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From |
Stas Kolenikov <skolenik@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Predicted GLLAMM probs don't check out |

Date |
Thu, 17 May 2012 23:08:52 -0400 |

I think what you see is the effect of Jensen's inequality. The probabilities that you generate by hand are f( E[x] ), and the probabilities that -gllamm- gives you are E[ f(x) ], x being the unobserved random effect. On Thu, May 17, 2012 at 8:17 PM, David Crow <david.crow@cide.edu> wrote: > Dear All- > > I'm having a slight problem with predicted probabilities in GLLAMM: the > probabilities predicted after estimation with the "mu" option don't equal > the probabilities obtained by suitable transformations of the score function > obtained with the "linpred" option. > > First, I estimate the following multi-level logit model: > > gllamm amlo pri pan prd news wave, i(folio) family(binomial) link(logit) > trace > > Then, I obtain the linear predictor (with random effects) and predicted > probabilities with: > > gllapred pr1, mu > gllapred lp1, linpred > > As a check, I estimate probabilities by the inverse logit transformation of > the score function (linear predictor including random effects): > > gen p1 = exp(lp1) / (1+exp(lp1)) > > The problem is that the probabilities obtained with the inverse logit (p1) > don't match the probabilities predicted directly by gllapred (pr1). > > list amlo pr1 p1 > > pr1 p1 1 .278 .204 > 2 .006 .001 > 3 .003 .001 > 4 .240 .157 > > &c. > > To check that the score functions are OK, I recovered the linear predictor > without random effects (using the "xb" option) and the random effects (using > the "u" option) and added the two: > > gllapred xb1, xb > gllapred re1, u > gen linpred1 = xb1+re1m1 > > This does check out (i.e., linpred1 = lp1). > > The same problem obtains with predicted probabilities for probit models > using gllamm. First, I estimate the same model as above with the probit > link: > > gllamm amlo pri pan prd news wave, i(folio) family(binomial) link(probit) > trace > > Also as above, I use the "mu" and "linpred" options to recover the predicted > probabilities and score function (linear predictor including random > effects). > > gllapred pr2, mu > gllapred lp2, linpred > > Then, I carry out the inverse probit transformation on the linear predictor > to check these probabilities against those predicted with "mu". > > gen p2 = normal(lp2) > > Again, though, the probabilities don't match up: > > list amlo pr2 p2 in 1/10 > > pr2 p2 > 1 .289 .226 > 2 .005 .000 > 3 .002 .000 > 4 .247 .175 > > Any idea why the probabilities differ from each other? Which of the two > probabilities should I believe, or should I believe neither? > > Many thanks, > David > > > > > > -- > Web site for México, las Américas y el Mundo: > http://mexicoyelmundo.cide.edu/ > > ==================================== > David Crow, Ph.D. > Profesor-Investigador/Assistant Professor > División de Estudios Internacionales > Carretera México-Toluca 3655 > Col. Lomas de Santa Fe 01210 México, D.F. > Tel.: 5727-9800, ext. 2152 > Fax: 5727-9872 > ==================================== > > Conmutador: 5727-98-00 Lada sin costo: 01 800 021 2433 (CIDE) |© > > * > * 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/ -- ---- Stas Kolenikov -- http://stas.kolenikov.name ---- Senior Survey Statistician, Abt SRBI -- Opinions stated in this email are mine only, and do not reflect the position of my employer * * 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: Predicted GLLAMM probs don't check out***From:*David Crow <david.crow@cide.edu>

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