An Introduction to Multilevel Modeling Techniques

Heck, Ronald H.; Thomas, Scott L.

doi:10.4324/9781410604767

Cited by 255 publications

(352 citation statements)

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“…In the first model we address, a cluster-level mediator is conjectured to mediate the effect of a cluster-level X j on a Level-1 Y ij (e.g., Takeuchi et al, 2009; for other treatments, see Bauer, 2003, andHeck &Thomas, 2009). In previous literature concerning mediation in 2-2-1 designs it has seemingly gone unrecognized that X j and M j can affect only the cluster-level variation in the Level-1 variable Y ij .…”

Section: Appendix a Bias Derivationmentioning

confidence: 99%

“…Although a few authors have implemented multilevel mediation analyses using MSEM for a specific model and have addressed the indirect effect specifically (Bauer, 2003;Heck & Thomas, 2009;Rowe, 2003), they did not allow generalizations for random slopes, did not provide a framework that accommodated all possible multilevel mediation models, and did not provide comparisons to other (MLM) methods (as is done here in the following sections).…”

Section: Multilevel Semmentioning

confidence: 99%

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A general multilevel SEM framework for assessing multilevel mediation.

Preacher

Zyphur

Zhang

2010

Psychological Methods

3,089

3,051

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Several methods for testing mediation hypotheses with 2-level nested data have been proposed by researchers using a multilevel modeling (MLM) paradigm. However, these MLM approaches do not accommodate mediation pathways with Level-2 outcomes and may produce conflated estimates of between-and within-level components of indirect effects. Moreover, these methods have each appeared in isolation, so a unified framework that integrates the existing methods, as well as new multilevel mediation models, is lacking. Here we show that a multilevel structural equation modeling (MSEM) paradigm can overcome these 2 limitations of mediation analysis with MLM. We present an integrative 2-level MSEM mathematical framework that subsumes new and existing multilevel mediation approaches as special cases. We use several applied examples and accompanying software code to illustrate the flexibility of this framework and to show that different substantive conclusions can be drawn using MSEM versus MLM. Researchers in behavioral, educational, and organizational research settings often are interested in testing mediation hypotheses with hierarchically clustered data. For example, Bacharach, Bamberger, and Doveh (2008) investigated the mediating role of distress in the relationship between the intensity of involvement in work-related incidents and problematic drinking behavior among firefighting personnel. They used data in which firefighters were nested within ladder companies and all three variables were assessed at the subject level. Using data from customer service engineers working in teams, Maynard, Mathieu, Marsh, and Ruddy (2007) found that team-level interpersonal processes mediate the relationship between team-level resistance to empowerment and individual job satisfaction. Both of these examples-and many others-involve data that vary both within and between higher level units. Traditional methods for assessing mediation (e.g., Baron & Kenny, 1986;MacKinnon, Lockwood, Hoffman, West, & Sheets, 2002;MacKinnon, Warsi, & Dwyer, 1995) are inappropriate in these multilevel settings, primarily because the assumption of independence of observations is violated when clustered data are used, leading to downwardly biased standard errors if ordinary regression is used. For this reason, several methods have been proposed for addressing mediation hypotheses when the data are hierarchically organized.These recommended procedures for testing multilevel mediation have been developed and framed almost exclusively within the standard multilevel modeling (MLM) paradigm (for thorough treatments of MLM, see Bryk, 2002, andSnijders &Bosker, 1999) and implemented with commercially available MLM software, such as SAS PROC MIXED, HLM, or MLwiN. For example, some authors have discussed models in which the independent variable X, mediator M, and dependent variable Y all are measured at Level 1 of a two-level hierarchy (a 1-1-1 design, adopting notation proposed by Krull & MacKinnon, 2001), 1 and slopes either are fixed (Pituch, Whittaker, & Stapleton, 2005...

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Section: Appendix a Bias Derivationmentioning

confidence: 99%

Section: Multilevel Semmentioning

confidence: 99%

A general multilevel SEM framework for assessing multilevel mediation.

Preacher

Zyphur

Zhang

2010

Psychological Methods

3,089

3,051

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“…To examine this assumption, different statistical methods for analysing data on teacher behaviour can be used. One possibility is to use multi-level path analytic methods (Heck & Thomas, 2000) which help us not only to examine relationships between factors operating at the same level but also relevant cross level relationships. Another approach is to use multivariate multilevel modelling techniques which allow us to have more than one dependent variable.…”

Section: A) Testing the Dynamic Model At The Classroom Level: Suggestmentioning

confidence: 99%

Critical analysis of the current approaches to modelling educational effectiveness: The importance of establishing a dynamic model

Creemers

Kyriakidēs

2006

School Effectiveness and School Improvement

186

114

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This paper argues that researchers in the area of educational effectiveness should attempt to develop a new theoretical framework. Thus, a critical analysis of the current models of educational effectiveness research is provided and reveals that a dynamic model of effectiveness must: a) be multilevel in nature, b) be based on the assumption that the relation of some effectiveness factors with achievement may be curvilinear, c) illustrate the dimensions upon which the measurement of each effectiveness factor should be based and d) define relations among the effectiveness factors. In principle each factor which refers to the classroom, school and system can be measured by taking into account five dimensions: frequency, focus, stage, quality and differentiation. Examples of measuring effectiveness factors operating at different levels using these five dimensions are given. More attention in describing in detail factors associated with teacher behaviour in the classroom is given since this is seen as the starting point for the development and the testing of the dynamic model. Thus, different methodological approaches that can be used to test this part of the model and suggestions for the next steps in the development of other parts of the model are made. Finally, suggestions for using the dynamic model in order to improve educational practice are provided.

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“…Their approach combines the advantages of structural equation modeling with multilevel modeling. It is not our purpose to go into a full explanation of their approach (see Heck & Thomas, 2000 for an elaborate explanation with examples). Basically, their approach uses the multigroup option of LISREL.…”

Section: Methodsmentioning

confidence: 99%

“…Multilevel modeling is becoming a more and more common way to analyze clustered data. Heck & Thomas (2000) showed how to take this one step further by introducing multilevel structural equation modeling. Their approach combines the advantages of structural equation modeling with multilevel modeling.…”

Section: Methodsmentioning

confidence: 99%