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From |
Maarten buis <maartenbuis@yahoo.co.uk> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
re: Re: st: Constructing a variable from standard deviations |

Date |
Mon, 22 Nov 2010 19:19:38 +0000 (GMT) |

So now Mathijs has 3 solutions: [Stas] use one -regres-, -predict- the residuals, compute the standard error of these residuals for each occupation separately. [me] use maximum likelihood to estimate a model with different residual standard errors for each occupation. [Kit] estimate a separate regression for each occupation, predict the residuals, and compute the standard error of each occupation. The solutions by me and Kit have the advantage that the model explicitly allows for differences in the residual variance, Stas' solution works, but is substantively awkward as in it you use a model that assumes that the residual variance is constant acros occupations to estimate differences in the residual variance across occupations. However, when comparing these models in the simulation below, all three seem to perform reasonably well. The bias is larger than one would have expected given the randomness inherit in Monte Carlo simulations (compare the biases with the MCse), but the biases are so small that based on this simulation I would be happy to use any of the three methods. The example below requires Ian White's -simsum-, which you can download by typing in Stata: -ssc install simsum-, and you can read more about it in Ian White (2010) "simsum: Analyses of simulation studies including Monte Carlo error" The Stata Journal, 10(3): 369--385. http://www.stata-journal.com/article.html?article=st0200 *--------------------------- begin simulation ------------------------ program drop _all program define mynormal_lf version 11 args lnfj mu ln_sigma quietly replace `lnfj' = /// ln(normalden($ML_y1, `mu', exp(`ln_sigma'))) end program define sim, rclass // create data drop _all set obs 500 gen occ = ceil(4*runiform()) gen x = rnormal() gen sd = cond(occ==1,.2, /// cond(occ==2,.6, /// cond(occ==3,.4, .8))) gen y = 1 + 2*(occ==2) + .5*(occ==3) + /// 3*(occ==4) + sd*rnormal() // Stas reg y x i.occ predict double resid, resid sum resid if occ == 2 return scalar stas = r(sd) // Maarten tempname b0 rmse matrix `b0' = e(b) scalar `rmse' = ln(e(rmse)) ml model lf mynormal_lf /// (mu: y = x i.occ) /// (ln_sigma: i.occ) ml init `b0' ml init ln_sigma:_cons = `= `rmse' ' ml maximize return scalar maarten = exp( [ln_sigma]_b[2.occ] + /// [ln_sigma]_b[_cons] ) // Kit reg y x if occ==2 qui predict double eps if e(sample), resid sum eps if occ == 2 return scalar kit = r(sd) end simulate stas=r(stas) maarten=r(maarten) kit=r(kit), reps(10000) : sim simsum stas maarten kit, true(.6) mcse bias twoway kdensity stas || kdensity maarten || kdensity kit *--------------------------- end simulation ---------------------------- Hope this helps, Maarten -------------------------- Maarten L. Buis Institut fuer Soziologie Universitaet Tuebingen Wilhelmstrasse 36 72074 Tuebingen Germany http://www.maartenbuis.nl -------------------------- * * 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**:**re: Re: st: Constructing a variable from standard deviations***From:*Christopher Baum <kit.baum@bc.edu>

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