Multilevel Analysis of Repeated Measures Data

Hierarchically structured data are common in many areas of scientific research. Such data are characterized by nested membership relations among the units of observation. Multilevel analysis is a class of methods that explicitly takes the hierarchical structure into account. Repeated measures data can be considered as having a hierarchical structure as well: measurements are nested within, for instance, individuals. In this paper, an overview is given of the multilevel analysis approach to repeated measures data. A simple application to growth curves is provided as an illustration. It is argued that multilevel analysis of repeated measures data is a powerful and attractive approach for several reasons, such as flexibility, and the emphasis on individual development.     

The Multilevel Approach to Repeated Measures for Complete and Incomplete Data

Repeated measurements often are analyzed by multivariate analysis of variance (MANOVA). An alternative approach is provided by multilevel analysis, also called the hierarchical linear model (HLM), which makes use of random coefficient models. This paper is a tutorial which indicates that the HLM can be specified in many different ways, corresponding to different sets of assumptions about the covariance matrix of the repeated measurements. The possible assumptions range from the very restrictive compound symmetry model to the unrestricted multivariate model. Thus, the HLM can be used to steer a useful middle road between the two traditional methods for analyzing repeated measurements. Another important advantage of the multilevel approach to analyzing repeated measures is the fact that it can be easily used also if the data are incomplete. Thus it provides a way to achieve a fully multivariate analysis of repeated measures with incomplete data. This revised version was published online in June 2006 with corrections to the Cover Date.     

Multilevel theory and the underspecification of multilevel models

This article emphasises the importance of the adequate specification of models of multilevel analysis in accordance with multilevel theories. Until recent times, multilevel theories tried only to explain the direct effect of group characteristics on an individual's characteristic. It seems to be more suited to adopt a more general theoretical approach, in which it is assumed that group characteristics affects individual processes. There a treshold effect and a process effect have to be distinguished. The propositions result in a model specification within the random coefficient model of multilevel analysis. The theory and model recommended are illustrated by means of data of Dar and Resh's (1986) study into social learning environment.     

Does class matter more than school? Evidence from a multilevel statistical analysis on Italian junior secondary school students

This paper assesses the differences in educational attainments between students across classes and schools they are grouped by, in the context of Italian educational system. The purpose is to identify a relationship between pupils' reading test scores and students' characteristics, stratifying for classes, schools and geographical areas. The dataset contains detailed information about more than 500,000 students at the first year of junior secondary school in the year 2012/2013. By means of multilevel linear models, it is possible to estimate statistically significant school and class effects, after adjusting for pupil's characteristics, including prior achievement. The results show that school and class effects are very heterogeneous across macro-areas (Northern, Central and Southern Italy), and that there are substantial discrepancies between and within schools; overall, class effects on achievement tend to be larger than school ones.     

A Tutorial on Multilevel Survival Analysis: Methods,Models and Applications

Data that have a multilevel structure occur frequently across a range of disciplines, including epidemiology, health services research, public health, education and sociology. We describe three families of regression models for the analysis of multilevel survival data. First, Cox proportional hazards models with mixed effects incorporate cluster‐specific random effects that modify the baseline hazard function. Second, piecewise exponential survival models partition the duration of follow‐up into mutually exclusive intervals and fit a model that assumes that the hazard function is constant within each interval. This is equivalent to a Poisson regression model that incorporates the duration of exposure within each interval. By incorporating cluster‐specific random effects, generalised linear mixed models can be used to analyse these data. Third, after partitioning the duration of follow‐up into mutually exclusive intervals, one can use discrete time survival models that use a complementary log–log generalised linear model to model the occurrence of the outcome of interest within each interval. Random effects can be incorporated to account for within‐cluster homogeneity in outcomes. We illustrate the application of these methods using data consisting of patients hospitalised with a heart attack. We illustrate the application of these methods using three statistical programming languages (R, SAS and Stata).     

Alternative Approaches to Multilevel Modelling of Survey Non‐Contact and Refusal

We review three alternative approaches to modelling survey non‐contact and refusal: multinomial, sequential, and sample selection (bivariate probit) models. We then propose a multilevel extension of the sample selection model to allow for both interviewer effects and dependency between non‐contact and refusal rates at the household and interviewer level. All methods are applied and compared in an analysis of household non‐response in the United Kingdom, using a data set with unusually rich information on both respondents and non‐respondents from six major surveys. After controlling for household characteristics, there is little evidence of residual correlation between the unobserved characteristics affecting non‐contact and refusal propensities at either the household or the interviewer level. We also find that the estimated coefficients of the multinomial and sequential models are surprisingly similar, which further investigation via a simulation study suggests is due to non‐contact and refusal having largely different predictors.     

Sample Size Considerations for Multilevel Surveys

Social and economic data commonly have a nested structure (for example, households nested within neighborhoods). Recently techniques and computer programs have become available for dealing with such data, permitting the formulation of explicit multilevel models with hypotheses about effects occurring at each level and across levels. If data users are planning to analyze survey data using multilevel models rather than concentrating on means, totals, and proportions, this needs to be accounted for in the survey design. The implications for determining sample sizes (for example, the number of neighborhoods in the sample and the number of households sampled within each neighborhood) are explored.     

