Theory of International Politics

Contents Dedication Preface Acknowledgements Notation A general classification notation and diagram Glossary Chapter 1 An introduction to multilevel models 1.1 Hierarchically structured data 1.2 School effectiveness 1.3 Sample survey methods 1.4 Repeated measures data 1.5 Event history and survival models 1.6 Discrete response data 1.7 Multivariate models 1.8 Nonlinear models 1.9 Measurement errors 1.10 Cross classifications and multiple membership structures. 1.11 Factor analysis and structural equation models 1.12 Levels of aggregation and ecological fallacies 1.13 Causality 1.14 The latent normal transformation and missing data 1.15 Other texts 1.16 A caveat Chapter 2 The 2-level model 2.1 Introduction 2.2 The 2-level model 2.3 Parameter estimation 2.4 Maximum likelihood estimation using Iterative Generalised Least Squares (IGLS) 2.5 Marginal models and Generalized Estimating Equations (GEE) 2.6 Residuals 2.7 The adequacy of Ordinary Least Squares estimates. 2.8 A 2-level example using longitudinal educational achievement data 2.9 General model diagnostics 2.10 Higher level explanatory variables and compositional effects 2.11 Transforming to normality 2.12 Hypothesis testing and confidence intervals 2.13 Bayesian estimation using Markov Chain Monte Carlo (MCMC) 2.14 Data augmentation Appendix 2.1 The general structure and maximum likelihood estimation for a multilevel model Appendix 2.2 Multilevel residuals estimation Appendix 2.3 Estimation using profile and extended likelihood Appendix 2.4 The EM algorithm Appendix 2.5 MCMC sampling Chapter 3. Three level models and more complex hierarchical structures. 3.1 Complex variance structures 3.2 A 3-level complex variation model example. 3.3 Parameter Constraints 3.4 Weighting units 3.5 Robust (Sandwich) Estimators and Jacknifing 3.6 The bootstrap 3.7 Aggregate level analyses 3.8 Meta analysis 3.9 Design issues Chapter 4. Multilevel Models for discrete response data 4.1 Generalised linear models 4.2 Proportions as responses 4.3 Examples 4.4 Models for multiple response categories 4.5 Models for counts 4.6 Mixed discrete - continuous response models 4.7 A latent normal model for binary responses 4.8 Partitioning variation in discrete response models Appendix 4.1. Generalised linear model estimation Appendix 4.2 Maximum likelihood estimation for generalised linear models Appendix 4.3 MCMC estimation for generalised linear models Appendix 4.4. Bootstrap estimation for generalised linear models Chapter 5. Models for repeated measures data 5.1 Repeated measures data 5.2 A 2-level repeated measures model 5.3 A polynomial model example for adolescent growth and the prediction of adult height 5.4 Modelling an autocorrelation structure at level 1. 5.5 A growth model with autocorrelated residuals 5.6 Multivariate repeated measures models 5.7 Scaling across time 5.8 Cross-over designs 5.9 Missing data 5.10 Longitudinal discrete response data Chapter 6. Multivariate multilevel data 6.1 Introduction 6.2 The basic 2-level multivariate model 6.3 Rotation Designs 6.4 A rotation design example using Science test scores 6.5 Informative response selection: subject choice in examinations 6.6 Multivariate structures at higher levels and future predictions 6.7 Multivariate responses at several levels 6.8 Principal Components analysis Appendix 6.1 MCMC algorithm for a multivariate normal response model with constraints Chapter 7. Latent normal models for multivariate data 7.1 The normal multilevel multivariate model 7.2 Sampling binary responses 7.3 Sampling ordered categorical responses 7.4 Sampling unordered categorical responses 7.5 Sampling count data 7.6 Sampling continuous non-normal data 7.7 Sampling the level 1 and level 2 covariance matrices 7.8 Model fit 7.9 Partially ordered data 7.10 Hybrid normal/ordered variables 7.11 Discussion Chapter 8. Multilevel factor