积项(即调节效应)的检验,仅对一阶项(即主效应)的检验有影响。讨论了简单斜率的检验方法,建议在调节变量为连续变量时,使用Johnson-Neyman法进行简单斜率检验;在调节变量为类别变量或研究者对某个调节变量值感兴趣时,使用选点法。并用一个实际例子演示如何进行调节效应分析。随后展望了调节效应检验的拓展方向。     

Modeling individual differences using Dirichlet processes

We introduce a Bayesian framework for modeling individual differences, in which subjects are assumed to belong to one of a potentially infinite number of groups. In this model, the groups observed in any particular data set are not viewed as a fixed set that fully explains the variation between individuals, but rather as representatives of a latent, arbitrarily rich structure. As more people are seen, and more details about the individual differences are revealed, the number of inferred groups is allowed to grow. We use the Dirichlet process—a distribution widely used in nonparametric Bayesian statistics—to define a prior for the model, allowing us to learn flexible parameter distributions without overfitting the data, or requiring the complex computations typically required for determining the dimensionality of a model. As an initial demonstration of the approach, we present three applications that analyze the individual differences in category learning, choice of publication outlets, and web-browsing behavior.     

定序变量回归模型在心理数据分析中的应用

定序变量在心理现象和心理数据中随处可见, 采用综合的定序变量回归分析模型可以对“镜像模式”和“漏斗模型”的心理现象做出合理的解释和预测。首先通过非参数检验对影响因素进行初步降维, 其次用Probit定序回归对降维后的影响因素贡献率进行判别, 从而进一步筛选具有显著性判断水平的有效指标, 最后用Logistic回归模型对某种特定的心理现象发生与否进行信息量足够大的解释和预测。大学毕业生工作生活质量满意度的预测对这种综合定序变量回归分析模型的实例拟合, 证实了综合定序变量回归分析模型在心理现象和心理数据分析中的应用价值。     

基于神经元群选择理论的脑信息处理模型研究

从认识论的角度,分析了国内外脑机能模型的研究概况。总结脑信息处理的三个特性:选择性、适应性及协同性,并论述了涵盖此三个特性的神经元群选择理论。基于神经元群选择理论,提出神经元群的三种类型,并据此建立脑信息处理的模型。     

文本阅读中数量比较信息整合的过程与内容

引入数量比较信息,采用移动窗口阅读技术对文本阅读中推理的过程与内容进行研究。实验1探讨当文本阅读中存在数量比较信息时,是否能够进行即时整合,实验2和实验3分别探讨了数量比较信息即时整合的过程与内容。结果发现:当文本阅读中存在数量比较信息时,读者能够进行即时的信息整合,这种整合是自下而上的,支持记忆基础文本加工理论,如果时间足够,这种整合能够达到量化程度。     

Estimation of Group Priorities and Value of Information

In this paper, we present a Bayesian approach to model uncertainty about a group's priorities in a multicriteria evaluation problem and develop a methodology to quantify amount of information provided by a sample of priorities. In so doing, we discuss how the quantification of the information content can be used to decide to elicit additional priorities from the group. We illustrate the implementation of our approach and discuss additional insights that it provides using real‐life data from an academic department's priority analysis. Copyright © 2013 John Wiley & Sons, Ltd.     

多项式回归与一致性研究：应用及分析

本文介绍了多项式回归的分析方法, 讨论并验证了它相比传统的差异分数分析法在检验一致性假设中的优势。针对目前该方法在国内应用方面的缺失状况, 本文从分析基准、理论推导、分析步骤和假设检验等方面完善了多项式回归与响应面分析相结合的应用分析框架。最后, 本文以个人-组织价值观一致性对员工情感性变革承诺的影响研究为例, 对分析框架的具体应用进行了说明。结果表明, 被传统差异分数很好支持的一致性效应并不一定完美, 新的分析框架能够揭示更多的有用信息并给管理实践带来更具体而准确的引导。     

大学生情绪智力与感恩的交叉滞后分析

以修订后的情绪智力量表(EIS)中文版、青少年感恩量表（AGS）为研究工具,对1所普通高校的 406名大一至大三学生进行为期5个月的追踪,考察大学生情绪智力和感恩的发展变化,以及情绪智力与感恩之间的关系。结果发现：（1）大学生的情绪智力相对稳定,感恩存在一定的发展变化;（2）情绪智力与感恩之间呈显著正相关;（3）交叉滞后回归分析结果表明,前测的情绪智力可以显著预测后测的感恩,而前测的感恩不能显著预测后测的情绪智力。     

Regression to the mean and football wagers

Football performances are an imperfect measure of abilities, and consequently exaggerate differences in abilities. The skills of those football teams that perform the best and the worst are not really that far from average; thus their future performances regress to the mean. Betting data indicate that gamblers do not fully account for this regression. Copyright © 2002 John Wiley & Sons, Ltd.     

Regression estimation and post-stratification in factor analysis

Regression estimation and poststratification are methods used in survey sampling to estimate a population mean, when additional information is available for some auxiliary variables. The extension of these methods to factor analysis is considered. These methods may be used either to improve the efficiency of estimation or to adjust for the effects of nonrandom selection. The estimation procedure may be formulated in a LISREL framework.The author is grateful to the referees for their comments.     

