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


From   "avwilson" <avwilson@web.de>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: xtlogit vs. gllamm. large condition numbers and group variances: what do they mean?
Date   Tue, 4 Sep 2007 12:30:59 +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). The variables do
not explain much of the variance, but the point here is to lokk at the
differences between the variables.
Now 92 of these 225 women are related to each other, as daughter, sisters,
mothers, 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


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