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CHAPTER 22

CHAPTER 22. ELEMENTS OF HIERARCHICAL REGRESSION LINEAR MODELS. HIERARCHICAL LINEAR MODELS (HLMs). Other names for these models (or ones with similar features) include: Multilevel models (MLM) Mixed-effect models (MEM) Random-effects models (REM) Random coefficient regression models (RCRM)

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CHAPTER 22

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  1. CHAPTER 22 ELEMENTS OF HIERARCHICAL REGRESSION LINEAR MODELS Damodar Gujarati Econometrics by Example, second edition

  2. HIERARCHICAL LINEAR MODELS(HLMs) • Other names for these models (or ones with similar features) include: • Multilevel models (MLM) • Mixed-effect models (MEM) • Random-effects models (REM) • Random coefficient regression models (RCRM) • Growth curve models (GCM) • Covariance components models (CCM) Damodar Gujarati Econometrics by Example, second edition

  3. BASIC IDEA OF HLM • Data often have a hierarchical structure: • Micro-level, or lower-level, data are often embedded in macro-level, or higher-level, data. • The primary goal of HLM is to predict the value of a micro-level dependent variable (i.e., regressand) as a function of other micro-level predictors (or regressors) as well as some predictors at the macro level. Damodar Gujarati Econometrics by Example, second edition

  4. BASIC IDEA OF HLM (CONT.) • Analysis at the micro level is Level 1 analysis. • Analysis at the macro level is Level 2 analysis. Damodar Gujarati Econometrics by Example, second edition

  5. HLM ANALYSIS OF THE NAÏVE MODEL • In HLM, we assume: • Where Y is the outcome, i is the micro-level observation, and j is the macro-level observation. • We further assume that the random intercept is distributed around its mean value with the error term vj: Damodar Gujarati Econometrics by Example, second edition

  6. HLM ANALYSIS OF THE NAÏVE MODEL • We obtain: • Composite error term wij is the sum of macro-specific error term vj (Level 2 error term) and micro-specific error term uij (Level 1 error term). • Assuming these errors are independently distributed, we obtain the following variance: Damodar Gujarati Econometrics by Example, second edition

  7. INTRA-CLASS CORRELATION COEFFICIENT • The ratio of the macro-specific variance to the total variance is called the intra-class correlation coefficient (ICC): • Gives the proportion of the total variation in Y attributable to the macro level. • Higher ICC means macro differences account for a larger proportion of the total variance. • So we cannot neglect the influence of macro differences. Damodar Gujarati Econometrics by Example, second edition

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