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# st: RE: How do the Wald test chi-square statistic and the pseudo r-square relate to each other in clogit?

 From LUCIA SUMMERS To Subject st: RE: How do the Wald test chi-square statistic and the pseudo r-square relate to each other in clogit? Date Thu, 2 Feb 2012 19:17:42 +0000

```Hello,

I am trying to understand some results I got (see below) and any assistance will be greatly appreciated.
I have run a number of conditional logit models (with cluster-adjusted robust SEs) and usually, if you get a greater Wald chi-square value, you also get a greater pseudo r-square.
But the models below are strange in that the first one has a great pseudo r-square value while the second one has a greater Wald chi-square value. The only thing that changes from one model to the next are the third and fourth variables starting from the bottom (i.e., in the second model, a_lneuclkm and m_lneuclkm have been substituted by a_lneuclmins and m_lneuclmins).
Does anyone have any information about how the Wald test statistic is calculated so that I can relate this to how the log-likelihood and the pseudo r-square are calculated (and work out why they might be behaving in this way)?
Thanks very much,
Lucia.

Model 1
. clogit choice commerc100 nostations popdens unemp10 imdincome imdhealth imdeducation imdhousing imdliving age15to29p10 seh100 eh100 mob10 a_lneuclkm m_lneuclkm sameethnic10 barrier, group(accno) vce(cluster crid) or
Iteration 0:   log pseudolikelihood = -3001.5126  Iteration 1:   log pseudolikelihood = -2981.3624  Iteration 2:   log pseudolikelihood = -2981.1934  Iteration 3:   log pseudolikelihood = -2981.1934
Conditional (fixed-effects) logistic regression   Number of obs   =    2434915                                                  Wald chi2(17)   =    2123.56                                                  Prob > chi2     =     0.0000Log pseudolikelihood = -2981.1934                 Pseudo R2       =     0.3111
(Std. Err. adjusted for 276 clusters in crid)------------------------------------------------------------------------------             |               Robust      choice | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]-------------+----------------------------------------------------------------  commerc100 |   1.085783   .0265569     3.36   0.001      1.03496    1.139101  nostations |   1.031757   .1310436     0.25   0.806     .8043889    1.323392     popdens |   .9933222   .0018225    -3.65   0.000     .9897565    .9969008     unemp10 |   2.113067   1.908653     0.83   0.408     .3597953    12.40998   imdincome |   8.174588   14.58476     1.18   0.239     .2476213    269.8633   imdhealth |   1.317499   .3145333     1.15   0.248     .8251607    2.103595imdeducation |   .9797458   .0111904    -1.79   0.073     .9580568    1.001926  imdhousing |   .9871881   .0132498    -0.96   0.337     .9615576    1.013502   imdliving |   1!
.007555   .0072077     1.05   0.293      .993527    1.021781age15to29p10 |   .9085186   .2040912    -0.43   0.669     .5849496    1.411072      seh100 |   1.080342   .0875577     0.95   0.340     .9216681    1.266333       eh100 |   1.002131   .0102836     0.21   0.836     .9821768    1.022491       mob10 |     1.5589   .4010742     1.73   0.084     .9415009    2.581164  a_lneuclkm |   .1852571   .0089984   -34.71   0.000      .168434    .2037605  m_lneuclkm |   .1642576   .0171001   -17.35   0.000     .1339401    .2014374sameethnic10 |   1.320282   .0669419     5.48   0.000     1.195387    1.458226     barrier |   .4008838   .0867893    -4.22   0.000     .2622634    .6127725------------------------------------------------------------------------------

Model 2
. clogit
choice commerc100 nostations popdens unemp10 imdincome imdhealth imdeducation
imdhousing imdliving age15to29p10 seh100 eh100 mob10 a_lneuclmins m_lneuclmins
sameethnic10 barrier, group(accno) vce(cluster crid) or

Iteration
0:   log pseudolikelihood =
-3055.2028

Iteration
1:   log pseudolikelihood =
-3035.5308

Iteration
2:   log pseudolikelihood =
-3035.4117

Iteration
3:   log pseudolikelihood =
-3035.4117

Conditional
(fixed-effects) logistic regression
Number of obs   =    2434915

Wald chi2(17)   =    3070.44

Prob
> chi2     =     0.0000

Log
pseudolikelihood = -3035.4117
Pseudo R2       =     0.2986

(Std. Err.
adjusted for 276 clusters in crid)

------------------------------------------------------------------------------

|               Robust

choice | Odds Ratio   Std. Err.      z
P>|z|     [95% Conf. Interval]

-------------+----------------------------------------------------------------

commerc100 |
1.080073   .0234639     3.55
0.000      1.03505    1.127055

nostations |    .973521
.1170455    -0.22   0.823
.7691413    1.232209

popdens |
.9921836   .0018916    -4.12
0.000      .988483     .995898

unemp10 |
2.280424   2.013854     0.93
0.351     .4039385    12.87407

imdincome |
5.966666   10.39074     1.03
0.305      .196514    181.1632

imdhealth |
1.307199    .289918     1.21
0.227     .8463645    2.018952

imdeducation
|   .9814027   .0110888
-1.66   0.097     .9599079
1.003379

imdhousing |    .984771
.0126269    -1.20   0.231
.9603312    1.009833

imdliving |
1.005372   .0071359     0.75
0.450      .991483    1.019456

age15to29p10
|   .9137366   .2075709
-0.40   0.691     .5854045
1.426218

seh100 |
1.080684   .0880311     0.95
0.341     .9212152    1.267759

eh100 |
1.003857   .0098699     0.39
0.695     .9846979    1.023389

mob10 |
1.478928   .3834865     1.51
0.131     .8896727    2.458464

a_lneuclmins
|    .100379   .0054367
-42.44   0.000     .0902694
.1116209

m_lneuclmins
|   .0900161   .0094458
-22.95   0.000     .0732825
.1105708

sameethnic10
|   1.329318   .0638578
5.93   0.000      1.20987
1.460558

barrier |
.2776155   .0561903    -6.33
0.000     .1867057    .4127905

------------------------------------------------------------------------------

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