Simple imputation methods versus direct likelihood analysis for missing item scores in multilevel educational data

Missing data, such as item responses in multilevel data, are ubiquitous in educational research settings. Researchers in the item response theory (IRT) context have shown that ignoring such missing data can create problems in the estimation of the IRT model parameters. Consequently, several imputation methods for dealing with missing item data have been proposed and shown to be effective when applied with traditional IRT models. Additionally, a nonimputation direct likelihood analysis has been shown to be an effective tool for handling missing observations in clustered data settings. This study investigates the performance of six simple imputation methods, which have been found to be useful in other IRT contexts, versus a direct likelihood analysis, in multilevel data from educational settings. Multilevel item response data were simulated on the basis of two empirical data sets, and some of the item scores were deleted, such that they were missing either completely at random or simply at random. An explanatory IRT model was used for modeling the complete, incomplete, and imputed data sets. We showed that direct likelihood analysis of the incomplete data sets produced unbiased parameter estimates that were comparable to those from a complete data analysis. Multiple-imputation approaches of the two-way mean and corrected item mean substitution methods displayed varying degrees of effectiveness in imputing data that in turn could produce unbiased parameter estimates. The simple random imputation, adjusted random imputation, item means substitution, and regression imputation methods seemed to be less effective in imputing missing item scores in multilevel data settings.     

Dual imputation model for incomplete longitudinal data

Missing values are a practical issue in the analysis of longitudinal data. Multiple imputation (MI) is a well‐known likelihood‐based method that has optimal properties in terms of efficiency and consistency if the imputation model is correctly specified. Doubly robust (DR) weighing‐based methods protect against misspecification bias if one of the models, but not necessarily both, for the data or the mechanism leading to missing data is correct. We propose a new imputation method that captures the simplicity of MI and protection from the DR method. This method integrates MI and DR to protect against misspecification of the imputation model under a missing at random assumption. Our method avoids analytical complications of missing data particularly in multivariate settings, and is easy to implement in standard statistical packages. Moreover, the proposed method works very well with an intermittent pattern of missingness when other DR methods can not be used. Simulation experiments show that the proposed approach achieves improved performance when one of the models is correct. The method is applied to data from the fireworks disaster study, a randomized clinical trial comparing therapies in disaster‐exposed children. We conclude that the new method increases the robustness of imputations.     

A Cautious Note on Auxiliary Variables That Can Increase Bias in Missing Data Problems

The treatment of missing data in the social sciences has changed tremendously during the last decade. Modern missing data techniques such as multiple imputation and full-information maximum likelihood are used much more frequently. These methods assume that data are missing at random. One very common approach to increase the likelihood that missing at random is achieved consists of including many covariates as so-called auxiliary variables. These variables are either included based on data considerations or in an inclusive fashion; that is, taking all available auxiliary variables. In this article, we point out that there are some instances in which auxiliary variables exhibit the surprising property of increasing bias in missing data problems. In a series of focused simulation studies, we highlight some situations in which this type of biasing behavior can occur. We briefly discuss possible ways how one can avoid selecting bias-inducing covariates as auxiliary variables.     

Methods for Mediation Analysis with Missing Data

Despite wide applications of both mediation models and missing data techniques, formal discussion of mediation analysis with missing data is still rare. We introduce and compare four approaches to dealing with missing data in mediation analysis including listwise deletion, pairwise deletion, multiple imputation (MI), and a two-stage maximum likelihood (TS-ML) method. An R package bmem is developed to implement the four methods for mediation analysis with missing data in the structural equation modeling framework, and two real examples are used to illustrate the application of the four methods. The four methods are evaluated and compared under MCAR, MAR, and MNAR missing data mechanisms through simulation studies. Both MI and TS-ML perform well for MCAR and MAR data regardless of the inclusion of auxiliary variables and for AV-MNAR data with auxiliary variables. Although listwise deletion and pairwise deletion have low power and large parameter estimation bias in many studied conditions, they may provide useful information for exploring missing mechanisms.     

Tests of Homoscedasticity,Normality, and Missing Completely at Random for Incomplete Multivariate Data

Test of homogeneity of covariances (or homoscedasticity) among several groups has many applications in statistical analysis. In the context of incomplete data analysis, tests of homoscedasticity among groups of cases with identical missing data patterns have been proposed to test whether data are missing completely at random (MCAR). These tests of MCAR require large sample sizes n and/or large group sample sizes n _i , and they usually fail when applied to nonnormal data. Hawkins (Technometrics 23:105–110, 1981) proposed a test of multivariate normality and homoscedasticity that is an exact test for complete data when n _i are small. This paper proposes a modification of this test for complete data to improve its performance, and extends its application to test of homoscedasticity and MCAR when data are multivariate normal and incomplete. Moreover, it is shown that the statistic used in the Hawkins test in conjunction with a nonparametric k-sample test can be used to obtain a nonparametric test of homoscedasticity that works well for both normal and nonnormal data. It is explained how a combination of the proposed normal-theory Hawkins test and the nonparametric test can be employed to test for homoscedasticity, MCAR, and multivariate normality. Simulation studies show that the newly proposed tests generally outperform their existing competitors in terms of Type I error rejection rates. Also, a power study of the proposed tests indicates good power. The proposed methods use appropriate missing data imputations to impute missing data. Methods of multiple imputation are described and one of the methods is employed to confirm the result of our single imputation methods. Examples are provided where multiple imputation enables one to identify a group or groups whose covariance matrices differ from the majority of other groups.     

