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From |
Alexandra Wilson <avwilson@bluebottle.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
st: xtlogit vs. gllamm. large condition numbers and group variances: what do they mean? |

Date |
Mon, 3 Sep 2007 22:37:12 +0300 |

I have a three-level hierarchical dataset, and have run both xtlogit and gllamm, with similar results apart from the condition number and group level variance, and I do not know what these large numbers are telling me. I have a dataset with various life history and social network attributes for women over their reproductive lives. The dataset contains one record for each woman-year combination, and has variables for whether they gave birth in that year to a child that survived (birth5), whether they were married polygnously or monogamously (mstat0-4plus), how many cowives they had (cowives), and whether and what sort of relatives they lived near in that year (frel). The years vary from 1921 to 1995, with any particular woman having a maximum of 40 records from her age 15 to 55 if she is 55 or older. There are 3226 records, for 225 women. I analysed this as a panel dataset with a binary dependent variable using xtlogit, This regression (output below) looks at the effect of different attributes of marital status (mstat1-4plus, and cowives), and presence of kin (frel) on the probability of giving birth to a surviving child in a particular year (birth5), controlling for age (using centred age, agex, and centred age squared, agexsq), year and number of previous marriages (prevmno). But a colleague pointed out that some of these 225 women are related to each other, as daughter, sisters, mothers: and indeed 92 women are related to each other, in clusters ranging from 1 to 8, mean 2.4. This is captured in the data through the variable oldmum, which is the id of the most senior related female, equal to self if the woman is not related to anyone else in the village sample. I thought that the best way to incorporate these relationships was to use gllamm, as described in chapter 3 of the gllamm manual. (reference below) So I ran gllamm, and the coefficients and significance of the variables are quite close to that obtained by xtlogit, but the condition number is large, 310220 and the variance for pno and oldmum is 5.863e-25 (9.488e-14) and 3.308e-24 (2.274e-13)respectively. The commands and results are listed below. I have 2 questions, plus 2 follow ups. 1. is gllamm the right tool to use? And if not, what should I do? 2. if yes, then should I worry about the condition number and variances? And what could I do to improve on them? Any help much appreciated, Alexandra Wilson Commands and results XTLOGIT iis pno xtlogit birth5 agex agexsq year cowives prevmno mstat1 mstat2 mstat3 mstat4plus frel,re Random-effects logistic regression Number of obs = 3266 Group variable (i): pno Number of groups = 225 Random effects u_i ~ Gaussian Obs per group: min = 1 avg = 14.5 max = 40 Wald chi2(10) = 73.09 Log likelihood = -1712.1297 Prob > chi2 = 0.0000 ---------------------------------------------------------------------------- -- birth5 | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+-------------------------------------------------------------- -- agex | .0318623 .0073886 4.31 0.000 .0173809 .0463436 agexsq | -.0048922 .0006102 -8.02 0.000 -.0060881 -.0036963 year | .0027409 .0034771 0.79 0.431 -.0040741 .0095559 cowives | .0102273 .1178123 0.09 0.931 -.2206805 .2411351 prevmno | .067444 .0962329 0.70 0.483 -.1211691 .256057 mstat1 | -.0539663 .180829 -0.30 0.765 -.4083846 .3004519 mstat2 | -.1910877 .1933577 -0.99 0.323 -.5700619 .1878866 mstat3 | -.2002851 .2967272 -0.67 0.500 -.7818598 .3812896 mstat4plus | .26714 .574198 0.47 0.642 -.8582674 1.392547 frel | .2079005 .0923417 2.25 0.024 .026914 .388887 _cons | -6.402292 6.862936 -0.93 0.351 -19.8534 7.048815 -------------+-------------------------------------------------------------- -- /lnsig2u | -3.826084 .2686081 -4.352547 -3.299622 -------------+-------------------------------------------------------------- -- sigma_u | .1476306 .0198274 .1134636 .1920862 rho | .0065812 .0017561 .003898 .011091 ---------------------------------------------------------------------------- -- Likelihood-ratio test of rho=0: chibar2(01) = 6.79 Prob >= chibar2 = 0.005 GLLAMM gllamm birth5 agex agexsq year cowives prevmno mstat1 mstat2 mstat3 mstat4plus frel, i(pno oldmum) family(binomial) link(logit) nip(5) adapt trace last output: number of level 1 units = 3266 number of level 2 units = 225 number of level 3 units = 142 Condition Number = 310220 gllamm model log likelihood = -1708.7352 ---------------------------------------------------------------------------- -- birth5 | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+-------------------------------------------------------------- -- agex | .0316857 .0072937 4.34 0.000 .0173902 .0459812 agexsq | -.0048713 .000607 -8.03 0.000 -.0060609 -.0036816 year | .0027582 .0033604 0.82 0.412 -.0038281 .0093445 cowives | .0065394 .1154256 0.06 0.955 -.2196907 .2327694 prevmno | .0663426 .0928466 0.71 0.475 -.1156334 .2483186 mstat1 | -.0529302 .1776275 -0.30 0.766 -.4010736 .2952133 mstat2 | -.1850067 .1896384 -0.98 0.329 -.5566912 .1866779 mstat3 | -.1957051 .2900493 -0.67 0.500 -.7641912 .372781 mstat4plus | .2568191 .5623738 0.46 0.648 -.8454132 1.359051 frel | .2073378 .0889529 2.33 0.020 .0329933 .3816823 _cons | -6.431496 6.631985 -0.97 0.332 -19.42995 6.566956 ---------------------------------------------------------------------------- -- Variances and covariances of random effects ---------------------------------------------------------------------------- -- ***level 2 (pno) var(1): 5.863e-25 (9.488e-14) ***level 3 (oldmum) var(1): 3.308e-24 (2.274e-13) references: Rabe-Hesketh, Sophia, Anders Skrondal and Andrew Pickles 2004 GLLAMM manual. Berkeley Electronic Press: University of California,Berkeley Division of Biostatistics Working papers no 160. http:/www.bepress.com/ucbiostat/paper160 * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

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