A Comparison of Imputation Strategies for Ordinal Missing Data on Likert Scale Variables

This article compares a variety of imputation strategies for ordinal missing data on Likert scale variables (number of categories = 2, 3, 5, or 7) in recovering reliability coefficients, mean scale scores, and regression coefficients of predicting one scale score from another. The examined strategies include imputing using normal data models with naïve rounding/without rounding, using latent variable models, and using categorical data models such as discriminant analysis and binary logistic regression (for dichotomous data only), multinomial and proportional odds logistic regression (for polytomous data only). The result suggests that both the normal model approach without rounding and the latent variable model approach perform well for either dichotomous or polytomous data regardless of sample size, missing data proportion, and asymmetry of item distributions. The discriminant analysis approach also performs well for dichotomous data. Naïvely rounding normal imputations or using logistic regression models to impute ordinal data are not recommended as they can potentially lead to substantial bias in all or some of the parameters.     

等级数据的测量不变性检验及影响因素模拟研究

研究介绍了针对等级数据的模型建构（LRV,潜在反应变量模型）和参数估计（WLSMV）方法,以及在此基础上的测量不变性检验（DIFFTEST）方法,同时采用蒙特卡洛模拟研究方法,考察样本总量大小、组间样本量对比情况、阈值差异程度、量表长度等因素,对DIFTEST进行针对等级数据的测量不变性检验效果的影响情况,以及WLSMV估计方法下的参数复原情况。研究结果发现WLSMV估计方法参数的复原效果很好;DIFFTEST的一类错误概率达到可接受水平,在大样本情况下、组间样本量基本相等、阈值差异程度较大时,DIFFTEST检测力较好。在控制测量不变性遭受破坏的项目个数情况下,随着测验长度的增加,DIFFTEST的检测力下降。     

追踪研究中缺失数据处理方法及应用现状分析

追踪研究中普遍存在缺失数据, 缺失数据处理方法的选择影响统计推断的精度及研究结果的有效性。首先, 阐述缺失机制及判断方法, 比较追踪研究中主要的缺失数据处理方法的特点、及实际应用中的缺失处理方法的选择和软件实现。其次, 对国内心理学中92篇追踪研究文献进行分析, 发现有59篇(64.13%)报告不同程度缺失, 其中仅39篇报告了处理方法且均为删除法。未来研究应深入探讨现有缺失数据处理方法的有效性, 进一步规范应用研究中缺失数据的处理。     

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。     

Self-Other Differentiation Scale: Dimensionality,IRT Parameterization,and Measurement Invariance

The Self-Other Differentiation Scale (Olver, Aries, &; Batgos, 1989 Olver, R. R., Aries, E., &; Batgos, J. (1989). Self-other differentiation and the mother-child relationship: The effects of sex and birth order. The Journal of Genetic Psychology, 150, 311–321. doi:10.1080/00221325.1989.9914600[Taylor &; Francis Online] , [Google Scholar]) is a self-report instrument assessing the experience of a separate sense of self from others. The authors aimed to examine its dimensionality, reliability, and measurement invariance across gender. It was completed by 348 participants (48% men) from 17 to 30 years old in Study 1, 348 participants (40% men) from 18 to 28 years old in Study 2, and 1,068 participants (49% men) from 17 to 28 years old in Study 3. The results supported the hypothesis of just one factor underlying the scale; they also showed an appropriate internal consistency and a partial measurement invariance across gender. Results also showed evidence for a 10-item version of the scale. Globally, the Self-Other Differentiation Scale can be considered a good scale to assess individual's sense of differentiation of one's own sense of self from others.     

Addressing Item-Level Missing Data: A Comparison of Proration and Full Information Maximum Likelihood Estimation

