Dear experts,

I used Nlogit to analyse data. First, I did not include noconst in level 2 equation. And I got a nlogit model that did not pass the Wald test. Then I put the noconst in level 2 equation. Then I got a nlogit model that showed somehow good result. Could you please tell that why noconst option made such big difference? In addition, in my case I did not put any case-specific regressors in level# equation. Is that ok? Thanks in advance for your help!

First try:
. nlogit choice rela pay item1 item2 item3 gov premium || type:, base(opt)|| alt:, case(k) n
> otree nolog
note: variable item1 has 1063 cases that are not alternative-specific: there is no
within-case variability
note: variable item2 has 1072 cases that are not alternative-specific: there is no
within-case variability
note: variable item3 has 1066 cases that are not alternative-specific: there is no
within-case variability
note: branch 2 of level 1 is degenerate and the associated dissimilarity parameter
([opt_tau]_cons) is not defined; see help nlogit for details

RUM-consistent nested logit regression Number of obs = 19,206
Case variable: k Number of cases = 6402

Alternative variable: alt Alts per case: min = 3
avg = 3.0
max = 3

Wald chi2(7) = 1.55
Log likelihood = -4224.9563 Prob > chi2 = 0.9806

------------------------------------------------------------------------------
choice | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
alt |
rela | .4448475 .3677247 1.21 0.226 -.2758797 1.165575
pay | .0005854 .0004825 1.21 0.225 -.0003603 .0015312
item1 | .1819879 .1553586 1.17 0.241 -.1225094 .4864852
item2 | .0514332 .0762191 0.67 0.500 -.0979535 .2008199
item3 | .0710548 .0755807 0.94 0.347 -.0770807 .2191903
gov | .0099813 .0083145 1.20 0.230 -.0063148 .0262774
premium | -.0018144 .0015109 -1.20 0.230 -.0047757 .001147
------------------------------------------------------------------------------
alt equations
------------------------------------------------------------------------------
1 |
_cons | 0 (base)
-------------+----------------------------------------------------------------
2 |
_cons | -.2953216 .2522398 -1.17 0.242 -.7897026 .1990594
-------------+----------------------------------------------------------------
3 |
_cons | -3.147264 2.060118 -1.53 0.127 -7.185021 .8904933
------------------------------------------------------------------------------
dissimilarity parameters
------------------------------------------------------------------------------
type |
/ltc_tau | 2.040344 1.684484 -1.261185 5.341872
/opt_tau | 1 . . .
------------------------------------------------------------------------------
LR test for IIA (tau = 1): chi2(1) = 0.38 Prob > chi2 = 0.5352


Second try:
. nlogit choice rela pay item1 item2 item3 gov premium || type:, base(opt)|| alt:, case(k) n
> otree nolog noconst
note: variable item1 has 1063 cases that are not alternative-specific: there is no
within-case variability
note: variable item2 has 1072 cases that are not alternative-specific: there is no
within-case variability
note: variable item3 has 1066 cases that are not alternative-specific: there is no
within-case variability
note: branch 2 of level 1 is degenerate and the associated dissimilarity parameter
([opt_tau]_cons) is not defined; see help nlogit for details

RUM-consistent nested logit regression Number of obs = 19,206
Case variable: k Number of cases = 6402

Alternative variable: alt Alts per case: min = 3
avg = 3.0
max = 3

Wald chi2(7) = 526.76
Log likelihood = -4241.3271 Prob > chi2 = 0.0000

------------------------------------------------------------------------------
choice | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
alt |
rela | .9457561 .072113 13.11 0.000 .8044172 1.087095
pay | .0012496 .0000622 20.10 0.000 .0011277 .0013714
item1 | .3680267 .122389 3.01 0.003 .1281487 .6079046
item2 | .1400546 .1213328 1.15 0.248 -.0977532 .3778625
item3 | .1180326 .1201411 0.98 0.326 -.1174396 .3535047
gov | .0210559 .0025576 8.23 0.000 .0160432 .0260686
premium | -.00384 .0004513 -8.51 0.000 -.0047245 -.0029555
------------------------------------------------------------------------------
dissimilarity parameters
------------------------------------------------------------------------------
type |
/ltc_tau | 4.388153 .2226322 3.951802 4.824504
/opt_tau | 1 . . .
------------------------------------------------------------------------------
LR test for IIA (tau = 1): chi2(1) = 1448.11 Prob > chi2 = 0.0000
------------------------------------------------------------------------------