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# Re: st: xtmixed: variation at the highest level

 From Michael Norman Mitchell To statalist@hsphsun2.harvard.edu Subject Re: st: xtmixed: variation at the highest level Date Mon, 08 Feb 2010 21:03:04 -0800

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
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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
peter.t.goff@vanderbilt.edu

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```
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```

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