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The two weeks are devoted, first, to covering the foundations of multilevel modelling and, second, to exploring extensions of this core framework to alternative data configurations. In the first week we explore common linear specifications: random-intercept and random-slope models. We go over statistical notation for these models, interpretation of coefficients, presenting uncertainty, reporting results from such models, testing and displaying the effect of interactions between group-level and observation-level variables, as well as what sample size considerations should be kept in mind when analysing such data.
In the second week we allocate each day to an extension of the standard hierarchical linear framework. We introduce generalised linear mixed specifications, with an application to a dichotomous response variable. We then show how to use a multilevel specification to analyse change over time, as well as how to produce sub-national estimates of public opinion based solely on national-level data. Finally, I highlight how multilevel specifications can be applied to data structures that are not hierarchical, as well as to data that has the added complication of spatial correlations.
Throughout the sessions we make intensive use of the lme4 and nlme packages, along with a variety of functions from connected packages that assist in plotting, model comparison, and data reshaping. By the end of the course you should be able to easily identify such nested data configurations in your own field of study, e. Finally, you will be equipped to interpret statistical output from these models, assess any misfit between model and data, and present substantive results to either a lay or a specialist audience. Day 1 We start by describing problems OLS faces when applied to data that is nested, and how multilevel models MLMs overcome these difficulties.
In addition to their statistical properties, MLMs also allow us to answer more sophisticated questions about the world. These insights will be complemented by a short practice session in R focusing on how OLS breaks down in certain situations, and how multilevel models are a compromise between two alternative strategies of analysing data in these instances. Day 2 I introduce notation for multilevel specifications, as well as the simplest type of such models, with only a varying intercept. We then cover interpretation and inference for these models, and what the implications are of allowing for a varying intercept.
Day 3 We gradually introduce more complex specifications, allowing for the effect of a predictor to vary between groups, and trying to understand whether any group-level predictors systematically explain how this effect varies.
Cross-level interactions will be presented, along with techniques to graphically present their estimates. Finally, we discuss how to do variable centering and rescaling in the case of nested data. Day 4 We discuss how to determine the best-fitting model from a series of specifications we might have tested, as well as how to assess the quality of our model. The latter topic brings us to the issue of assumptions for multilevel models, where we cover a few diagnostic tools. Day 5 This day is reserved for a set of smaller topics, as well as a review of the most important ideas from the previous four days.
I show that the insights gained apply relatively seamlessly to data with more than two levels of nestation. I also broach the topic of sample size requirements at all levels of the nesting structure, which frequently plague empirical analyses in political science.
Multilevel Modeling for Quantitative Research
Day 6 We begin with a coverage of generalised linear mixed models GLMMs , with a specific focus on dichotomous dependent variables. By working through a practical example, we cover the interpretation of estimates from these models, the presentation of marginal effects, and sample size considerations. Day 7 I introduce multilevel models as a solution to the need to model change over time in a phenomenon, and to explain such change with time-varying and time-invariant predictors. I explain how to see such a setup as a nested data configuration, plotting and modelling trajectories of change, as well as choosing from a variety of error covariance structure options.
Day 8 We tackle cross-classified and multiple-membership models. These specifications accommodate situations where observations are simultaneously nested in two non-overlapping hierarchies, or where observations can be members of multiple higher-level units at the same time. Although this complicates our setup, we will see that multilevel models are well equipped to handle this situation. We finish the day by covering one way in which these models can help us disentangle age-period-cohort APC effects.
Day 9 We continue the discussion on cross-classified models by introducing multilevel regression with post-stratification MRP.
This is a specialised modelling technique that produces estimates of public opinion for sub-national units and population sub-groups from nationally representative surveys. Given the adaptability of this technique to varying types of attitudes such as vote preferences , as well as to contexts where no census information is available MRSP , it represents a valuable potential tool for you to master. Day 10 We wrap up by considering the extension of multilevel models to situations where the data exhibits spatial dependence between observations.
Following a practical example, I showcase the implementation of such models in R, as well as the interpretation of the estimates obtained. Note on readings Some of the days require extensive preparatory readings. Before starting the class, I strongly recommend you review regression-related considerations, so please allocate extra time before the course to familiarise yourself with the reading workload.
Lecture topics. Lab topics. Kreft, Ita, and Jan De Leeuw. Chapter 1. Gelman, Andrew, and Jennifer Hill. Chapters 1 and Snijders, Tom A. Chapters 2 and 3. Bickel, Robert. New York: Guilford Press. Scott, Marc A. Shrout, and Sharon L. Scott, Jeffrey S. Simonoff, and Brian D. Chapter 2 pp. Chapter Enders, Craig K. Gill, Jeff, and Andrew J. Chapter 1 pp. Chapter 4. Raudenbush, Stephen W. Chapter 2. Steenbergen, Marco R. McNeish, Daniel M. Chapter 5. Brambor, T. Steele, Russell. Chapter 7 pp. Chapter 9. Meijer Eds. Goldstein, Harvey.
London: Wiley. Chapter 3 sections 3. McNeish, Daniel, and Kathryn R. Brincks, Ahnalee M.
Enders, Maria M. This week is focused on the historical background and usage of multilevel models across statistics, psychometrics, biostatistics, and econometrics. Typical multilevel classes start by presenting conditional clustering as a theoretical problem and then introducing the random intercept model and random slope model and then talking mainly about things like diagnostics.
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- [PDF] The Sage handbook of multilevel modeling - Semantic Scholar!
I start out with the history of multilevel modeling across a few different fields. The biggest practical problem with how I approach this material is that I pull from very different fields where terms mean fundamentally different things between fields and even within the same fields over time e. Readings Gill, J.
Womack The Multilevel Model Framework. Hodges, J. Random Effects Old and New. Richly parameterized linear models: additive, time series, and spatial models using random effects, CRC Press. Searle, S. Nerlove, M. Each Part starts with a non-mathematical introduction to the method covered in that section, giving readers a basic knowledge of the method's logic, scope and unique features.
Next, the mathematical and statistical basis of each method is presented along with advanced aspects. Toon meer Toon minder. Recensie s Best and Wolf have put together a powerful collection. It covers all major topics and varieties of regression analysis used by social scientists and is especially valuable in its separate discussions of uses for both cross-sectional and panel data analysis.
Best and Wolf have recruited top specialists from both Europe and North America and they comprehensively cover regression analysis for both cross-sectional and panel data. It provides an up-to-date overview of the most prominent data analysis methods employed in modern social science research. The authors do a great job in explaining the various statistical methods in a clear and simple way - focussing on fundamental understanding, interpretation of results, and practical application - yet being precise in their exposition.
The book will be invaluable as a source for basic reading assignments for graduate students.
ohosusajah.tk | The SAGE Handbook of Regression Analysis and Causal Inference | |
It will also serve well as a primer for researchers who want to update and advance their methodological skills. Reviews Schrijf een review. Bindwijze: Hardcover. Verwacht over 6 weken Levertijd We doen er alles aan om dit artikel op tijd te bezorgen. Verkoop door bol.