Download MLA. Software for multilevel analysis of data with two levels. User's

• Vi = one of the variables from the data file (as explained above). In this case, it is a Level-2
predictor variable. It means that this variable is considered to have the same value for all
Level-1 units within a particular Level-2 unit. To be certain that this is the case, for each
Level-2 variable the average is computed over all Level-1 units within the particular Level-2
unit. Note that this feature may be used to create an aggregated Level-1 variable, serving as
a Level-2 predictor variable, simply by specifying a Level-1 variable as a Level-2 variable
as well.
• Uk = Level-2 random term k, i.e., u jk , the k-th element of a typical u j . As with the first
level, this component is considered a residual or error term, but now for the second level.
The second level may have more than one error term: one for each Level-2 equation (i.e.,
for each β element). The variances and the covariances of these terms have to be estimated
from the data.
In the equations each term is followed by a number (except for the Level-1 random term E). For
the Vi term this number is the variable number, the position of the variable in the data file (e. g., V4,
the fourth variable in the data file). The other terms only use a number for identification, without
any additional meaning (e. g., G3, one of the fixed parameters). The Bk terms have meaning in the
equations of both levels. Every equation consists of one term before and at least one term after
the equals sign.
Example:
/MODEL
B1 = G1 + G2*V6 + U1
B2 = G3 + G4*V6 + U2
V4 = B1 + B2*V5 + E
% random intercepts, dependent on level-2 predictor
% random slopes, dependent on the same level-2 predictor
% level-1 equation, dependent on level-1 predictor
As shown above, terms on the right hand side of the equations are connected by plus signs. A
variable and a corresponding parameter are connected by an asterisk (*). This is used to connect a
fixed parameter and an observed predictor variable in Level-2 equations and to connect a Level-1
regression coefficient and an observed predictor variable in the Level-1 equation. In chapter 4,
several variations of the two-level model will be presented and discussed in more detail.
Because a Level-1 equation and at least one Level-2 equation are required, the minimal specification of a model is:
/MODEL
B1 = G1
V4 = B1 + E
% fixed intercept
% level-1 variation
or
/MODEL
B1 = U1
V4 = B1 + E
3.4
% random intercept
% level-1 variation
/CONSTRAINTS (optional)
MLA has a limited option for imposing parameter constraints. The /CONSTRAINTS statement allows
parameters to be fixed to a certain value. Constraints are imposed as: “parameter = value”. The
parameter is held fixed during estimation and is not used for estimation of the standard errors
either. The standard error will be zero and no t-test is performed for this parameter. This feature is
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