Often when participants have missing scores on one or more of the items comprising a scale, researchers compute prorated scale scores by averaging the available items. Methodologists have cautioned that proration may make strict assumptions about the mean and covariance structures of the items comprising the scale (Schafer &; Graham, 2002 Schafer, J.L., &; Graham, J.W. (2002). Missing data: Our view of the state of the art. Psychological Methods, 7, 147–177.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]; Graham, 2009 Graham, J.W. (2009). Missing data analysis: Making it work in the real world. Annual Review of Psychology, 60, 549–576.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]; Enders, 2010 Enders, C.K. (2010). Applied missing data analysis. New York, NY: Guilford Press. [Google Scholar]). We investigated proration empirically and found that it resulted in bias even under a missing completely at random (MCAR) mechanism. To encourage researchers to forgo proration, we describe a full information maximum likelihood (FIML) approach to item-level missing data handling that mitigates the loss in power due to missing scale scores and utilizes the available item-level data without altering the substantive analysis. Specifically, we propose treating the scale score as missing whenever one or more of the items are missing and incorporating items as auxiliary variables. Our simulations suggest that item-level missing data handling drastically increases power relative to scale-level missing data handling. These results have important practical implications, especially when recruiting more participants is prohibitively difficult or expensive. Finally, we illustrate the proposed method with data from an online chronic pain management program.     

2PL模型的两种马尔可夫蒙特卡洛缺失数据处理方法比较

马尔科夫蒙特卡洛（MCMC）是项目反应理论中处理缺失数据的一种典型方法。文章通过模拟研究比较了在不同被试人数,项目数,缺失比例下两种MCMC方法（M-H within Gibbs和DA-T Gibbs）参数估计的精确性,并结合了实证研究。研究结果表明,两种方法是有差异的,项目参数估计均受被试人数影响很大,受缺失比例影响相对更小。在样本较大缺失比例较小时,M-H within Gibbs参数估计的均方误差（RMSE）相对略小,随着样本数的减少或缺失比例的增加,DA-T Gibbs方法逐渐优于M-H within Gibbs方法     

计划缺失设计——通过有意缺失让研究更高效

缺失值是社会科学研究中非常普遍的现象。全息极大似然估计和多重插补是目前处理缺失值最有效的方法。计划缺失设计利用特殊的实验设计有意产生缺失值, 再用现代的缺失值处理方法来完成统计分析, 获得无偏的统计结果。计划缺失设计可用于横断面调查减少(或增加)问卷长度和纵向调查减少测量次数, 也可用于提高测量有效性。常用的计划缺失设计有三式设计和两种方法测量。     

Factor Retention Using Machine Learning With Ordinal Data

Determining the number of factors in exploratory factor analysis is probably the most crucial decision when conducting the analysis as it clearly influences the meaningfulness of the results (i.e., factorial validity). A new method called the Factor Forest that combines data simulation and machine learning has been developed recently. This method based on simulated data reached very high accuracy for multivariate normal data, but it has not yet been tested with ordinal data. Hence, in this simulation study, we evaluated the Factor Forest with ordinal data based on different numbers of categories (2–6 categories) and compared it to common factor retention criteria. It showed higher overall accuracy for all types of ordinal data than all common factor retention criteria that were used for comparison (Parallel Analysis, Comparison Data, the Empirical Kaiser Criterion and the Kaiser Guttman Rule). The results indicate that the Factor Forest is applicable to ordinal data with at least five categories (typical scale in questionnaire research) in the majority of conditions and to binary or ordinal data based on items with less categories when the sample size is large.     

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.     

心理测量平衡性研究与实例

心理测量研究中,测量不变性(或称平衡性)是量表稳定性问题中的一个难题而且在比较研究中受到特别重视。结构方程模型因在平衡性形式捕捉方面功能强大而受到广泛应用。该研究讨论了测量平衡性的各种形式并演示了应用结构方程模型评估测量平衡性的过程。     

Measuring Creativity with Planned Missing Data

This paper introduces a method for the assessment of creativity that relies on creativity tasks, a subjective evaluation procedure, and a planned missing data design that offers a drastic reduction in the overall implementation costs (administration time and scoring procedure). This method was tested on a sample of 149 people, using three creativity tasks as a basis. Participants were instructed to produce several ideas in each task and then to select what they considered to be their best two ideas (i.e., “Top 2” procedure; Silvia, Winterstein, Willse, Barona, et al., Psychology of Aesthetics, Creativity, and the Arts, 2 , 2008 and 68). These ideas were then evaluated by a panel of peers and experts. Creativity ratings were analyzed with structural equations; measurement models were estimated for each task and correlations between factor-scores across the three tasks were investigated. Further insights regarding validity are provided through systematic investigation of the relationship between fluency scores, creativity ratings, intelligence tasks, self-reported idea generation abilities, and creative activities and achievements. Overall, the results support the viability of this new approach, providing evidence of convergent and discriminant validity. They are discussed in relation to past research and avenues for further extension are proposed.     

