Multilevel Model - Level 1 Regression Equation

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:

    Preschoolers sound much brighter and more knowledgeable than they really are, which is why so many parents and grandparents are so sure their progeny are gifted and super-bright. Because children’s questions sound so mature and sophisticated, we are tempted to answer them at a level of abstraction far beyond the child’s level of comprehension. That is a temptation we should resist.
    David Elkind (20th century)

    Jail sentences have many functions, but one is surely to send a message about what our society abhors and what it values. This week, the equation was twofold: female infidelity twice as bad as male abuse, the life of a woman half as valuable as that of a man. The killing of the woman taken in adultery has a long history and survives today in many cultures. One of those is our own.
    Anna Quindlen (b. 1952)