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。     

Biases in multilevel analyses caused by cluster-specific fixed-effects imputation

When datasets are affected by nonresponse, imputation of the missing values is a viable solution. However, most imputation routines implemented in commonly used statistical software packages do not accommodate multilevel models that are popular in education research and other settings involving clustering of units. A common strategy to take the hierarchical structure of the data into account is to include cluster-specific fixed effects in the imputation model. Still, this ad hoc approach has never been compared analytically to the congenial multilevel imputation in a random slopes setting. In this paper, we evaluate the impact of the cluster-specific fixed-effects imputation model on multilevel inference. We show analytically that the cluster-specific fixed-effects imputation strategy will generally bias inferences obtained from random coefficient models. The bias of random-effects variances and global fixed-effects confidence intervals depends on the cluster size, the relation of within- and between-cluster variance, and the missing data mechanism. We illustrate the negative implications of cluster-specific fixed-effects imputation using simulation studies and an application based on data from the National Educational Panel Study (NEPS) in Germany.     

Data‐driven Methods for Modeling Social Perception

How do we model the complexity of social perception? A major methodological problem is that the space of possible variables driving social perceptions is infinitely large, thus posing an insurmountable hurdle for conventional approaches. Here, we describe a set of data‐driven methods whose objective is to identify quantitative relationships between high‐dimensional variables (e.g., visual images) and behaviors (e.g., perceptual decisions) with as little bias as possible. We focus on social perception of faces, although the methods could be applied to other visual and nonvisual categories. We review two reverse correlation approaches: (a) psychophysical methods based on judgments of images altered with randomly generated noise, where the analysis relates the random variations of the images to judgments; and (b) methods based on judgments of randomly generated faces from a statistical, multidimensional face space model, where the analysis relates the dimensions of the face model to judgments.     

2PLM下缺失数据处理方法及其比较

项目反应理论(IRT)是用于客观测量的现代教育与心理测量理论之一,广泛用于缺失数据十分常见的大尺度测验分析。IRT中两参数逻辑斯蒂克模型(2PLM)下仅有完全随机缺失机制下缺失反应和缺失能力处理的EM算法。本研究推导2PLM下缺失反应忽略的EM 算法,并提出随机缺失机制下缺失反应和缺失能力处理的EM算法和考虑能力估计和作答反应不确定性的多重借补法。研究显示：在各种缺失机制、缺失比例和测验设计下,缺失反应忽略的EM算法和多重借补法表现理想。     

Alternative Multiple Imputation Inference for Categorical Structural Equation Modeling

The use of item responses from questionnaire data is ubiquitous in social science research. One side effect of using such data is that researchers must often account for item level missingness. Multiple imputation is one of the most widely used missing data handling techniques. The traditional multiple imputation approach in structural equation modeling has a number of limitations. Motivated by Lee and Cai’s approach, we propose an alternative method for conducting statistical inference from multiple imputation in categorical structural equation modeling. We examine the performance of our proposed method via a simulation study and illustrate it with one empirical data set.     

Maternal employment and child development: a fresh look using newer methods

The employment rate for mothers with young children has increased dramatically over the past 25 years. Estimating the effects of maternal employment on children's development is challenged by selection bias and the missing data endemic to most policy research. To address these issues, this study uses propensity score matching and multiple imputation. The authors compare outcomes across 4 maternal employment patterns: no work in first 3 years postbirth, work only after 1st year, part-time work in 1st year, and full-time work in 1st year. Our results demonstrate small but significant negative effects of maternal employment on children's cognitive outcomes for full-time employment in the 1st year postbirth as compared with employment postponed until after the 1st year. Multiple imputation yields noticeably different estimates as compared with a complete case approach for many measures. Differences between results from propensity score approaches and regression modeling are often minimal.     

A Nonparametric,Multiple Imputation-Based Method for the Retrospective Integration of Data Sets

Complex research questions often cannot be addressed adequately with a single data set. One sensible alternative to the high cost and effort associated with the creation of large new data sets is to combine existing data sets containing variables related to the constructs of interest. The goal of the present research was to develop a flexible, broadly applicable approach to the integration of disparate data sets that is based on nonparametric multiple imputation and the collection of data from a convenient, de novo calibration sample. We demonstrate proof of concept for the approach by integrating three existing data sets containing items related to the extent of problematic alcohol use and associations with deviant peers. We discuss both necessary conditions for the approach to work well and potential strengths and weaknesses of the method compared to other data set integration approaches.     

