多水平模型(英文原著)intro

1、ContentsPrefaceAcknowledgementsGlossaryNotationChapter 1 1.1 Multilevel data1.2 School effectiveness1.3 Sample survey methods1.4 Repeated measures data1.5 Event history models1.6 Discrete response data1.7 Multivariate models1.8 Nonlinear models1.9 Measurement errors1.10 Random cross classifications1

2、.11 Structural equation models1.12 Levels of aggregation and ecological fallacies1.13 Causality1.14 A caveatChapter 22.1 The 2-level model and basic notation2.2 The 2-level model2.3 Parameter estimation for the variance components model2.4 The general 2-level model including random coefficients2.5 E

3、stimation for the multilevel model2.6 Other estimation procedures2.7 Residuals2.8 The adequacy of Ordinary Least Squares estimates.2.9 A 2-level example using longitudinal educational achievement data2.9.1 Checking model assumptions2.9.2 Checking for influential units2.10 Higher level explanatory va

4、riables and compositional effects2.11 Hypothesis testing and confidence intervals2.11.1 Fixed parameters2.11.2 Random parameters2.11.3 ResidualsAppendix 2.1 The general structure and estimation for a multilevel modelAppendix 2.2 Multilevel residuals estimationAppendix 2.3 The EM algorithmAppendix 2.

5、4 Markov Chain Monte Carlo (MCMC) estimationChapter 33.1 Complex variance structures3.1.1 Variances for subgroups defined at level 13.1.2 Variance as a function of predicted value3.1.3 Variances for subgroups defined at higher levels3.2 A 3-level complex variation model3.3 Parameter Constraints3.4 W

6、eighting units3.5 Robust, Jacknife and Bootstrap Uncertainty Estimates3.6 Aggregate level analyses3.7 Meta AnalysisChapter 44.1 Multivariate Multilevel models4.2 The basic 2-level multivariate model4.3 Rotation Designs4.4 A rotation design example using Science test scores4.5 Principal Components an

7、alysis4.6 Multiple Discriminant analysis4.7 Other ProceduresChapter 55.1 Nonlinear models5.2Nonlinear functions of linear components5.8 Estimating population means5.4 Nonlinear functions for variances and covariances5.5 Examples of nonlinear growth and nonlinear level 1 variance5.6 Multivariate Nonl

8、inear ModelsAppendix 5.1 Nonlinear model estimation5.1.1 Modelling linear components5.1.2 Modelling variances and covariances as nonlinear functions5.1.3 Likelihood valuesChapter 66.1 Models for repeated measures6.2 A 2-level repeated measures model6.3 A polynomial model example for adolescent growt

9、h and the prediction of adult height6.4 Modelling an autocorrelation structure at level 16.5 A growth model with autocorrelated residuals6.6 Multivariate repeated measures models6.7 Scaling across time6.8 Cross-over designsChapter 77.1 Models for discrete response data7.2 Proportions as responses7.3

10、 An example from a survey of voting behaviour7.4 Models for multiple response categories7.5 An example of voting behaviour with multiple responses7.6 Models for counts7.7 Ordered responses7.8 Mixed discrete - continuous response modelsAppendix 7.1 Differentials for some discrete response modelsChapt

11、er 88.1 Random cross classifications8.2 A basic cross classified model8.3 Examination results for a cross classification of schools8.4 Computational considerations8.5 Interactions in cross classifications8.6 Level 1 cross classifications8.7 Cross-unit membership models8.8 Multivariate cross classifi

12、ed modelsAppendix 8.1 Random cross classified data structuresChapter 99.9 Event history models9.2 Censoring9.3 Hazard based models in continuous time9.4 Parametric proportional hazard models9.5 The semiparametric Cox model9.6 Tied observations9.7 Repeated measures proportional hazard models9.8 Examp

13、le using birth interval data9.9 The discrete time (piecewise) proportional hazards model9.10 Log duration modelsChapter 1010.1 Errors of measurement10.2 Measurement errors in level 1 variables10.3 Measurement errors in higher level variables10. 4 A 2-level example with measurement error at both leve

14、ls.10.5 Multivariate responses10. 6 Nonlinear models10.7 Measurement errors for discrete explanatory variablesAppendix 10.1 Measurement errors10.1.1 The Basic 2-level Model10.1.2 Parameter estimation10.1.3 Random coefficients for explanatory variables measured with error10.1.4 Nonlinear modelsChapte

