st: Clarification Re: Stata 13, +

[rraciborski@stata.com (Rafal Raciborski, StataCorp)]

Sam <lucaselastic@gmail.com> has a question about Stata licensing:

> Am I correct in understanding that the perpetual license entails
> exactly the same terms as before if I do not choose the maintenance
> option?  Am I correct in understanding that I will be able to update
> stata (as long as it is still stata 13.x) if I choose not to pay the
> maintenance option?  Or, am I mistaken, and the maintenance fee is
> required to "maintain" an up-to-date stata prior to the next major
> release?

Your understanding is correct.  A perpetual Stata license still works exactly
as it always has, including free updates via the -update- command along the
way, whether you have maintenance or not.  If you have maintenance in effect
and another major version of Stata comes out (i.e. Stata 14), you automatically
receive a new perpetual license to that major version.

Sam also asked about multilevel mixed-effects models where level-2 variables
are introduced for level-1 slopes:

> It is great that stata allows users to look through the manual for the
> new release early.  I did, and found myself wishing for one simple
> change in the multilevel segment, an addition, really.  Many analysts
> use the multilevel model to introduce level-2 variables into equations
> for level-1 slopes.  So, for example, the analyst might add a variable
> for per pupil expenditure to the model such that it alters the slope
> for parents' income in a model predicting student test score.

To fit such models in Stata, one needs to translate the multistage formulation
of a mixed-effects model into a one-equation formulation specified for the
outcome.  For example, consider a two-stage formulation:

  y_ij    = eta_i0 + eta_i1*x_ij + e_ij         (level 1)
  eta_i0  = b_00 + b_01*z0_i + u_i0             (level-2 intercept)
  eta_i1  = b_10 + b_11*z0_i + u_i1             (level-2 slope)

which contains one level-1 variable x and one level-2 variable z0,
which varies at the slope and intercept levels.

To obtain a one-equation formulation, we substitute eta_i0 and eta_i1 into
the level-1 equation:

  y_ij = (b_00+b_01*z0_i+u_i0) + (b_10+b_11*z0_i+u_i1)*x_ij + e_ij
        (after rearranging terms)
       = (b_00 + b_01*z0_i + b_10*x_ij + b_11*z0_i*x_ij)        <-- fixed
       + (u_i0 + x_ij*u_i1 + e_ij                               <-- random

To fit this model using, for example, -mixed-, we would type

  . mixed y x z0 c.x#c.z0 || id: x

where 'id' is the level-2 identifier, y is the outcome variable, and x and z0
are the corresponding level-1 and level-2 variables.  We assumed that x and z0
are continuous and used the factor notation to include their interaction in
the model.

We will consider including an example of a multistage formulation in our
documentation.  For more examples, Sam may also look at Rabe-Hesketh &
Skrondal (2012), for example, chapters 4.9 and 7.4.

--Rafal
rraciborski@stata.com

References

S. Rabe-Hesketh & A. Skrondal. 2012. Multilevel and Longitudinal Modeling
using Stata. Stata Press, 3rd edition.

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