CHAPTER 22 ELEMENTS OF HIERARCHICAL REGRESSION LINEAR MODELS

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

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

HIERARCHICAL LINEAR MODELS (HLMs) ØOther names for these models (or ones with similar features)

HIERARCHICAL LINEAR MODELS (HLMs) ØOther names for these models (or ones with similar features) include: ØMultilevel models (MLM) ØMixed-effect models (MEM) ØRandom-effects models (REM) ØRandom coefficient regression models (RCRM) ØGrowth curve models (GCM) ØCovariance components models (CCM) Damodar Gujarati Econometrics by Example, second edition

BASIC IDEA OF HLM ØData often have a hierarchical structure: ØMicro-level, or lower-level, data

BASIC IDEA OF HLM ØData often have a hierarchical structure: ØMicro-level, or lower-level, data are often embedded in macro-level, or higher-level, data. ØThe 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

BASIC IDEA OF HLM (CONT. ) ØAnalysis at the micro level is Level 1

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

HLM ANALYSIS OF THE NAÏVE MODEL ØIn HLM, we assume: Ø Where Y is

HLM ANALYSIS OF THE NAÏVE MODEL ØIn HLM, we assume: Ø Where Y is the outcome, i is the micro-level observation, and j is the macro-level observation. Ø 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

HLM ANALYSIS OF THE NAÏVE MODEL ØWe obtain: Ø Composite error term wij is

HLM ANALYSIS OF THE NAÏVE MODEL ØWe obtain: Ø 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). Ø Assuming these errors are independently distributed, we obtain the following variance: Damodar Gujarati Econometrics by Example, second edition

INTRA-CLASS CORRELATION COEFFICIENT ØThe ratio of the macro-specific variance to the total variance is

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

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