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Re: st: xtmixed: variation at the highest level
Thanks to Garry Anderson who noted an error in my reply, who correctly
wrote the following...
Quoting Garry...
You mention "The slope between "year" and "ln_wage" is -0.049 for
non-college graduates, but for college graduates, the slope is higher by
0.0056 (p< 0.001)."
Is not the slope for non-college graduates equal to the coefficient for year, that is 0.0175735? The coefficient of -.0493273 for 1.collgrad is the change in ln_w for being a college graduate compared with a non-college graduate when year is zero. (strange that it is negative but has p=0.67)
The interaction coefficient of 0.0056061 is the increase in slope for college graduates compared with non-college graduates. The slope for college graduates would be 0.01757 + 0.0056 = 0.02318. You are correct
when you say 'the slope is higher by 0.0056'
Michael N. Mitchell
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On 2010-02-08 7.16 PM, Michael Norman Mitchell wrote:
Dear Peter
I share your confusion about these particular examples. As I look at
the "nlswork" dataset, it seems that this data represents repeated
observations of women across years, with "idcode" representing the
identifier of the woman (the level 2 identifier) and "year"
representing the year of measurement of the woman within the year.
Using "year" as a level 1 variable (that varies within each woman), we
could form a simple random intercept model as
* Random intercept model
xtmixed ln_w year || idcode:
and then extend this to a random slope model, assessing the extent to
which the slope of "year" varies across women.
xtmixed ln_w year || idcode: year
Seeing that there is variation in the slope of "year" predicting
"ln_w" across women, we could then try to explain this variation, by,
as you suggested, introducing a cross level interaction. For example,
perhaps women who are college graduates have higher slopes that
non-college graduates (i.e. the relationship between "year" and "ln_w"
is higher for college graduates than non-college grads). We could try
this model like this...
xtmixed ln_w i.collgrad##c.year || idcode: year, cov(unstruct)
In fact, the results show exactly this result. The slope between
"year" and "ln_wage" is -0.049 for non-college graduates, but for
college graduates, the slope is higher by 0.0056 (p < 0.001).
------------------------------------------------------------------------------
ln_wage | Coef. Std. Err. z P>|z| [95% Conf.
Interval]
-------------+----------------------------------------------------------------
1.collgrad | -.0493273 .115747 -0.43 0.670 -.2761872
.1775326
year | .0175735 .0006167 28.50 0.000 .0163648
.0187822
|
collgrad#|
c.year |
1 | .0056061 .001491 3.76 0.000 .0026838
.0085284
|
_cons | .2003554 .0465266 4.31 0.000 .1091649
.291546
------------------------------------------------------------------------------
I hope this helps.
Best regards,
Michael N. Mitchell
See the Stata tidbit of the week at...
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Peter Goff wrote:
I have a question that pertains to one of the examples given in the
xtmixed help file. Using the two-level data set "webuse nlswork" from
the first example in the help file, I see that the command:
xtmixed ln_w grade age c.age#c.age ttl_exp tenure c.tenure#c.tenure
|| id: grade, cov(unstruct)
can be used to create a random coefficient model. However, the data
file itself shows that the variable grade does not vary at the
highest level (level 2), i.e. it is constant within id (level 1).
From a multi-level modeling approach I have interpreted random
coefficient models to mean that the slope (of grade, in this example)
for each cluster can have a different impact upon the dependent
variable (ln_w, here). Although within this context there is no
variation of grade within individuals so I'm not clear how to
interpret this model.
Taking this a step further, if the model included an interaction
between the level 2 variable and a level 1 variable such as:
xtmixed ln_w grade c.grade#c.age age c.age#c.age ttl_exp tenure
c.tenure#c.tenure || id: grade, cov(unstruct)
would this change the interpretation of the random component of grade?
Kind thanks,
~Peter
Peter Trabert Goff
PhD student
Department of Leadership, Policy, and Organizations
Vanderbilt University
Peabody #514
230 Appleton Place
Nashville, TN 37203-5721
Tel. 615-415-7844
Fax. 615-322-6596
[email protected]
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