二次响应面回归方法及其在个体-环境匹配研究中的使用

二次响应面回归分析是指二次多项式回归与响应面分析相结合的一种研究方法, 该方法在工业与组织心理学领域起源于个体−环境(P-E)匹配研究。它使用对个体−环境进行间接匹配测量的策略, 考察二者间的最佳匹配以及与结果变量的复杂关系, 并在三维空间对其进行检验和解释。该文在分析以往P-E匹配研究方法(例如差异分数)缺陷性的基础上, 阐述了二次响应面回归方法的产生与发展, 逻辑思想, 统计分析方法, 并以实例演示其操作步骤与结果解释, 以及相对于其他方法的优势与不足。     

A model for repeat trial product tests

A non-forced choice model is developed that describes subject behavior on repeat trial discrimination tests of the pick 1 ofk form. The model is developed from the Dirichlet distribution, and it allows for the derivation of individual true scores and of sampling properties for various constructs of interest. These results permit the analysis and comparison of test designs. The model is applied to issues such as forced vs. non-forced choice formats, the best number of alternatives at a choice point, and the selection of expert panels.     

Effects of Media and Collaborative Distributed Information on Concept-Learning

1IntroductionSuchman,an anthropologist,argued that actionswere always situated in particular social and physi-cal circumstances[1].In this view actions emergefrom moment-by-moment interactions between ac-tors,and between actors and their environments.The social and environmental aspects of cognitionhave been stressed in Hutchins′work[2].He hadstudied relatively structured decision environments,for example ship navigation and aeroplane piloting.His conclusions are that cognition in such situa…     

Entropy,information and predictability of evolutionary systems

We investigate first several entropy concepts, from static to dynamic entropy. Dynamic entropy is introduced as a measure of predictability. Then the relation between entropy and information is studied. Following Wiener information is considered as a non‐physical quantity, not matter or energy. Information is understood as a binary relation between a sender and a receiver. We differentiate between bound and free information. Information can be created by selforganization, historically it is connected with the origin of life. The structure and predictability of informational strings is investigated. For example we study symbolic sequences generated by evolution, as e.g. texts. It is shown that several information carriers show criticality connected with the existence of long‐range correlations, long memory in time and historical behaviour (self‐tuned criticality). The higher order Shannon entropies and the conditional entropies (dynamical entropies and there limit) are calculated, characteristic scaling laws are found.     

Integration of Analytic Hierarchy Process with Regression Analysis to Identify Attractive Locations for Market Expansion

Selection of new geographies in which to expand is a key decision for businesses aspiring to go beyond the opportunities in the existing markets. The conventional approaches of market selection can only provide a set of systematic steps for problem solving without considering the relationships between the decision factors. Decision models based on statistical techniques are able to examine the relationship between decision factors but are unable to effectively assist decision makers in identifying the most promising market, particularly in terms of prioritizing across decision factors. Analytic Hierarchy Process (AHP) is a commonly used approach for choosing alternatives by prioritizing across multiple decision factors. The typical AHP modelling requires knowledge of criteria and/or alternatives along with their relative weights, generally elicited from field experts. Quite often, firms encounter situations where decision makers are aware of only the overall objective and a set of earmarked geographies for setting up market locations while being relatively unaware of decision criteria and relative weights. This precludes using AHP to identify promising market locations. This paper conceptualizes a market selection decision model that integrates AHP with statistical modelling techniques to identify the attractive market locations for the purpose of expansion. The model first uses principal component analysis and multiple regression to determine significant decision criteria and their weights. Thereafter, it applies AHP to prioritize the market locations across the decision criteria. This integrative approach is illustrated for identifying the attractive locations in rural markets for a steel firm in India. The major advantage of this approach is that unlike the existing models, it works in situations when firms have not enough knowledge about factors for evaluating alternative market locations. Another key advantage of the proposed model is that of economizing resources for data collection on variables representing decision factors. Copyright © 2012 John Wiley & Sons, Ltd.     

A Comparative Investigation of Confidence Intervals for IndependentVariables in Linear Regression

In linear regression, the most appropriate standardized effect size for individual independent variables having an arbitrary metric remains open to debate, despite researchers typically reporting a standardized regression coefficient. Alternative standardized measures include the semipartial correlation, the improvement in the squared multiple correlation, and the squared partial correlation. No arguments based on either theoretical or statistical grounds for preferring one of these standardized measures have been mounted in the literature. Using a Monte Carlo simulation, the performance of interval estimators for these effect-size measures was compared in a 5-way factorial design. Formal statistical design methods assessed both the accuracy and robustness of the four interval estimators. The coverage probability of a large-sample confidence interval for the semipartial correlation coefficient derived from Aloe and Becker was highly accurate and robust in 98% of instances. It was better in small samples than the Yuan-Chan large-sample confidence interval for a standardized regression coefficient. It was also consistently better than both a bootstrap confidence interval for the improvement in the squared multiple correlation and a noncentral interval for the squared partial correlation.