15、r 1111.1 Software for multilevel analysis11.2 Design issues11.3 Missing data11.4 Creating a completed data set11. 5 Multiple imputation and error corrections11.6 Discrete variables with missing data11.7 An example with missing data11.8 Multilevel structural equation models11.9 A factor analysis exam

16、ple using Science test scores11.10 Future developmentsAppendix 11.1 Addresses for multilevel software packagesReferencesPrefaceIn the mid 1980's a number of researchers began to see how to introduce systematic approaches to the statistical modelling and analysis of hierarchically structured data

17、. The early work of Aitkin et al (1981) on the teaching styles' data and Aitkins subsequent classic work with Longford (1986) initiated a series of developments that, by the early 1990's had resulted in a core set of established techniques, experience and software packages that could be appl

18、ied routinely. These methods and further extensions of them are described in this book and are coming to be applied widely in areas such as education, epidemiology, geography, child growth, household surveys and many others. In addition to the first edition of the present text (Goldstein, 1987b), tw

19、o expository volumes appeared in the early 1990s. That by Bryk and Raudenbush (1992) discusses 2 and 3-level linear multilevel models with applications especially to educational data and also to repeated measures designs. Longford (1993) gives a more theoretically oriented account and includes addit

20、ionally discussion of a multilevel factor analysis model, models with categorical responses and multivariate models. The present volume aims to integrate existing methodological developments within a consistent terminology and notation, provide examples and explain a number of new developments, espe

21、cially in the areas of discrete response data, time series models, random cross classifications, errors of measurement, missing data and nonlinear models. In many cases these developments are the subject of continuing research, so that we can expect further elaborations of the procedures described.T

22、he main text seeks to avoid undue statistical complexity, with methodological derivations occurring in appendices. Examples and diagrams are used to illustrate the application of the techniques and references given to other work. The book is intended to be suitable for graduate level courses and as

23、a general reference.Harvey GoldsteinAugust, 1994Preface to the first Internet editionIt is now nearly 5 years since the second edition was completed. Since then there have been many developments; in methodology, in applications and in computation. A new edition of Multilevel Statistical Models is no

24、w being planned and it will incorporate these developments. In the meantime the second edition has been corrected and one or two topics amplified, with some additional references. This edition does not contain a subject index; readers can search the text electronically for topics. Information about

25、current issues in multilevel modelling can be obtained from the folowing web site which has further useful links; www.ioe.ac.uk/multilevel/ .Harvey Goldsteinh.goldsteinioe.ac.ukApril 1999AcknowledgementsThis book would not have been possible without the support and dedication of all those who have w

26、orked on or been closely associated with the Multilevel Models Project at the Institute of Education: Jon Rasbash, Min Yang, Bob Prosser, Geoff Woodhouse, Pan Huiqui, Michael Healy, Ian Plewis and Bill Browne. I am also most grateful to the Economic and Social Research Council for their continuing f

27、unding support since 1986, most recently under the auspices of the programme for the Analysis of Large and Complex Datasets.In addition, the following most generously have allowed me access to datasets, commented critically on chapter drafts or pointed out errors: Bob Carpenter, Arto Demirjian, Davi

28、d Draper, Peter Egger, Anthony Heath, Kelvyn Jones, Ita Kreft, Iuri da Costa leite, Toby Lewis, Mac MacDonald, Rod McDonald, Colm OMuircheartaigh, Lindsay Paterson, Steve Raudenbush, German Rodriguez, Pamela Sammons, Richard Tanguay, and Sally Thomas.NotationThe following definitions refer to a 2-le

29、vel model. The extension to three and higher level models is usually straightforward. Where this is not clear, a three level definition is included.DefinitionSymbolResponse variable vectorExplanatory variable design matrixFixed part explanatory variable design matrix for a single unitTotal residuals

30、 at each level for a 3-level modelExplanatory variable design matrix for level 2 and level 1 random coefficientsPredicted value from fixed part of modelRaw or total residual for level 1 unit Mean raw residual for level 2 unitEstimated residual or posterior residual estimateCovariance matrix of rando

31、m coefficients at level iParentheses denoting vector or matrix of elementsCovariance matrix of response vector for k-level model or just VContribution to covariance matrix of response vector from level i for k-level modelDirect sum of matrices Kronecker product of conformable matrices vec operator on matrix GlossaryClusterA grouping containing 'lower level' elements. For example in a sample survey the set