Consequences of Ignoring Guessing Effects on Measurement Invariance Analysis

Pseudo-guessing parameters are present in item response theory applications for many educational assessments. When sample size is not sufficiently large, the guessing parameters may be ignored from the analysis. This study examines the impact of ignoring pseudo-guessing parameters on measurement invariance analysis, specifically, on item difficulty, item discrimination, and mean and variance of ability distribution. Results show that when non-zero guessing parameters are ignored from the measurement invariance analysis, item discrimination estimates tend to decrease particularly for more difficult items, and item difficulty estimates decrease unless the items are highly discriminating and difficult. As the guessing parameter increases, the size of the decrease in item discrimination and difficulty tends to increase, and the estimated mean and variance of ability distribution tend to be inaccurate. When two groups have heterogeneous ability distributions, ignoring the guessing parameter affects the reference group and the focal group differently. Implications of result findings are discussed.     

Nesselroade and Molenaar's Measurement Concerns and Proposals: An Introduction

In this special section Nesselroade and Molenaar (N & M) propose a provocative new approach to measurement invariance. When measures are collected repeatedly over time (e.g., daily diary studies), a potentially unique measurement model relating the items to the underlying construct can be created for each individual. If hypothesized causal paths specified between constructs (e.g., frustration → aggression) can be constrained to be equal across the individuals, a model with idiographic measurement of the constructs, but with nomothetic structural relationships can be specified. Three commentaries react to N & M's proposal. Revelle and Wilt challenge the priority given by N & M to unique individual measurement structures, arguing that between subjects differences in structural relationships are empirically important and meaningful. Markus's uses David Hume's framework to raise philosophy of science challenges for N & M's approach. Maydeu-Olivares challenges the incremental validity of N & M's approach, arguing that N & M's approach is unlikely to improve the prediction of between subjects criteria. Finally, N & M present a rejoinder to the three commentaries.     

Testing Measurement Invariance of the Dark Triad Dirty Dozen in a Belgian Adult Sample

The Dirty Dozen (Jonason & Webster, 2010) is a frequently used concise version of the Dark Triad to measure three socially aversive personality traits: Machiavellianism, psychopathy and, narcissism. The present study has examined measurement invariance in a sample of Belgian adults. The present study aims to assess measurement invariance of the Dutch version of the Dirty Dozen measure across gender in a large city-based representative adult sample in Belgium (N = 1587). Multi-group first-order confirmatory factor analysis for categorical indicators was utilized. In addition, unique associations between Dirty Dozen traits, trait self-control and, acceptance of illegitimate norms were examined in a series of structural equation models. Results indicated that the internal consistency of the Dirty Dozen subscales was good for Machiavellianism (α = 0.80) and narcissism (α = 0.80), but modest for psychopathy (α = 0.64). The hypothesized three correlated factors model with separate factors for Machiavellianism, psychopathy and, narcissism provided a poor fit for men and women. Invariance testing across gender showed evidence for weak invariance only, indicating that the underlying latent factors are measured the same way with the same metric in the two populations. However, we were not able to establish strong measurement invariance. Observed group differences should be interpreted with caution. Furthermore, Machiavellianism and psychopathy were strongly associated with trait self-control in both men and women. Strong correlations were found between acceptance of illegitimate norms and Dirty Dozen traits, Machiavellianism and, psychopathy, but not with narcissism.     

二阶因素模型的测量等价性检验——以大学生网络利他行为量表为例

与一阶因素模型相比,二阶因素模型具有较多优点,但二阶因素模型的测量等价性检验要更复杂,它需要依次进行七个不同水平的检验：形等价、一阶弱等价、二阶弱等价、一阶强等价、二阶强等价、二阶严等价和一阶严等价。低水平的等价性满足之后,才能进行更为严格的高一水平的等价性检验。运用均值和协方差结构（MACS）模型对大学生网络利他行为量表（IABSU）进行二阶因素模型的测量等价性检验,结果表明,IABSU具有跨地域的完全一阶、二阶严等价性。     