analysis, structural equation and mixture models 8.1 A 2-stage 2-level factor model 8.2 A general multilevel factor model 8.3 MCMC estimation for the factor model 8.4 Structural equation models 8.5 Discrete response multilevel structural equation models 8.6 More complex hierarchical latent variable models 8.7 Multilevel mixture models Chapter 9. Nonlinear multilevel models 9.1 Introduction 9.2 Nonlinear functions of linear components 9.3 Estimating population means 9.4 Nonlinear functions for variances and covariances 9.5 Examples of nonlinear growth and nonlinear level 1 variance Appendix 9.1 Nonlinear model estimation Chapter 10. Multilevel modelling in sample surveys 10.1 Sample survey structures 10.2 Population structures 10.3 Small area estimation Chapter 11 Multilevel event history and survival models 11.1 Introduction 11.2 Censoring 11.3 Hazard and survival funtions 11.4 Parametric proportional hazard models 11.5 The semiparametric Cox model 11.6 Tied observations 11.7 Repeated events proportional hazard models 11.8 Example using birth interval data 11.9 Log duration models 11.10 Examples with birth interval data and children s activity episodes 11.11 The grouped discrete time hazards model 11.12 Discrete time latent normal event history models Chapter 12. Cross classified data structures 12.1 Random cross classifications 12.2 A basic cross classified model 12.3 Examination results for a cross classification of schools 12.4 Interactions in cross classifications 12.5 Cross classifications with one unit per cell 12.6 Multivariate cross classified models 12.7 A general notation for cross classifications 12.8 MCMC estimation in cross classified models Appendix 12.1 IGLS Estimation for cross classified data. Chapter 13 Multiple membership models 13.1 Multiple membership structures 13.2 Notation and classifications for multiple membership structures 13.3 An example of salmonella infection 13.4 A repeated measures multiple membership model 13.5 Individuals as higher level units 13.5.1 Example of research grant awards 13.6 Spatial models 13.7 Missing identification models Appendix 13.1 MCMC estimation for multiple membership models. Chapter 14 Measurement errors in multilevel models 14.1 A basic measurement error model 14.2 Moment based estimators 14.3 A 2-level example with measurement error at both levels. 14.4 Multivariate responses 14.5 Nonlinear models 14.6 Measurement errors for discrete explanatory variables 14.7 MCMC estimation for measurement error models Appendix 14.1 Measurement error estimation 14.2 MCMC estimation for measurement error models Chapter 15. Smoothing models for multilevel data. 15.1 Introduction 15.2. Smoothing estimators 15.3 Smoothing splines 15.4 Semi parametric smoothing models 15.5 Multilevel smoothing models 15.6 General multilevel semi-parametric smoothing models 15.7 Generalised linear models 15.8 An example Fixed Random 15.9 Conclusions Chapter 16. Missing data, partially observed data and multiple imputation 16.1 Creating a completed data set 16.2 Joint modelling for missing data 16.3 A two level model with responses of different types at both levels. 16.4 Multiple imputation 16.5 A simulation example of multiple imputation for missing data 16.6 Longitudinal data with attrition 16.7 Partially known data values 16.8 Conclusions Chapter 17 Multilevel models with correlated random effects 17.1 Non-independence of level 2 residuals 17.2 MCMC estimation for non-independent level 2 residuals 17.3 Adaptive proposal distributions in MCMC estimation 17.4 MCMC estimation for non-independent level 1 residuals 17.5 Modelling the level 1 variance as a function of explanatory variables with random effects 17.6 Discrete responses with correlated random effects 17.7 Calculating the DIC statistic 17.8 A growth data set 17.9 Conclusions Chapter 18. Software for multilevel modelling References Author index Subject index

