Raudenbush and bryk 2002 pdf

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raudenbush and bryk 2002 pdf

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Analyzing data in the exercise sciences can be challenging when trying to account for physical changes brought about by maturation e. In this paper, we present an argument for using hierarchical linear modeling HLM as an approach to analyzing physical performance data. Using an applied example from Butterfield, Lehnhard, Lee, and Coladarci, we will show why HLM is an appropriate analysis technique and provide other examples of where HLM will be beneficial.

Stephen Raudenbush

Joseph F. This paper aims to discuss multilevel modeling for longitudinal data, clarifying the circumstances in which they can be used.

The authors estimate three-level models with repeated measures, offering conditions for their correct interpretation. From the concepts and techniques presented, the authors can propose models, in which it is possible to identify the fixed and random effects on the dependent variable, understand the variance decomposition of multilevel random effects, test alternative covariance structures to account for heteroskedasticity and calculate and interpret the intraclass correlations of each analysis level.

Understanding how nested data structures and data with repeated measures work enables researchers and managers to define several types of constructs from which multilevel models can be used.

Regression models for longitudinal data are very useful when the researcher wishes to study the behavior of a given phenomenon in the presence of nested data structures with repeated, or longitudinal, measures. For example, certain school data that does not vary among students, such as location and size, can be compared with data from other schools; and certain student data, such as sex and religion, that do not vary over time, can be compared with data from other students, which allows the different influences in the dependent variable to be analyzed.

In all of these situations nested data without or with repeated measures , datasets provide structures from which hierarchical models can be estimated.

Multilevel regression models have become considerably important in several fields of knowledge, and the publication of papers that use estimations related to these models has become more and more frequent Goldstein, The reason for the importance of multilevel modeling is due mainly to the determination of research constructs that consider the existence of nested data structures, in which certain variables show variation between distinct units that represent groups but do not assess variation between observations that belong to the same group.

Theoretically, researchers can define a construct with a greater number of levels of analysis, even if the interpretation of model parameters is not something trivial.

For instance, imagine the study of school performance, throughout time, of students nested into schools, these nested into municipal districts, these into municipalities, and these into states of the federation.

In this case, we would be working with six analysis levels temporal evolution, students, schools, municipal districts, municipalities and states. Multilevel models correct for the fact that observations in the same group are not independent and thus, compared to OLS models, lead to unbiased estimates of standard errors SEs.

But one could say that the same can be obtained with clustered standard errors in OLS. Indeed, if the number of clusters is plentiful i. On the other hand, if there are less than 20 clusters, researchers should avoid using clustered SEs and adopt multilevel modeling. According to Courgeau , within a model structure with a single equation, there seems to be no connection between individuals and the society in which they live. Ignoring this relationship means to elaborate incorrect analyzes about the behavior of the individuals and, equally, about the behavior of the groups.

Only the recognition of these reciprocal influences allows the correct analysis of the phenomena. This is in line with what is called by Mathieu and Chen the multilevel paradigm, which refers to a way of thinking: considering management phenomena in context and looking for driving variables not only from the focal unit of analysis but also from levels above and below.

Such an approach often implies the development of multidisciplinary theories and investigations, what is the spirit articulated by Hitt, Beamish, Jackson, and Mathieu when discussing the built of theoretical and empirical bridges across levels through multilevel modeling.

In an effort to make multilevel modeling more accessible, we provide the syntax for the mixed procedures in Stata for each step and show how to test and compare these designs in the model-building process.

That is, they can be inserted into components with fixed effects, as well as into components with random effects. While the estimated fixed effects parameters indicate the relationship between explanatory variables and the metric dependent variable, the random effects components can be represented by the combination of explanatory variables and non-observed random effects. Models that take into account the presence of nested structures in the data offer benefits to researchers since they make possible the study of the sources of variance, in different levels, of an outcome variable.

Raudenbush and Bryk discuss the applications of multilevel modeling from nested data structures in various areas of knowledge, particularly education. Therefore, multilevel regression models enable us to formally investigate the behavior of a certain dependent variable Y , which represents the phenomenon we are interested in, based on the behavior of explanatory variables, whose changes may occur for clustered data, between observations and between groups to which these observations belong, and for data with repeated measures throughout time.

In other words, there must be variables that have data that change between individuals that represent a certain level. But these variables remain unchanged for certain groups of individuals, and these groups represent a higher level. Therefore, this dataset can have certain explanatory variables X 1 , …, X Q that refer to each individual i , and other explanatory variables W 1 , …, W S that refer to each group j ; but they are invariable for the individuals of a certain group.

Table I. Based on Table I , we can see that X 1 , …, X Q columns 4 to 6 are level-1 variables data change between individuals , and W 1 , …, W S columns 7 to 9 are level-2 variables data change between groups; however, not for the individuals in each group.

