Multilevel model: Difference between revisions

Revision as of 13:21, 10 October 2022

Revision as of 14:32, 10 October 2022

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When there is a single level 1 independent variable, the level 1 model is:

<math> Y_{ij} = \beta_alpha_{0jij} + \beta_{1jij} X_{ij} + e_{ij}</math>

*<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>\beta_alpha_{0jij} </math> refers to the intercept of the dependent variable for individual case i in group j (Level 2).

*<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>\beta_alpha_{0jij} = \gamma_{00}gamma + u_{0jij}</math>

<math>\beta_{1jij} = \gamma_{10}delta + W_jW_{ij} \gamma_tau_{01ij} +u_v_{1jij} </math>

*<math>\gamma_{00}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>W_jW_{ij}</math> refers to the Level 2 predictor.

*<math>\gamma_tau_{01ij}</math> refers to the overall regression coefficient, or the slope, between the dependent variable and the Level 2 predictor.

*<math>u_{0j}</math> refers to the random error component for the deviation of the intercept of a group from the overall intercept.

*<math>\gamma_{10}delta</math> refers to the overall regression coefficient, or the slope, between the dependent variable and the Level 1 predictor.

*<math>u_v_{1jij}</math> refers to the error component for the slope (meaning the deviation of the group slopes from the overall slope).<ref name="Fidell" />

==Types of models==