Multilevel Statistical Models

Geert Hofstede University of Limburg Bram Neuijen University of Groningen Denise Davat Ohayv Institute for Research on intercultural Cooperation Geert Sanders University of Groningen This paper presents the results of a study on organizational cultures in twenty units from ten different organizations in Denmark and the Netherlands. Data came from in-depth interviews of selected informants and a questionnaire survey of a stratified random sample of organizational members. Data on task, structure, and control characteristics of each unit were collected separately. Quantitative measures of the cultures of the twenty units, aggregated at the unit level, showed that a targe part of the differences among these twenty units could be explained by six factors, related to established concepts from organizational sociology, that measured the organizational cultures on six independent dimensions. The organizational culture differences found resided mainly at the levei of practices as perceived by members. Scores of the units on the six dimensions were partly explainable from organizational idiosyncrasies but were also significantly correlated with a variety of task, structural, and control-system characteristics of the units.

Measuring organizational cultures: A qualitative and quantitative study across twenty cases.

This book demonstrates that people's basic values and beliefs are changing, in ways that affect their political, sexual, economic, and religious behaviour. These changes are roughly predictable: to a large extent, they can be interpreted on the basis of a revised version of modernisation theory presented here. Drawing on a massive body of evidence from societies containing 85 percent of the world's population, the authors demonstrate that modernisation is a process of human development, in which economic development gives rise to cultural changes that make individual autonomy, gender equality, and democracy increasingly likely. The authors present a model of social change that predicts how the value systems play a crucial role in the emergence and flourishing of democratic institutions - and that modernisation brings coherent cultural changes that are conducive to democratisation.

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Modernization, Cultural Change, and Democracy: The Human Development Sequence

This article describes the control-value theory of achievement emotions and its implications for educational research and practice. The theory provides an integrative framework for analyzing the antecedents and effects of emotions experienced in achievement and academic settings. It is based on the premise that appraisals of control and values are central to the arousal of achievement emotions, including activity-related emotions such as enjoyment, frustration, and boredom experienced at learning, as well as outcome emotions such as joy, hope, pride, anxiety, hopelessness, shame, and anger relating to success or failure. Corollaries of the theory pertain to the multiplicity and domain specificity of achievement emotions; to their more distal individual and social antecedents, their effects on engagement and achievement, and the reciprocal linkages between emotions, antecedents and effects; to the regulation and development of these emotions; and to their relative universality across genders and cultures. Implications addressed concern the conceptual integration of emotion, motivation, and cognition, and the need to advance mixed-method paradigms. In closing, implications for educational practice are discussed.

The Control-Value Theory of Achievement Emotions: Assumptions, Corollaries, and Implications for Educational Research and Practice

Ecological correlations and the behavior of individuals.

AN INDIVIDUAL CORRELATION is a correlation in which the statistical object or thing described is indivisible. The correlation between color and illiteracy for persons in the United States, shown later in Table I, is an individual correlation, because the kind of thing described is an indivisible unit, a person. In an individual correlation the variables are descriptive properties of individuals, such as height, income, eye color, or race, and not descriptive statistical constants such as rates or means. In an ecological correlation the statistical object is a group of persons. The correlation between the percentage of the population which is Negro and the percentage of the population which is illiterate for the 48 states, shown later as Figure 2, is an ecological correlation. The thing described is the population of a state, and not a single individual. The variables are percentages, descriptive properties of groups, and not descriptive properties of individuals. Ecological correlations are used in an impressive number of quantitative sociological studies, some of which by now have attained the status of classics: Cowles’ ‘‘Statistical Study of Climate in Relation to Pulmonary Tuberculosis’’; Gosnell’s ‘‘Analysis of the 1932 Presidential Vote in Chicago,’’ Factorial and Correlational Analysis of the 1934 Vote in Chicago,’’ and the more elaborate factor analysis in Machine Politics; Ogburn’s ‘‘How women vote,’’ ‘‘Measurement of the Factors in the Presidential Election of 1928,’’ ‘‘Factors in the Variation of Crime Among Cities,’’ and Groves and Ogburn’s correlation analyses in American Marriage and Family Relationships; Ross’ study of school attendance in Texas; Shaw’s Delinquency Areas study of the correlates of delinquency, as well as The more recent analyses in Juvenile Delinquency in Urban Areas; Thompson’s ‘‘Some Factors Influencing the Ratios of Children to Women in American Cities, 1930’’; Whelpton’s study of the correlates of birth rates, in ‘‘Geographic and Economic Differentials in Fertility;’’ and White’s ‘‘The Relation of Felonies to Environmental Factors in Indianapolis.’’ Although these studies and scores like them depend upon ecological correlations, it is not because their authors are interested in correlations between the properties of areas as such. Even out-and-out ecologists, in studying delinquency, for example, rely primarily upon data describing individuals, not areas. In each study which uses ecological correlations, the obvious purpose is to discover something about the behavior of individuals. Ecological correlations are used simply because correlations between the properties of individuals are not available. In each instance, however, the substitution is made tacitly rather than explicitly. The purpose of this paper is to clarify the ecological correlation problem by stating, mathematically, the exact relation between ecological and individual correlations, and by showing the bearing of that relation upon the practice of using ecological correlations as substitutes for individual correlations.

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W. S. Robinson

Papers

Ecological correlations and the behavior of individuals.

Ecological Correlations and the Behavior of Individuals