Zero LR test statistic for melogit

[Peter Baade]

When using the following code

melogit goodprog i.screen i.dxagecat  i.remoteness || sa3: , or

I obtain the following output. What I don't understand is why the LR test statistic is 0 comparing with the logistic model.

The variable goodprog is 0/1, with 34% of records=1. the general data characteristics are consistent with the first example in the stata melogit documentation.

Any suggestions would be very appreciated.

Thanks.

Mixed-effects logistic regression Number of obs = 3,074
Group variable: sa3 Number of groups = 80

Obs per group:
min = 8
avg = 38.4
max = 124

Integration method: mvaghermite Integration pts. = 7

Wald chi2(7) = 270.05
Log likelihood = -1826.6925 Prob > chi2 = 0.0000
------------------------------------------------------------------------------------
goodprog | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval]
-------------------+----------------------------------------------------------------
1.screen | 3.380587 .288287 14.28 0.000 2.86025 3.995583
|
dxagecat |
2. 40-49 | 2.532121 .6644552 3.54 0.000 1.51398 4.234954
3. 50-59 | 2.312459 .6022525 3.22 0.001 1.387998 3.852649
4. 60-69 | 2.757566 .7171189 3.90 0.000 1.656405 4.590765
5. 70-79 | 3.076532 .8337443 4.15 0.000 1.808775 5.232849
|
remoteness |
2. Inner regional | .9092641 .1170525 -0.74 0.460 .7064999 1.170221
3. Major city | 1.221622 .1362389 1.79 0.073 .9817663 1.520076
|
_cons | .0964161 .025415 -8.87 0.000 .0575142 .1616308
-------------------+----------------------------------------------------------------
sa3 |
var(_cons)| 1.14e-33 3.75e-18 . .
------------------------------------------------------------------------------------
Note: Estimates are transformed only in the first equation.
Note: _cons estimates baseline odds (conditional on zero random effects).
LR test vs. logistic model: chi2(0) = 0.00 Prob > chi2 = .

Note: LR test is conservative and provided only for reference.

[Joseph Coveney]

What I don't understand is why the LR test statistic is 0 comparing with the logistic model. . . . Any suggestions would be very appreciated.

Look at the coefficient for variance of sa3—it's essentially zero.

[Clyde Schechter]

If you look at the final portion of the output table, you see that the variance of the random intercept at the sa3 level is 1.14x10^-33 , which for practical purposes is zero. So the data say that there is essentially no variance at the sa3 level. Which means that the multi-level model is in fact the same as the single level. The likelihood ratio would thus be 1, and the chi square statistic 0. (If you had them shown to a large number of decimal places you might see some very tiny deviation from those.)

Added: Crossed with #2.

[Peter Baade]

Hi Joseph and Clyde. Thanks for your prompt responses. I should have also alluded to the incredibly low modeled variance at the SA3 level. The confusing part is that there is substantial variation in the raw data.

 collapse (mean) goodprog=goodprog, by(sa3)

summ goodprog

    Variable |        Obs        Mean    Std. Dev.       Min        Max
-------------+---------------------------------------------------------
    goodprog |         80    .3499919    .1002473   .1111111        .75

[Joseph Coveney]

The confusing part is that there is substantial variation in the raw data.

But it's all accounted for by the fixed effects. That's what Stata (and Clyde and I) are telling you.

[Peter Baade]

Thanks Joseph Coveney and Clyde Schechter .