缺失数据处理的期望-极大化算法与马尔可夫蒙特卡洛方法

缺失数据普遍存在于心理学研究中, 影响着统计推断。极大似然估计(MLE)与基于贝叶斯的多重借补(MI)是处理缺失数据的两类重要方法。期望-极大化算法(EM)是寻求MLE的一种强有力的方法。马尔可夫蒙特卡洛方法(MCMC)可以相对简易地实现MI, 而且可以适用于复杂情况下的缺失数据处理。结合研究的需要讨论了实现这两类方法的适用软件。     

Bayesian Analysis of Nonlinear Structural Equation Models with Nonignorable Missing Data

A Bayesian approach is developed for analyzing nonlinear structural equation models with nonignorable missing data. The nonignorable missingness mechanism is specified by a logistic regression model. A hybrid algorithm that combines the Gibbs sampler and the Metropolis–Hastings algorithm is used to produce the joint Bayesian estimates of structural parameters, latent variables, parameters in the nonignorable missing model, as well as their standard errors estimates. A goodness-of-fit statistic for assessing the plausibility of the posited nonlinear structural equation model is introduced, and a procedure for computing the Bayes factor for model comparison is developed via path sampling. Results obtained with respect to different missing data models, and different prior inputs are compared via simulation studies. In particular, it is shown that in the presence of nonignorable missing data, results obtained by the proposed method with a nonignorable missing data model are significantly better than those that are obtained under the missing at random assumption. A real example is presented to illustrate the newly developed Bayesian methodologies. This research is fully supported by a grant (CUHK 4243/03H) from the Research Grant Council of the Hong Kong Special Administration Region. The authors are thankful to the editor and reviewers for valuable comments for improving the paper, and also to ICPSR and the relevant funding agency for allowing the use of the data. Requests for reprints should be sent to Professor S.Y. Lee, Department of Statistics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong.     

SWLS网络测验中可靠性变量的测量不变性检验

测量不变性在自我报告问卷或量表的心理测量应用中非常重要,是跨组比较的前提条件。测量不变性检验模型包括无任何约束的分组验证性因素分析(M_group)、形态的不变性(M1)、负荷的不变性(M2)、截距的不变性(M3)、严格不变性(M4)、因子方差-协方差的不变性(M5)以及潜均值的不变性(M6)。以生活满意度量表(SWLS)为例,针对1343名大学生(年龄17-25岁,20.01±1.53),进行有急事需要处理(否vs.是),答题时感受(积极情绪vs.消极情绪),噪音水平(无噪音vs.有噪音),答题用时(长vs.短),性别(男vs.女),户口(非农业户口vs.农业户口)等不同组别的生活满意度量表(SWLS)完全因素不变性检验。结果表明:(1)是否有急事需要处理的不变性成立(Δχ²=0.49～10.59,p>0.05);(2)答题时感受不变性部分成立,M5、M6模型不变性不成立(Δχ²₍₁=3.96、20.89,p<0.05);(3)噪音水平不变性部分成立,M3与M4模型不变性检验不成立(Δχ²₍₄₎=14.75,Δχ²₍₅₎=23.91,p<0.05);(4)答题用时不变性不成立(Δχ²=11.01～41.95,均p<0.05);(5)性别的不变性部分成立,M4模型不变性检验不成立(Δχ²₍₅₎=64.40,p<0.05);(6)户口的不变性部分成立,M6模型不变性检验不成立(Δχ²₍₁₎=11.49,p<0.05)。     

Measurement invariance in mentoring research: A cross-cultural examination across Taiwan and the U.S.

Workplace mentoring in the international context is an emerging research area with significant potential for global integration. However, although measurement equivalence is a prerequisite for examining cross-cultural differences, this assumption has yet to be examined in mentoring research. This study contributes to the mentoring literature by assessing the measurement equivalence of the Mentoring Functions Questionnaire (MFQ-9) across two diverse cultural settings, the U.S. and Taiwan. Results of a series of multi-group confirmatory factor analyses supported full configural invariance, full metric invariance, and partial scalar invariance across the two groups. These findings suggest MFQ-9 may provide acceptable comparisons and meaningful interpretations across cultures. Implications for future international mentoring research and managerial practice are discussed.