Figure 1 shows the existing nesting between the level-1 units individuals and the level-2 units groups , which characterizes the existence of clustered data. Figure 1. Two-level nested structure of clustered data. Imagine another dataset in which, in addition to the nesting presented for clustered data, there is temporal evolution.

That is, data with repeated measures. Consequently, this new dataset can have the same explanatory variables X 1 , …, X Q that refer to each j individual. But now they are invariable for each j individual during the periods of monitoring. Moreover, the dataset can also have the same explanatory variables W 1 , …, W S that refer to each group k.

But W 1 , …, W S are also invariable throughout time for each group k. Table II provides the logic to describe a dataset with a three-level nested data structure with repeated measures time, individual and group. Table II. General model of a dataset with a three-level nested data structure with repeated measures.

Based on Table II , we can now see the variable that corresponds to the period is a level-1 explanatory variable column 1 , since the data change is in each row of the dataset, and that X 1 , …, X Q columns 5 to 7 become level-2 variables data change between individuals, but not for the same individual throughout time , and that W 1 , …, W S columns 8 to 10 become level-3 variables data change between K groups column 3 , but not for the same group throughout time.

Similar to what was shown for the case with two levels, Figure 2 enables us to see the existing nesting between the level-1 units temporal variation , the level-2 units individuals , and the level-3 units groups , which characterizes a data structure with repeated measures.

Figure 2. Three-level nested structure with repeated measures. Through Tables I and II , as well as through the corresponding Figures 1 and 2 , we can see that the data structures present absolute nesting. That is, a certain observation can be nested into only one group, and this group into only another higher-level group, and so on.

In the next section, we will estimate multilevel models with repeated measures in Stata, whose econometric development is in Appendix 1. Appendix 2 is intended for the presentation of the commands in Stata. For our example, we will use the step-up strategic multilevel analysis proposed by Raudenbush and Bryk , and Snijders and Bosker That is, we first studied the variance decomposition from the definition of a null model non-conditional model , so that afterwards, a random intercepts model and a random intercepts and slopes model could be estimated.

Finally, from the definition of the random nature of the error terms, we estimated the complete model by including level-2 variables into the analysis. We, therefore, estimate a three-level hierarchical linear model, in which the nesting of data will be characterized due to the presence of repeated measures. Thus, there is temporal evolution in the behavior of the dependent variable.

In addition, if yes, if there are certain student and school characteristics that explain this variability. This dataset follows the logic of the seminal work developed by Raudenbush, Rowan, and Kang The dataset PerformanceTimeStudentSchool.

In this paper, as discussed below, we estimate all models through REML. We have a balanced longitudinal data structure since all students are monitored in the four periods. Figure 3 enables us to analyze the temporal evolution of the school performance of the first 50 students in the sample. From the trends in the lines, we can see that the temporal evolutions of the school performance have different intercepts and slopes between students.

These different intercepts and slopes justify the use of multilevel modeling and provide reasons to include intercept and slope random effects in Level 2 of the models that will be estimated. Figure 3. Temporal evolution of the school performance of the first 50 students in the sample.

Figure 4 shows the temporal evolutions of the average school performance. The increasing trend over time provides further justification for estimating a three-level hierarchical model. Figure 4 also shows the linear adjustment through OLS of the school performance behavior over time for each school.

In addition, the figure enables us to display the intercept and slope random effects in Level 3 of the models that will be estimated, since the temporal evolutions of the school performance present different intercepts and slopes between the schools. Figure 4. Having characterized the temporal nesting of the students from different schools in the data with repeated measures, we can initially estimate a null model non-conditional model that enables us to determine if there is variability in the school performance between students from the same school and between those from different schools.

The model to be estimated has the following expression:. At the top of Figure 5 , we can initially demonstrate that we have a balanced longitudinal data structure since for each student we have minimum and maximum quantities of periods of monitoring equal to four, with a mean also equal to four.

Figure 5. Null model. We can, therefore, define two intraclass correlations, given the existence of two variance proportions. Therefore, we have:. Hence, the correlation between annual school performances is equal to Therefore, for the model without explanatory variables, while the annual school performance is slightly correlated between schools, the same becomes strongly correlated when the calculation is carried out for the same student from a certain school.

In this last case, we estimate that students and schools random effects representing approximately 92 per cent of the total variance of the residuals[ 2 ]. This information is essential to underpin the choice of the multilevel modeling, instead of a simple and traditional regression model through OLS.

At the bottom of Figure 5 , we can verify this fact by analyzing the result of the likelihood-ratio test. Given Sig. Even though researchers frequently ignore the estimation of null models, analyzing the results may help to reject the research hypotheses or not. It may even provide adjustments in relation to the constructs proposed. For our data, the results of the null model allow us to state that there is significant variability in the school performance throughout the four years under analysis.