校企合作背景下在中职生心理健康教育中渗透积极心理学研究

校企合作是中职学校培养职业技术人才的重要途径。校企合作能够促进中职学校的发展，使学生在校所学与企业实践有机结合。文章阐述了校企合作背景下创新心理健康教育方式，用积极心理学渗透的方法，开展中职生心理健康教育，提升中职生的综合素质，使他们成为受企业欢迎的技能型人才。     

Effective investment strategies on mathematics performance in rural areas

Taiwan has noticed relative disadvantages in rural areas and offered more scholarship opportunities for aboriginal and low-income students. Moreover, the Educational Priority Area program was implemented in 1996 to invest additional funds in rural schools. Although the average mathematics ability of Taiwanese students ranks high in the Programme for International Student Assessment (PISA), the cost-benefit outcome of government funding in rural areas is inadequate. This paper, therefore, tries to explain low student achievement in rural areas with the multilevel modeling (HLM). Data were gathered from 5,581 Taiwanese students in 236 junior high schools using stratified random sampling. Of the data, 2,358 students from 112 rural area schools and 3,223 students from 124 non-rural area schools were sampled. The results demonstrate the importance of distinguishing between resources and investments, and shifts focus from comparisons of the influence of families and schools preexisting conditions to discussions of improvement strategies on mathematics performance. Both families and schools are limited by their resources, but the findings presented in this study suggest that families and schools can improve student achievement with appropriate investments.     

The Problem of Time Dependent Explanatory Variables at the Context-Level in Discrete Time Multilevel Event History Analysis: A Comparison of Models Considering Mobility Between Local Labour Markets as an Example

The paper deals with the question of how to include time dependent explanatory variables at the context-level in multilevel event history models. In general, context-level explanatory variables in multilevel models are assumed to be time constant. Only time constant context-level explanatory variables perform the task of reducing context-level error variance. Thus, it will be suggested that the analysis should be extended to a three-level model. In this model, time periods of persons constitute level 1 units, time periods of contexts constitute level 2 units and the contexts themselves constitute level 3 units – in which in turn level 2 units are clustered. Considering mobility between local labour markets as an example, four different ways of modelling time varying context-level variables are compared. The result is that the proposed three-level model leads to the most conservative results.     

Advanced Multilevel Monte Carlo Methods

This article reviews the application of some advanced Monte Carlo techniques in the context of multilevel Monte Carlo (MLMC). MLMC is a strategy employed to compute expectations, which can be biassed in some sense, for instance, by using the discretization of an associated probability law. The MLMC approach works with a hierarchy of biassed approximations, which become progressively more accurate and more expensive. Using a telescoping representation of the most accurate approximation, the method is able to reduce the computational cost for a given level of error versus i.i.d. sampling from this latter approximation. All of these ideas originated for cases where exact sampling from couples in the hierarchy is possible. This article considers the case where such exact sampling is not currently possible. We consider some Markov chain Monte Carlo and sequential Monte Carlo methods, which have been introduced in the literature, and we describe different strategies that facilitate the application of MLMC within these methods.     

Work Design–Related Antecedents of Turnover Intention: A Multilevel Approach

Previous research on employee‐turnover intention has focused mostly on a single level of analysis. This multilevel study of 1,149 employees and 144 managers from a 21‐store Taiwanese retail home improvement chain demonstrated that individual and store‐level factors were significantly associated with employee‐turnover intention. Job characteristics explain within‐store variance. In addition to age and tenure similarity among employees, transformational leadership and compensation explain between‐store variance. Theoretical and practical implications of the research are also discussed.     

Multivariate Small Area Estimation of Multidimensional Latent Economic Well-being Indicators

Factor analysis models are used in data dimensionality reduction problems where the variability among observed variables can be described through a smaller number of unobserved latent variables. This approach is often used to estimate the multidimensionality of well-being. We employ factor analysis models and use multivariate empirical best linear unbiased predictor (EBLUP) under a unit-level small area estimation approach to predict a vector of means of factor scores representing well-being for small areas. We compare this approach with the standard approach whereby we use small area estimation (univariate and multivariate) to estimate a dashboard of EBLUPs of the means of the original variables and then averaged. Our simulation study shows that the use of factor scores provides estimates with lower variability than weighted and simple averages of standardised multivariate EBLUPs and univariate EBLUPs. Moreover, we find that when the correlation in the observed data is taken into account before small area estimates are computed, multivariate modelling does not provide large improvements in the precision of the estimates over the univariate modelling. We close with an application using the European Union Statistics on Income and Living Conditions data.     

