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From |
John Holmes <johnholmesyork@googlemail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Multiple group latent growth models with xtmixed |

Date |
Tue, 24 Nov 2009 08:53:06 +0000 |

Thanks for this Scott but I was hoping to be able to go further than the re-parameterisation. The texts on LGM suggest that group modelling can be done so you are not simply estimating a single uniform effect on all coefficients from the grouping variable (as you say this is equivalent to including it as a main effect); but instead having two separate but simultaneously estimated models so that in practice each parameter has been given its own individual grouping variable effect. I think this is possible in Mplus but was hoping to be able to do it in Stata as I don't have easy access to the former. 2009/11/23 Scott Baldwin <baldwinlist@gmail.com>: > John Holmes asked: > > "I have been estimating latent growth models using -xtmixed- with a > continuous income measure as the dependent variable and long-term > family status (14 categories) as an independent variable. However, I > am wanting to estimate simultaneous models for two separate groups - > those poor at time=0 and those not poor at time=0. Is this possible > using xtmixed?" > > You can. Given that you are calling your analysis a latent growth > model, I assume you are coming from SEM framework. Anyhow, you can fit > the mixed model version of a multiple group model using a separate > intercepts separate slopes model. Note, however, this is equivalent to > including the grouping variable as a main effect and as an interaction > with the time variable. It is just a reparamaterization of the typical > interaction model. In any case, the following code using the > "childweight" data described in the xtmixed documentation will > illustrate what you have to do. > > Hope this helps. > > Best, > Scott > > ****************************** > use http://www.stata-press.com/data/r11/childweight, clear > > *fit the typical interaction model > gen agegirl=age*girl > xtmixed weight age girl agegirl || id: age, var cov(un) ml > > ------------------------------------------------------------------------------ > weight | Coef. Std. Err. z P>|z| [95% Conf. Interval] > -------------+---------------------------------------------------------------- > age | 3.575854 .1770211 20.20 0.000 3.228899 3.922809 > girl | -.4639727 .2933195 -1.58 0.114 -1.038868 .1109229 > agegirl | -.2358053 .2501978 -0.94 0.346 -.726184 .2545733 > _cons | 5.345483 .2063143 25.91 0.000 4.941114 5.749851 > ------------------------------------------------------------------------------ > > ------------------------------------------------------------------------------ > Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval] > -----------------------------+------------------------------------------------ > id: Unstructured | > var(age) | .1988519 .1258059 .0575449 .6871511 > var(_cons) | .0540533 .0844623 .0025279 1.155816 > cov(age,_cons) | .103675 .0602908 -.0144927 .2218428 > -----------------------------+------------------------------------------------ > var(Residual) | 1.350626 .1634692 1.065399 1.712214 > ------------------------------------------------------------------------------ > > *log-likelihood > display(e(ll)) > -338.6593 > > *note that the _cons is equivalent to the boys' intercept when age > equals zero and the the coefficient for girl is the difference between > the boys' intercept and the girls' intercepts. Likewise, the age > coefficient is the slope for boys and the age x girl interaction is > the difference between the boys' and girls' slopes. > > > *fit the separate intercepts and slopes model. You need to create > indicator variables for each level of your grouping variable. We're > going include both and suppress the intercept. So I will create two > new dummy variables called male (1 for boys, 0 for girls) and female > (1 for girls, 0 for boys). We're also going to create the interaction > between the new dummy variables and the age variable. We aren't going > to include a main effect for age. > tab girl, gen(sex) > rename sex1 male > rename sex2 female > gen agemale=age*male > gen agefemale=age*female > xtmixed weight male agemale female agefemale, nocons || id:age, var cov(un) ml > ------------------------------------------------------------------------------ > weight | Coef. Std. Err. z P>|z| [95% Conf. Interval] > -------------+---------------------------------------------------------------- > male | 5.345483 .2063144 25.91 0.000 4.941115 5.749852 > agemale | 3.575854 .1770212 20.20 0.000 3.228899 3.922809 > female | 4.88151 .2084964 23.41 0.000 4.472865 5.290156 > agefemale | 3.340048 .1768121 18.89 0.000 2.993503 3.686594 > ------------------------------------------------------------------------------ > > ------------------------------------------------------------------------------ > Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval] > -----------------------------+------------------------------------------------ > id: Unstructured | > var(age) | .1988517 .1258081 .0575436 .687166 > var(_cons) | .0540512 .0844627 .0025274 1.155925 > cov(age,_cons) | .103673 .0602922 -.0144975 .2218435 > -----------------------------+------------------------------------------------ > var(Residual) | 1.35063 .1634699 1.065402 1.712219 > ------------------------------------------------------------------------------ > > *log-likelihood > display(e(ll)) > -338.6593 > > *note that the fit is identical to the previous model. We just > reparamaterized things. The male and female coefficients are the > intercepts for males and females, respectively. The agemale and > agefemale coefficients are the slopes for age for males and females, > respectively. > > *With a little arithmetic, you can move between the coefficients in > this model and the coefficients in the previous model. For example, to > get the coefficient for girl from the first model take the difference > between the female and male coefficients. > display 4.88151-5.345483 > -.463716 > > *You can also estimate separate random effects across groups > xtmixed weight male agemale female agefemale, nocons || id:male > agemale, nocons cov(un) || id:female agefemale, nocons var cov(un) ml > > *And if you have Stata 11, you can easily estimate separate residual > errors. It is more complicated in Stata 10. > xtmixed weight male agemale female agefemale, nocons || id:male > agemale, nocons cov(un) || id:female agefemale, nocons var cov(un) > residuals(independent, by(girl)) ml > > *Finally, you could use an likelihood ratio-test to see if fitting > separate intercepts and slopes improves model fit. > > xtmixed weight age || id:age, var cov(un) ml > estimates store model1 > xtmixed weight male agemale female agefemale, nocons || id:age, var cov(un) ml > estimates store model2 > lrtest model1 model2 > * > * 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/ > -- John Holmes Research Associate Institute for Social Change University of Manchester 4th Floor Arthur Lewis Building Oxford Road Manchester M13 9PL Email: johnholmesyork@gmail.com * * 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/

**Follow-Ups**:**Re: st: Multiple group latent growth models with xtmixed***From:*Stas Kolenikov <skolenik@gmail.com>

**Re: st: Multiple group latent growth models with xtmixed***From:*Maarten buis <maartenbuis@yahoo.co.uk>

**References**:**Re: st: Multiple group latent growth models with xtmixed***From:*Scott Baldwin <baldwinlist@gmail.com>

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