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level 2 equation |
level 1/2 equations |
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When there is a single level 1 independent variable, the level 1 model is:
<math> Y_{ij} = \alpha_{
*<math>Y_{ij} </math> refers to the score on the dependent variable for an individual observation at Level 1 (subscript i refers to individual case, subscript j refers to the group).
*<math>X_{ij} </math> refers to the Level 1 predictor.
*<math>\alpha_{
*<math> \beta_{1j}</math> refers to the slope for individual case i for the relationship in group j (Level 2) between the Level 1 predictor and the dependent variable.
*<math> e_{ij}</math> refers to the random errors of prediction for the Level 1 equation (it is also sometimes referred to as <math>r_{ij}</math>).
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The dependent variables are the intercepts and the slopes for the independent variables at Level 1 in the groups of Level 2.
<math>\alpha_{
<math>\beta_{ij} = \delta + \tau_{ij} +v_{ij} </math>
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*<math>\gamma</math> refers to the overall intercept. This is the grand mean of the scores on the dependent variable across all the groups when all the predictors are equal to 0.
*<math>\tau_{ij}</math> refers to the overall regression coefficient, or the slope, between the dependent variable and the Level 2 predictor.
*<math>\nu_{
*<math>u_{
*<math>\delta</math> refers to the overall regression coefficient, or the slope, between the dependent variable and the Level 1 predictor.
*<math>v_{ij}</math> refers to the error component for the slope (meaning the deviation of the group slopes from the overall slope).<ref name="Fidell" />
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