## Multilevel Analysis: An Introduction to Basic and Advanced Multilevel ModelingThe main methods, techniques and issues for carrying out multilevel modeling and analysis are covered in this book. The book is an applied introduction to the topic, providing a clear conceptual understanding of the issues involved in multilevel analysis and will be a useful reference tool. Information on designing multilevel studies, sampling, testing and model specification and interpretation of models is provided. A comprehensive guide to the software available is included. Multilevel Analysis is the ideal guide for researchers and applied statisticians in the social sciences, including education, but will also interest researchers in economics, and biological, medical and health disciplines. |

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### Contents

1 | |

6 | |

13 | |

The Random Intercept Model | 38 |

The Hierarchical Linear Model | 67 |

Testing and Model Specification | 86 |

How Much Does the Model Explain? | 99 |

Heteroscedasticity | 110 |

Designing Multilevel Studies | 140 |

Crossed Random Coefficients | 155 |

Longitudinal Data | 166 |

Multivariate Multilevel Models | 200 |

Discrete Dependent Variables | 207 |

Software | 239 |

252 | |

261 | |

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### Common terms and phrases

average between-group variance Chapter Coefficient of IQ cortisol covariance matrix cross-level interaction crossed random data set defined denoted dependent variable dummy variables Effect Coefficient S.E. effect of IQ empty model equation example explained variance explanatory variables Fixed Effect Coefficient formula fully multivariate model function gender given group means group sizes heteroscedasticity hierarchical linear model homoscedastic implies individual interaction effect intercept variance intraclass correlation coefficient level-one residual level-one units level-one variables Level-two random effects level-two units level-two variables logistic regression macro-units micro-level multilevel analysis multilevel modeling multilevel software neighborhoods normal distribution observed parameter estimates population predictor pupils quadratic random coefficients random intercept model random slope models regression coefficient regression line regression model relations REML residual variance S.E. Level-two schools score Section significant specification spline standard deviation standard error statistical Table two-stage sample variance components variance parameters vector within-group regression