Aggregate Versus Disaggregate Data in Measuring School Quality

This article develops a measure of efficiency to use with aggregated data. Unlike the most commonly used efficiency measures, our estimator adjusts for the heteroskedasticity created by aggregation. Our estimator is compared to estimators currently used to measure school efficiency. Theoretical results are supported by a Monte Carlo experiment. Results show that for samples containing small schools (sample average may be about 100 students per school but sample includes several schools with about 30 or less students), the proposed aggregate data estimator performs better than the commonly used OLS and only slightly worse than the multilevel estimator. Thus, when school officials are unable to gather multilevel or disaggregate data, the aggregate data estimator proposed here should be used. When disaggregate data are available, standardizing the value-added estimator should be used when ranking schools.     

物流包装设计的灰色多层次综合评价模型

物流包装的合理化是有效降低物流成本,提高物流效率的主要途径,对物流包装设计方案的定量评价是其中重要问题。在给出物流包装性能评价指标体系的基础上,建立了一种基于灰色系统理论的物流包装设计多层次灰色评价模型。最后给出了对三种方案进行综合评估的实例,结果表明灰色多层次评价法适用于对物流包装设计方案进行客观公正的综合评价,有力于促进物流系统总体最优化的运作。     

A Multilevel Multinomial Analysis of Interviewer Effects on Various Components of Unit Nonresponse

This note demonstrates an application of a multilevel multinomial model. We use that model to analyse interviewer effects on various components of unit nonresponse to a face-to-face survey: refusals and noncontacts. The model allows for an analysis of these two interviewer effects and a possible connection between both at the same time. Our results show that both the chances for refusals as for noncontacts are subject to interviewer effects. We also find some evidence for a relation between both interviewer effects: interviewers who obtain more refusals are also more likely to report noncontacts. That result is however at least partly dependent on an outlier, an interviewer with a high number of refusals and noncontacts.     

“登校拒否”凸现的危机及其启示——日本义务教育的危机

登校拒否现象主要指日本中小学中因讨厌学校或对学校感到恐惧而拒绝上学的现象,自92年开始调查统计以来,呈现逐年上升趋势。登校拒否不仅让学生本身受到极大的影响,其家庭也会因此陷入极大的危机之中。更重要的是,造成登校拒否的原因复杂,但社会环境变化以及竞争的下移无疑是该现象的主要成因之一,认真分析并吸取登校拒否的教训对于我国教育意义重大。     

Multilevel analysis of the changing relationship between class and party in Britain 1964–1992

Previous analyses of the changing relationship between class and vote in Britain have assumed that the British Election Surveys constitute simple random samples. In fact, they are all clustered samples, and the number of sampling points has varied substantially over time. The paper uses the statistical technique of multi-level modelling to investigate the effects of this clustering and compares the results with those obtained with single-level logistic models. In general, the multilevel and single-level models lead to similar conclusions about the changing relation between class and vote; they both show evidence of a change in the class/vote relationship over time. However, the multilevel models also show that, while the clustering does not affect conclusions about the class dealignment debate, there are other important substantive findings which emerge from the multilevel approach. First, there is clear evidence of substantial constituency differences in the intercepts; that is, individuals had very different propensities to vote Conservative in different constituencies. Second, there were also significant constituency differences in class voting, that is, constituencies seemed to vary in their level of class polarization.     

Closing schools in a shrinking district: Do student outcomes depend on which schools are closed?

In the last decade, many cities around the country have needed to close schools due to declining enrollments and low achievement. School closings raise concerns about the possible negative impacts on student achievement, neighborhoods, families, and teaching staff. This study examines an anonymous urban district that, faced with declining enrollment, chose to make student achievement a major criterion in determining which schools would be closed. The district targeted low-performing schools in its closure plan, and sought to move their students to higher-performing schools. We estimate the impact of school closures on student test scores and attendance rates by comparing the growth of these measures among students differentially affected by the closures. We use residential assignment to school as an instrument to address non-random sorting of students into new schools. We also statistically control for the contemporaneous effects of other reforms within the district. Results show that students displaced by school closures can experience adverse effects on test scores and attendance, but these effects can be minimized when students move to schools that are higher-performing (in value-added terms). Moreover, the negative effect on attendance disappears after the first year in the new school. Meanwhile, we find no adverse effects on students in the schools that are receiving the transferring students.     

Advancing multilevel thinking in human resource management research: Applications and guidelines

Strategic Human Resource Management (SHRM) researchers have recently turned their attention to using various levels of analysis in examining the relationship between HRM and performance. Despite several calls for research that integrates multiple levels of analysis, HRM research has yet to apply a multilevel approach to its full advantage. In our view, the paucity of multilevel research is rooted in the lack of what we label multilevel thinking: the application of multilevel principles. In this conceptual paper, we develop 9 guidelines based on tailored multilevel HRM principles that offer a course of action for scholars who are interested in conducting multilevel HRM research. Following Kozlowski and Klein (2000), we build these principles around the what, how, where, when, and why questions in multilevel HRM research. Based on an analysis of 88 empirical multilevel HRM studies, we identify the approaches commonly applied when using multilevel principles, explain the weaknesses in current multilevel HRM studies, and offer what we consider good examples of a rigorous approach.