# st: Parallell regression assumption and -gllamm-

 From Mirko <[email protected]> To [email protected] Subject st: Parallell regression assumption and -gllamm- Date Fri, 26 Jan 2007 18:20:23 +0000

```Dear statlister,

I have a simple question regarding item-specific thresholds models
using -gllamm-. Why -gllamm- with -lv- option gives different
coefficients and different significance levels than -gllamm- with
-thresh- option (and -gologit2-)? And how should I interpret the
results in the two cases? According to the gllamm manual they are
supposed to be two ways of specifying the same model.

Please look at the examples below.

Using a data set called 'delinq.txt' available at www.gllamm.org and
collapsing as follows (and as as shown in the GLLAMM manual p. 94):

infile sex y1 y2 y3 y4 y5 y6 using delinq.txt, clear
gen cons=1
collapse (sum) wt2=cons, by(sex y1-y6)
gen id=_n
reshape long y, i(id) j(item)
qui tab item, gen(d)
qui gllamm y, i(id) init weight(wt) l(oprob) f(binom) adapt
matrix a=e(b)

********GLLAMM WITH THRESH OPTION**********
. eq het: d2-d6
. gllamm y, i(id) init weight(wt) l(oprob) f(binom) thresh(het) from(a) adapt

number of level 1 units = 38652

Condition Number = 23.922058

gllamm model

log likelihood = -11234.722

------------------------------------------------------------------------------
y |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
_cut11       |
d2 |  -.0918488   .0309726    -2.97   0.003    -.1525541   -.0311436
d3 |    .265209   .0345849     7.67   0.000     .1974237    .3329942
d4 |   .2789123   .0347704     8.02   0.000     .2107635    .3470611
d5 |   .3703148   .0361224    10.25   0.000     .2995163    .4411133
d6 |   .0890254   .0325388     2.74   0.006     .0252505    .1528002
_cons |   1.379795   .0224225    61.54   0.000     1.335848    1.423743
-------------+----------------------------------------------------------------
_cut12       |
d2 |  -.1488803   .0497142    -2.99   0.003    -.2463183   -.0514423
d3 |   .0250053   .0533519     0.47   0.639    -.0795625    .1295731
d4 |    .083541   .0548724     1.52   0.128    -.0240069    .1910889
d5 |   .2239623   .0592946     3.78   0.000     .1077469    .3401776
d6 |  -.2864294   .0475729    -6.02   0.000    -.3796705   -.1931882
_cons |   2.093281   .0373036    56.11   0.000     2.020167    2.166394
-------------+----------------------------------------------------------------
_cut13       |
d2 |  -.1526825   .0655524    -2.33   0.020    -.2811628   -.0242021
d3 |  -.0389145    .068981    -0.56   0.573    -.1741147    .0962858
d4 |   .0429358   .0719935     0.60   0.551    -.0981688    .1840404
d5 |   .2201123   .0805448     2.73   0.006     .0622473    .3779773
d6 |  -.4127709   .0601531    -6.86   0.000    -.5306687    -.294873
_cons |   2.391813   .0497493    48.08   0.000     2.294306     2.48932
------------------------------------------------------------------------------

I used the -init- option to make it comparable with -gologit2- by
Richard Williams. The results of -gologit2- are reported below and
they confirm the -gllamm- model above.

