I'm having some convergence troubles with xtmlogit (Stata 17). In trying to isolate exactly what aspects of my data are causing the convergence problems, I came across the following curious result.
I have a regression (described in more detail below) where convergence is not achieved. But, if I recode the dependent variable, by flipping which outcome I label as "0" and which I label as "1", then the regression converges. This seems remarkable to me, as the two regressions are essentially the same! Can someone explain to me what is going on here? Is this a bug?
I run the regression:
Code:
xtset subj_id xtmlogit logit_var ib4.treatment_pair round if round >= 17 & link_changed == 0, covariance(unstructured)
Code:
Iteration 300: log likelihood = -426.40849 (not concave)
convergence not achieved
Random-effects multinomial logistic regression Number of obs = 1,057
Group variable: subj_id Number of groups = 144
Random effects u_i ~ Gaussian Obs per group:
min = 2
avg = 7.3
max = 14
Integration method: mvaghermite Integration pts. = 7
Wald chi2(13) = 828.70
Log likelihood = -426.40849 Prob > chi2 = 0.0000
--------------------------------------------------------------------------------
logit_var | Coefficient Std. err. z P>|z| [95% conf. interval]
---------------+----------------------------------------------------------------
0 | (base outcome)
---------------+----------------------------------------------------------------
1 |
treatment_pair |
1 | 4.58505 .6412856 7.15 0.000 3.328153 5.841947
2 | 5.909073 1.016015 5.82 0.000 3.917719 7.900427
3 | 4.878214 1.256084 3.88 0.000 2.416335 7.340093
5 | -.3215998 .8442502 -0.38 0.703 -1.9763 1.3331
6 | -241.1137 . . . . .
7 | .6811586 .8322975 0.82 0.413 -.9501144 2.312432
8 | -4.345004 1.127134 -3.85 0.000 -6.554146 -2.135861
9 | .2189924 1.167607 0.19 0.851 -2.069476 2.507461
10 | -1.108863 1.253222 -0.88 0.376 -3.565133 1.347406
11 | -240.9129 . . . . .
12 | -3.05133 1.635172 -1.87 0.062 -6.256207 .1535481
|
round | -.0256789 .0161091 -1.59 0.111 -.0572521 .0058943
_cons | -1.270844 .8370925 -1.52 0.129 -2.911515 .369827
---------------+----------------------------------------------------------------
2 |
treatment_pair |
1 | 30.59764 1.450718 21.09 0.000 27.75428 33.44099
2 | 32.43751 1.511915 21.45 0.000 29.47421 35.40081
3 | 29.23225 . . . . .
5 | -212.6786 . . . . .
6 | -214.0909 . . . . .
7 | -212.1836 . . . . .
8 | -213.6546 . . . . .
9 | -212.361 . . . . .
10 | -213.0046 . . . . .
11 | -213.9432 . . . . .
12 | -213.0525 . . . . .
|
round | -.0188885 .027518 -0.69 0.492 -.0728229 .0350459
_cons | -29.6336 1.59356 -18.60 0.000 -32.75692 -26.51028
---------------+----------------------------------------------------------------
var(u1)| 8.485527 2.115422 5.205665 13.83189
var(u2)| 7.613658 3.133812 3.398094 17.05891
---------------+----------------------------------------------------------------
cov(u1,u2)| 3.780754 1.99461 1.90 0.058 -.1286094 7.690118
--------------------------------------------------------------------------------
convergence not achievedNext, I can recode the dependent variable as follows:
Code:
gen logit_var_alt = logit_var replace logit_var_alt = 1 if logit_var == 0 replace logit_var_alt = 0 if logit_var == 1
Code:
xtmlogit logit_var_alt ib4.treatment_pair round if round >= 17 & link_changed == 0, covariance(unstructured)
Code:
Iteration 12: log likelihood = -426.40849
Random-effects multinomial logistic regression Number of obs = 1,057
Group variable: subj_id Number of groups = 144
Random effects u_i ~ Gaussian Obs per group:
min = 2
avg = 7.3
max = 14
Integration method: mvaghermite Integration pts. = 7
Wald chi2(23) = 131.59
Log likelihood = -426.40849 Prob > chi2 = 0.0000
--------------------------------------------------------------------------------
logit_var_alt | Coefficient Std. err. z P>|z| [95% conf. interval]
---------------+----------------------------------------------------------------
0 |
treatment_pair |
1 | 4.585051 .6412858 7.15 0.000 3.328154 5.841948
2 | 5.90909 1.016016 5.82 0.000 3.917735 7.900445
3 | 4.878216 1.256084 3.88 0.000 2.416337 7.340096
5 | -.321584 .8442495 -0.38 0.703 -1.976283 1.333115
6 | -32.31822 496390.9 -0.00 1.000 -972940.5 972875.9
7 | .6811845 .8322974 0.82 0.413 -.9500883 2.312457
8 | -4.344991 1.127134 -3.85 0.000 -6.554133 -2.13585
9 | .2190115 1.167607 0.19 0.851 -2.069456 2.507479
10 | -1.108861 1.253222 -0.88 0.376 -3.56513 1.347408
11 | -32.18744 508699.5 -0.00 1.000 -997065 997000.6
12 | -3.051317 1.635172 -1.87 0.062 -6.256194 .1535607
|
round | -.0256789 .0161091 -1.59 0.111 -.0572521 .0058943
_cons | -1.270844 .8370924 -1.52 0.129 -2.911515 .3698269
---------------+----------------------------------------------------------------
1 | (base outcome)
---------------+----------------------------------------------------------------
2 |
treatment_pair |
1 | 24.07116 4716.124 0.01 0.996 -9219.363 9267.505
2 | 25.91103 4716.125 0.01 0.996 -9217.523 9269.345
3 | 22.70577 4716.125 0.00 0.996 -9220.729 9266.14
5 | -10.66647 624273.3 -0.00 1.000 -1223564 1223543
6 | -11.58321 967995.4 -0.00 1.000 -1897248 1897225
7 | -10.29275 686931.6 -0.00 1.000 -1346372 1346351
8 | -11.33954 593606.4 -0.00 1.000 -1163458 1163436
9 | -10.51976 1281540 -0.00 1.000 -2511783 2511762
10 | -3665.568 . . . . .
11 | -11.48309 980922.5 -0.00 1.000 -1922584 1922561
12 | -11.00178 1101679 -0.00 1.000 -2159261 2159239
|
round | -.0188885 .027518 -0.69 0.492 -.0728229 .0350459
_cons | -23.10713 4716.125 -0.00 0.996 -9266.541 9220.327
---------------+----------------------------------------------------------------
var(u0)| 8.485526 2.115426 5.205661 13.8319
var(u2)| 7.613663 3.133809 3.398101 17.0589
---------------+----------------------------------------------------------------
cov(u0,u2)| 3.780776 1.994613 1.90 0.058 -.1285933 7.690145
--------------------------------------------------------------------------------
LR test vs. multinomial logit: chi2(2) = 262.17 Prob > chi2 = 0.0000Note that my data is sparse, which is likely the root cause of my convergence problems. In particular, the outcome of "2" can only ever occur when treatment_pair < 4.
0 Response to Strange convergence properties using xtmlogit
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