Handling of missing values in path models for opinions or attitudes

In this article we show, by means of a practical example of a path model to explain opinions or attitudes and using a dataset well-known in The Netherlands, that the intercorrelations of the variables may be highly dependent on the number of variables and the corresponding number of missing data involved. As a consequence, differences could arise in the results of multiple regressions and path analyses. (The role of a suppressant variable in a path model will be touched on in passing.) Subsequently, the way that the character of the sample can change when a more rigid listwise selection of cases is applied is demonstrated. Since a practical example is involved, substantive arguments may be used for choosing a strategy of handling of the missing values. In our view, with reference to path models of opinions or attitudes, these arguments lead not to the use of one of the current imputation techniques or sophisticated methods to estimate the population values of the model parameters, but to what may be called a differentiated listwise selection.     

Modeling competence development in the presence of selection bias

A major challenge for representative longitudinal studies is panel attrition, because some respondents refuse to continue participating across all measurement waves. Depending on the nature of this selection process, statistical inferences based on the observed sample can be biased. Therefore, statistical analyses need to consider a missing-data mechanism. Because each missing-data model hinges on frequently untestable assumptions, sensitivity analyses are indispensable to gauging the robustness of statistical inferences. This article highlights contemporary approaches for applied researchers to acknowledge missing data in longitudinal, multilevel modeling and shows how sensitivity analyses can guide their interpretation. Using a representative sample of N = 13,417 German students, the development of mathematical competence across three years was examined by contrasting seven missing-data models, including listwise deletion, full-information maximum likelihood estimation, inverse probability weighting, multiple imputation, selection models, and pattern mixture models. These analyses identified strong selection effects related to various individual and context factors. Comparative analyses revealed that inverse probability weighting performed rather poorly in growth curve modeling. Moreover, school-specific effects should be acknowledged in missing-data models for educational data. Finally, we demonstrated how sensitivity analyses can be used to gauge the robustness of the identified effects.     

Estimating Optimal Weights for Compound Scores: A Multidimensional IRT Approach

A method is proposed for constructing indices as linear functions of variables such that the reliability of the compound score is maximized. Reliability is defined in the framework of latent variable modeling [i.e., item response theory (IRT)] and optimal weights of the components of the index are found by maximizing the posterior variance relative to the total latent variable variance. Three methods for estimating the weights are proposed. The first is a likelihood-based approach, that is, marginal maximum likelihood (MML). The other two are Bayesian approaches based on Markov chain Monte Carlo (MCMC) computational methods. One is based on an augmented Gibbs sampler specifically targeted at IRT, and the other is based on a general purpose Gibbs sampler such as implemented in OpenBugs and Jags. Simulation studies are presented to demonstrate the procedure and to compare the three methods. Results are very similar, so practitioners may be suggested the use of the easily accessible latter method. A real-data set pertaining to the 28-joint Disease Activity Score is used to show how the methods can be applied in a complex measurement situation with multiple time points and mixed data formats.     

Randomization tests for ABAB designs: comparing-data-division- specific and common distributions

Monte Carlo simulations were used to generate data for ABAB designs of different lengths. The points of change in phase are randomly determined before gathering behaviour measurements, which allows the use of a randomization test as an analytic technique. Data simulation and analysis can be based either on data-division-specific or on common distributions. Following one method or another affects the results obtained after the randomization test has been applied. Therefore, the goal of the study was to examine these effects in more detail. The discrepancies in these approaches are obvious when data with zero treatment effect are considered and such approaches have implications for statistical power studies. Data-division-specific distributions provide more detailed information about the performance of the statistical technique.     

Suicide as an interpersonal phenomenon: Dyadic methodological and statistical considerations in suicide research

Interpersonal risk and resilience factors are prominent in current conceptual models of suicide. A growing body of empirical evidence links suicidal thoughts and behaviors to a range of interpersonal phenomenon adding further support to the value of this line of inquiry. At present, research on interpersonal phenomenon focuses on assessing individuals' perceptions of interpersonal phenomenon, such as appraisals of burdensomeness, experienced loneliness, and thwarted belongingness. As this line of research continues to develop, we argue that it would be valuable to consider incorporating conceptual models of interpersonal phenomenon and corresponding methodological approaches from closely allied fields. After providing a brief overview of interpersonal models of suicide, we present an introduction to conceptual models of interpersonal phenomenon developed in relationship science, describe how these models can be applied to the study of interpersonal phenomenon in suicide research, and close with a guided tutorial on data collection and statistical analysis methods for testing hypotheses derived from these conceptual approaches. References for additional reading are provided, and the Appendix S1 provides simulated data sets and statistical code for the analyses in the tutorial section.