SamL <[email protected]> asks:
> I've attempted to figure out how to specify a slopes-as-outcomes multilevel
> model using _xtmixed- and at this point I am swirling in confusion. I have
> checked statalist and the manual, and cannot find an example that I am
> confident matches my aim. So, if my data has persons (i) nested within
> univerities (j), and Model 1, a 2-equation model I seek to estimate, is:
> Y_ij = b0 + b1_j*X1_ij + b2*X2_ij + e_ij
> b0 = g00
> b1_j = g10 + g11*Z1_j + u1_j
> b2 = g20
> what would be the appropriate syntax?
This is equivalent to
Y_ij = g00 + g10*X1_ij + g11*X1_ij*Z1_j + u1_j*X1_ij + g20*X2_ij + e_ij
= (g00 + g10*X1_ij + g11*X1_ij*Z1_j + g20*X2_ij) + u1_j*X1_ij + e_ij
fix in -xtmixed- using
. gen x1z1 = x1*z1
. xtmixed y x1 x1z1 x2 || university: x1, noconstant
Note the -noconstant- option. This is because you have a random slope on
-x1-, but no random intercept.
> And, if Model 2 has a slightly different specification:
> Y_ij = b0_j + b1*X1_ij + b2*X2_ij + e_ij
> b0 = g00 + g01*Z1_j + u0_j
> b1 = g10
> b2 = g20
This implies
Y_ij = g00 + g01*Z1_j + u0_j + g10*X1_ij + g20*X2_ij + e_ij
= g00 + g01*Z1_j + g10*X1_ij + g20*X2_ij + u0_j + e_ij
fitted as
. xtmixed y z1 x1 x2 || university:
i.e., as a random-intercept (at the university level) model.
They key is to manipulate your multilevel specification so that it reads as
fixed effects part + random effects part.
--Bobby
[email protected]
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