Furthermore, there is significant variability in the school performance over time between students of the same school, and there is significant variability in the school performance over time between students from different schools. H1 can be supported, i. Since our main objective is to verify if there are student and school characteristics that would explain the variability in the school performance between students from the same school and between those from different schools, we will continue with the next modeling steps, respecting the step-up strategic multilevel analysis.

Therefore, new intraclass correlations can be calculated, as follows: Level-2 intraclass correlation:. Both variance proportions are higher than the ones obtained in the estimation of the null model, which shows the importance of including the variable that corresponds to the repeated measure in level 1.

Besides, the result of the likelihood-ratio test at the bottom of Figure 6 allows us to prove that the estimation of a simple traditional linear regression model performance based on year only with fixed effects must be ruled out H3 supported.

Figure 6. Linear trend model with random intercepts. Figures 7 and 8 provide better visualization of the random intercepts per school and per student.

Figure 7.

Multilevel modelling books

Table of contents. Please choose whether or not you want other users to be able to see on your profile that this library is a favorite of yours. Finding libraries that hold this item In fact, I think the book does a wonderful job by using lots of examples with lots of details. This is definitely one of its strengths as it makes it much easier for the reader to follow the text and understand the capabilities of the HLM approach. This Second Edition should come highly recommended. I think it gives a very good and thorough overview of HLM, and it does so in a manner that is easy to follow.

A textbook, Multilevel Analysis: An introduction to basic and advanced multilevel modeling , written by myself and Roel Bosker, appeared October at Sage Publishers. You can go the Sage announcement of this book by clicking here. A second revised edition was published November , and has a separate website.

Joseph F. This paper aims to discuss multilevel modeling for longitudinal data, clarifying the circumstances in which they can be used. The authors estimate three-level models with repeated measures, offering conditions for their correct interpretation. From the concepts and techniques presented, the authors can propose models, in which it is possible to identify the fixed and random effects on the dependent variable, understand the variance decomposition of multilevel random effects, test alternative covariance structures to account for heteroskedasticity and calculate and interpret the intraclass correlations of each analysis level. Understanding how nested data structures and data with repeated measures work enables researchers and managers to define several types of constructs from which multilevel models can be used.


Raudenbush, S.W., & Bryk, A.S. (). Hierarchical Linear Models: Applications and data analysis methods. (2nd ed.). Thousand Oaks, CA: Sage Publications.


A Case for Using Hierarchical Linear Modeling in Exercise Science Research

Stephen Webb Raudenbush born c. He is best known for his development and application of hierarchical linear models HLM in the field of education but he has also published on other subjects such as health and crime. Hierarchical linear models, which go by many other names, are used to study many natural processes.

In your search for publications, if you work in a university you may be able to access Web of Knowledge subscribable service or, use Google Scholar. In recent years, there have been a growing number of books explaining how to undertake multilevel modelling. Here we have grouped them into these broad categories.

Their content expands the coverage of the book to include models for discrete level-1 outcomes, non-nested level-2 units, incomplete data, and measurement errorall vital topics in contemporary social statistics. In the tradition of the first edition, they are clearly written and make good use of interesting substantive examples to illustrate the methods. Advanced graduate students and social researchers will find the expanded edition immediately useful and pertinent to their research. There was a new revelation on practically every page. I found the exposition to be extremely clear.

Eine anwendungsbezogene Einführung in die Hierarchische Lineare Modellierung (HLM)

Hierarchical linear models : applications and data analysis methods

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Methodik der empirischen Forschung pp Cite as. Eine solche Struktur liegt vor, wenn ein Datensatz Variablen auf verschiedenen Untersuchungsebenen wie z. Skip to main content Skip to sections. This service is more advanced with JavaScript available. Advertisement Hide. Download book PDF.

Он мог отключить ТРАНСТЕКСТ, мог, используя кольцо, спасти драгоценную базу данных. Да, подумал он, время еще. Он огляделся - кругом царил хаос. Наверху включились огнетушители. ТРАНСТЕКСТ стонал. Выли сирены.


Hierarchical Linear Models. Applications and Data Analysis Methods. Second Edition. Stephen W. Raudenbush - University of Chicago, USA; Anthony S. Bryk.


COMMENT 3

  • same analysis (Raudenbush & Bryk, ). Methods for Dealing with Nested Data. An effective way of explaining HLM is to compare and. Carolina S. - 24.05.2021 at 03:08
  • Bryk, Anthony S. Venancio C. - 31.05.2021 at 11:00
  • presented here, I recommend Raudenbush and Bryk (), Hox (), and (​Snijders & Bosker,. ) for a comprehensive overview of HLM and Singer and​. Anacegse - 01.06.2021 at 10:28

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