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Re: st: xtreg - continuous or discrete time


From   Ricardo Ovaldia <ovaldia@yahoo.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: xtreg - continuous or discrete time
Date   Tue, 16 Aug 2011 17:49:05 -0700 (PDT)

Thank you Jose Maria. I did understand why the coefficients are different, What I do know is which is the most appropriate parametrization of time. Or how to decide.

Ricardo

Ricardo Ovaldia, MS
Statistician 
Oklahoma City, OK


--- On Tue, 8/16/11, José Maria Pacheco de Souza <jmpsouza@usp.br> wrote:

> From: José Maria Pacheco de Souza <jmpsouza@usp.br>
> Subject: Re: st: xtreg - continuous or discrete time
> To: statalist@hsphsun2.harvard.edu
> Date: Tuesday, August 16, 2011, 4:10 PM
> Em 16/08/2011 15:45, Ricardo Ovaldia
> escreveu:
> > I have a longitudinal data on children measured at
> ages 5, 10, 15 and 20.
> > They were all measured within two weeks of their
> birthday.
> > When using -xtreg-, I get very different results
> depending of whether I use time as a continuous or
> categorical variable.
> >
> > I am tempted to use time as continuous, but I am not
> sure which to use. Any suggestions will be appreciated.
> >
> > Below is my output from the two models. I am
> interested in the group differences:
> >
> > Than you,
> > Ricardo
> >
> > Ricardo Ovaldia, MS
> > Statistician
> > Oklahoma City, OK
> >
> >
> >
> > xtreg instad group##time ses
> >
> > Random-effects GLS regression     
>              Number
> of obs      =      1413
> > Group variable: id         
>                
>     Number of groups   = 
>      360
> >
> > R-sq:  within  = 0.1989     
>                
>    Obs per group: min =     
>    1
> >         between =
> 0.0435             
>                
>           avg =   
>    3.9
> >         overall =
> 0.1426             
>                
>           max =     
>    4
> >
> >               
>                
>                
>   Wald chi2(12)      =   
> 275.48
> > corr(u_i, X)   = 0 (assumed) 
>                
>   Prob>  chi2       
> =    0.0000
> >
> >
> ------------------------------------------------------------------------------
> >        instad |   
>   Coef.   Std. Err.     
> z    P>|z|     [95% Conf.
> Interval]
> >
> -------------+----------------------------------------------------------------
> >         group |
> >            2 
> |  -.3593535   .8898889   
> -0.40   0.686    -2.103504 
>   1.384797
> >            3 
> |  -1.664428   .8971943   
> -1.86   0.064    -3.422897 
>   .0940402
> >           
>    |
> >          time |
> >           10 
> |   5.120189    .786916 
>    6.51   0.000 
>    3.577862    6.662516
> >           15 
> |   6.054063   .7869046 
>    7.69   0.000 
>    4.511758    7.596368
> >           20 
> |   .6104585   .7870224 
>    0.78   0.438 
>    -.932077    2.152994
> >           
>    |
> >    group#time |
> >         2 10 
> |  -1.245678   1.122178   
> -1.11   0.267    -3.445106 
>   .9537501
> >         2 15 
> |  -1.581695   1.126637   
> -1.40   0.160    -3.789864 
>   .6264734
> >         2 20 
> |  -2.830481    1.12774   
> -2.51   0.012 
>    -5.04081   -.6201511
> >         3 10 
> |  -.3909519   1.135047   
> -0.34   0.731    -2.615604 
>     1.8337
> >         3 15 
> |  -.7709906   1.134923   
> -0.68   0.497    -2.995398 
>   1.453417
> >         3 20 
> |  -.5713752   1.135312   
> -0.50   0.615    -2.796547 
>   1.653796
> >           
>    |
> >           ses
> |  -.0209192   .0203155   
> -1.03   0.303    -.0607368 
>   .0188984
> >         _cons
> |   104.1393   1.187133 
>   87.72   0.000 
>    101.8125     106.466
> >
> -------------+----------------------------------------------------------------
> >       sigma_u | 
> 3.1002125
> >       sigma_e | 
> 6.1590537
> >           rho
> |  .20215091   (fraction of variance due
> to u_i)
> >
> ------------------------------------------------------------------------------
> >
> > . xtreg instad group##c.time ses
> >
> > Random-effects GLS regression     
>              Number
> of obs      =      1413
> > Group variable: id         
>                
>     Number of groups   = 
>      360
> >
> > R-sq:  within  = 0.0049     
>                
>    Obs per group: min =     
>    1
> >         between =
> 0.0414             
>                
>           avg =   
>    3.9
> >         overall =
> 0.0193             
>                
>           max =     
>    4
> >
> >               
>                
>                
>   Wald chi2(6)       = 
>    21.62
> > corr(u_i, X)   = 0 (assumed) 
>                
>   Prob>  chi2       
> =    0.0014
> >
> >
> ------------------------------------------------------------------------------
> >        instad |   
>   Coef.   Std. Err.     
> z    P>|z|     [95% Conf.
> Interval]
> >
> -------------+----------------------------------------------------------------
> >         group |
> >            2 
> |   .4061883   1.137796 
>    0.36   0.721   
> -1.823851    2.636228
> >            3 
> |  -1.590677   1.146674   
> -1.39   0.165    -3.838116 
>    .656763
> >           
>    |
> >          time
> |   .0580776   .0553659 
>    1.05   0.294   
> -.0504374    .1665927
> >           
>    |
> > group#c.time |
> >            2 
> |  -.1741696    .079296   
> -2.20   0.028 
>    -.329587   -.0187523
> >            3 
> |  -.0427001    .079865   
> -0.53   0.593    -.1992325 
>   .1138324
> >           
>    |
> >           ses
> |  -.0261362   .0206384   
> -1.27   0.205    -.0665867 
>   .0143142
> >         _cons | 
>   106.608   1.288649   
> 82.73   0.000 
>    104.0823    109.1337
> >
> -------------+----------------------------------------------------------------
> >       sigma_u | 
> 2.6938033
> >       sigma_e | 
> 6.8485734
> >           rho
> |   .1339852   (fraction of
> variance due to u_i)
> >
> ------------------------------------------------------------------------------
> >
> >
> >
> >
> >
> > Ricardo Ovaldia, MS
> > Statistician
> > Oklahoma City, OK
> >
> >
> > *
> > *   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/
> >
> >
> >
> Dear Ricardo:
> probably some other Statalister will explain better than I,
> but I hope I 
> can give some initial explanation.
> When you use the first model, time is categorical and the
> meanings of 
> the  coeficients are differences in means of the
> "category" 10 against 
> the "category" 5, of the "category" 15 against "category" 5
> etc. and 
> does not must use the intervals 5, 5, 5 and 5 between the
> categories, 
> because the variable is not numeric.
> For the second model, the variable is continuous and the
> coeficient says 
> that there is an increase of .05 in instad for each unity
> of time, that 
> maybe 0 1 2 3 4 5 6 7 8 9 ......20.
> The values are not exatly what I mentioned because you use
> interaction 
> which interferes in the linear estimation, and the data
> presents a 
> possible squared form.
> FRegards,
> josé maria
> -- 
> Jose Maria Pacheco de Souza
> Professor Titular (aposentado), Colaborador Senior
> Departamento de Epidemiologia/Faculdade de Saude Publica,
> USP
> Av. Dr. Arnaldo, 715
> 01246-904  -  S. Paulo/SP - Brasil
> fones (11)3061-7747; (11)3768-8612
> www.fsp.usp.br/~jmpsouza
> *
> *   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/


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