*******GOLOGIT2*************

. gologit2 y d2-d6 [fw=wt], npl(d2-d6) link(p)

Generalized Ordered Probit Estimates              Number of obs   =      38652
LR chi2(15)     =     408.46
Prob > chi2     =     0.0000
Log likelihood = -11234.722                       Pseudo R2       =     0.0179

------------------------------------------------------------------------------
y |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
0            |
d2 |   .0918486   .0309719     2.97   0.003     .0311448    .1525525
d3 |  -.2652093   .0345842    -7.67   0.000     -.332993   -.1974256
d4 |  -.2789124   .0347697    -8.02   0.000    -.3470598   -.2107649
d5 |   -.370315   .0361217   -10.25   0.000    -.4411123   -.2995177
d6 |  -.0890261   .0325379    -2.74   0.006    -.1527992   -.0252531
_cons |  -1.379795   .0224217   -61.54   0.000    -1.423741   -1.335849
-------------+----------------------------------------------------------------
1            |
d2 |   .1488806   .0497093     3.00   0.003     .0514521    .2463091
d3 |  -.0250053   .0533468    -0.47   0.639     -.129563    .0795524
d4 |  -.0835403   .0548676    -1.52   0.128    -.1910789    .0239982
d5 |   -.223962   .0592905    -3.78   0.000    -.3401692   -.1077548
d6 |   .2864288   .0475671     6.02   0.000     .1931989    .3796586
_cons |  -2.093281   .0372978   -56.12   0.000    -2.166383   -2.020178
-------------+----------------------------------------------------------------
2            |
d2 |   .1526919   .0655437     2.33   0.020     .0242286    .2811552
d3 |   .0389239   .0689719     0.56   0.573    -.0962586    .1741063
d4 |  -.0429254   .0719849    -0.60   0.551    -.1840131    .0981624
d5 |  -.2201027   .0805377    -2.73   0.006    -.3779536   -.0622518
d6 |   .4127791   .0601427     6.86   0.000     .2949016    .5306565
_cons |  -2.391822    .049739   -48.09   0.000    -2.489309   -2.294336
------------------------------------------------------------------------------

However, -gllamm- with the -lv- option gives different thresholds with
different significance level:

***************GLLAMM WITH -LV- OPTION****************
. gllamm y, i(id) weight(wt) init link(oprob oprob oprob oprob oprob

number of level 1 units = 38652

Condition Number = 6.1160595

gllamm model

log likelihood = -11234.722

------------------------------------------------------------------------------
y |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
_cut11       |
_cons |   1.379795   .0224217    61.54   0.000     1.335849    1.423741
-------------+----------------------------------------------------------------
_cut12       |
_cons |   2.093281   .0372978    56.12   0.000     2.020179    2.166383
-------------+----------------------------------------------------------------
_cut13       |
_cons |   2.391823    .049739    48.09   0.000     2.294337     2.48931
-------------+----------------------------------------------------------------
_cut21       |
_cons |   1.287946   .0213666    60.28   0.000     1.246069    1.329824
-------------+----------------------------------------------------------------
_cut22       |
_cons |     1.9444   .0328618    59.17   0.000     1.879992    2.008808
-------------+----------------------------------------------------------------
_cut23       |
_cons |    2.23913    .042685    52.46   0.000     2.155469    2.322792
-------------+----------------------------------------------------------------
_cut31       |
_cons |   1.645004   .0263312    62.47   0.000     1.593396    1.696612
-------------+----------------------------------------------------------------
_cut32       |
_cons |   2.118286   .0381412    55.54   0.000      2.04353    2.193041
-------------+----------------------------------------------------------------
_cut33       |
_cons |   2.352898   .0477824    49.24   0.000     2.259246     2.44655
-------------+----------------------------------------------------------------
_cut41       |
_cons |   1.658708   .0265745    62.42   0.000     1.606622    1.710793
-------------+----------------------------------------------------------------
_cut42       |
_cons |   2.176822    .040241    54.09   0.000     2.097951    2.255692
-------------+----------------------------------------------------------------
_cut43       |
_cons |   2.434749   .0520372    46.79   0.000     2.332758     2.53674
-------------+----------------------------------------------------------------
_cut51       |
_cons |    1.75011   .0283205    61.80   0.000     1.694603    1.805617
-------------+----------------------------------------------------------------
_cut52       |
_cons |   2.317243   .0460895    50.28   0.000     2.226909    2.407577
-------------+----------------------------------------------------------------
_cut53       |
_cons |   2.611926   .0633431    41.23   0.000     2.487775    2.736076
-------------+----------------------------------------------------------------
_cut61       |
_cons |   1.468821   .0235793    62.29   0.000     1.422606    1.515035
-------------+----------------------------------------------------------------
_cut62       |
_cons |   1.806852   .0295213    61.21   0.000     1.748991    1.864712
-------------+----------------------------------------------------------------
_cut63       |
_cons |   1.979043   .0338109    58.53   0.000     1.912775    2.045311
------------------------------------------------------------------------------

Any help and reference to other works will be greatly appreciated.
Thank you very much for your time.

Mirko Moro
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```