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From |
Michael Norman Mitchell <Michael.Norman.Mitchell@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: xtmixed: variation at the highest level |

Date |
Mon, 08 Feb 2010 21:03:04 -0800 |

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 See the Stata tidbit of the week at... http://www.MichaelNormanMitchell.com Visit me on Facebook at... http://www.facebook.com/MichaelNormanMitchell On 2010-02-08 7.16 PM, Michael Norman Mitchell wrote:

Dear PeterI share your confusion about these particular examples. As I look atthe "nlswork" dataset, it seems that this data represents repeatedobservations of women across years, with "idcode" representing theidentifier 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), wecould 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 towhich the slope of "year" varies across women.xtmixed ln_w year || idcode: yearSeeing 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 thatnon-college graduates (i.e. the relationship between "year" and "ln_w"is higher for college graduates than non-college grads). We could trythis 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 forcollege 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 -.2761872.1775326year | .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... http://www.MichaelNormanMitchell.com Visit me on Facebook at... http://www.facebook.com/MichaelNormanMitchell Peter Goff wrote:I have a question that pertains to one of the examples given in thextmixed help file. Using the two-level data set "webuse nlswork" fromthe 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 datafile itself shows that the variable grade does not vary at thehighest level (level 2), i.e. it is constant within id (level 1).From a multi-level modeling approach I have interpreted randomcoefficient models to mean that the slope (of grade, in this example)for each cluster can have a different impact upon the dependentvariable (ln_w, here). Although within this context there is novariation of grade within individuals so I'm not clear how tointerpret this model.Taking this a step further, if the model included an interactionbetween 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 tenurec.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 * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

* * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: xtmixed: variation at the highest level***From:*Peter Goff <peter.t.goff@vanderbilt.edu>

**Re: st: xtmixed: variation at the highest level***From:*Michael Norman Mitchell <Michael.Norman.Mitchell@gmail.com>

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