Level 1 Regression Equation
Yij = β0j + β1j(X1ij) + β2j(X2ij) + eij
- Yij 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).
- Xij refers to the Level 1 predictor.
- β0j refers to the intercept of the dependent variable in group j (Level 2).
- β1j refers to the slope for the relationship in group j (Level 2) between the Level 1 predictor and the dependent variable.
- eij refers to the random errors of prediction for the Level 1 equation (it is also sometimes referred to as rij). At Level 1, both the intercepts and slopes in the groups can be either fixed (meaning that all groups have the same values, although in the real world this would be a rare occurrence), non-randomly varying (meaning that the intercepts and/or slopes are predictable from an independent variable at Level 2), or randomly varying (meaning that the intercepts and/or slopes are different in the different groups, and that each have their own overall mean and variance).
Read more about this topic: Multilevel Model
Famous quotes containing the words level and/or equation:
“When science, art, literature, and philosophy are simply the manifestation of personality, they are on a level where glorious and dazzling achievements are possible, which can make a man’s name live for thousands of years. But above this level, far above, separated by an abyss, is the level where the highest things are achieved. These things are essentially anonymous.”
—Simone Weil (1909–1943)
“A nation fights well in proportion to the amount of men and materials it has. And the other equation is that the individual soldier in that army is a more effective soldier the poorer his standard of living has been in the past.”
—Norman Mailer (b. 1923)