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Re: st: Markov processes and xttrans


From   Maarten buis <maartenbuis@yahoo.co.uk>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Markov processes and xttrans
Date   Wed, 30 Sep 2009 21:34:54 +0000 (GMT)

--- On Wed, 30/9/09, Dmitriy Krichevskiy wrote:
> I have a large panel data in which I have discretized
> income into quintiles. I then tested to see if transition
> processes (governing quintile transitions) are stationary.
> I found that I can characterize transitions as Markov. So
> I followed with xttrans command estimating transition
> probabilities. But I also want to know what my confidence
> intervals for transition probabilities estimates are?

Here is a quick stab at an approximate solution. It copies the strategy
of the official Stata command -proportion-, which is that these 
proportions/transition probabilities are nothing other means, so we
can use the standard formulas for inference about the mean to get an
approximation of the confidence intervals about these proportions. I
am thus conveniently ignoring lots of potential problems here, and I
leave it up to you to decide whether you find that acceptable.

Hope this helps,
Maarten

*------------------ begin example ------------------------------
program drop _all
program define xttransci, rclass byable(recall) sort
*! version 1.0.0 MLB 30Sept2009
*! based on xttrans
        version 6, missing
        syntax varname [if] [in] [, I(varname) T(varname) ]
        xt_iis `i'
        local ivar "`s(ivar)'"

        xt_tis `t'
        local tvar "`s(timevar)'"

        tempvar touse
        mark `touse' `if' `in'
        markout `touse' `varlist' `ivar' `tvar'

        tempvar was is
        quietly { 
                sort `ivar' `tvar' 
                by `ivar': gen float `was' = `varlist' if _n<_N
                by `ivar': gen float `is'  = `varlist'[_n+1] if _n<_N
                by `ivar': replace `touse'=0 if `touse'[_n+1]==0 & _n<_N
                levelsof `was'
                local levs `r(levels)'
                local k : word count `levs'

                tempname res
                matrix `res' = J(`=3*`k'',`k', .)
                tokenize `levs'
                forvalues i = 1/`k' {
                        tempvar d`i'
                        gen byte `d`i'' = `is' == ``i''
                }
                forvalues i = 1/`k' {
                        mean `d1'-`d`k'' if `touse' & `was' == ``i''
                        local ilb = (`i'-1)*3+1
                        local ip  = (`i'-1)*3+2
                        local iub = (`i'-1)*3+3
                        local rown `"`rown' ``i'':lb ``i'':p ``i'':ub"'
                        forvalues j = 1/`k' {
                                matrix `res'[`ilb',`j'] = _b[`d`j''] - invttail(e(df_r),0.025)*_se[`d`j'']
                                matrix `res'[`ip',`j'] = _b[`d`j''] 
                                matrix `res'[`iub',`j'] = _b[`d`j''] + invttail(e(df_r),0.025)*_se[`d`j'']
                        }
                }
                matrix rownames `res' = `rown'
                matrix colnames `res' = `levs'
        }
        matlist `res', format(%9.3f)
        return matrix result `res'
end

webuse nlswork, clear
xttransci msp


exit
*------------------------- end example ----------------------------
(For more on examples I sent to the Statalist see: 
http://www.maartenbuis.nl/example_faq )

--------------------------
Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen
Germany

http://www.maartenbuis.nl
--------------------------


      

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