Hello everyone,
I have conducted a brant test after an ordered logistic regression in order to test for the parallel regression assumption. My main independent variable is foreign_bakgrnd which does not seem to violate the assumption. However, I'm worried about the significant value of all the variables, i.e. "All" with a p<0.05. Should I consider doing mlogit instead or is ologit better in this case? I also conducted other tests which seem to point to ordered logistic regression as the best fit. However, I'm not 100% sure.
Some background information: The dependent variable ranges from 1 to 5 "very good, good, neither good nor bad, bad, very bad," to a proposal regarding immigration. Foreign_bakgrnd is the percentage of immigrants in each municipality.
Ologit
Mlogit
I have also used the oparallel command:
I also compared the saved model (ologit) to the current model (mlogit):
I have conducted a brant test after an ordered logistic regression in order to test for the parallel regression assumption. My main independent variable is foreign_bakgrnd which does not seem to violate the assumption. However, I'm worried about the significant value of all the variables, i.e. "All" with a p<0.05. Should I consider doing mlogit instead or is ologit better in this case? I also conducted other tests which seem to point to ordered logistic regression as the best fit. However, I'm not 100% sure.
Some background information: The dependent variable ranges from 1 to 5 "very good, good, neither good nor bad, bad, very bad," to a proposal regarding immigration. Foreign_bakgrnd is the percentage of immigrants in each municipality.
Ologit
Code:
ologit refugee gender age educ income student unemp foreign_bakgrnd tax total_unemp welfare if raised_swe==1 & mom==1 & dad==1 & f
> 80a==1 & citizen==1, cluster (kommun)
Iteration 0: log pseudolikelihood = -3262.2904
Iteration 1: log pseudolikelihood = -3140.9864
Iteration 2: log pseudolikelihood = -3140.2161
Iteration 3: log pseudolikelihood = -3140.2157
Iteration 4: log pseudolikelihood = -3140.2157
Ordered logistic regression Number of obs = 2035
Wald chi2(10) = 313.20
Prob > chi2 = 0.0000
Log pseudolikelihood = -3140.2157 Pseudo R2 = 0.0374
(Std. Err. adjusted for 50 clusters in kommun)
---------------------------------------------------------------------------------
| Robust
refugee | Coef. Std. Err. z P>|z| [95% Conf. Interval]
----------------+----------------------------------------------------------------
gender | .3089709 .070089 4.41 0.000 .171599 .4463427
age | .0055836 .0043592 1.28 0.200 -.0029603 .0141275
educ | .471975 .0498627 9.47 0.000 .3742459 .5697041
income | .0187043 .0176838 1.06 0.290 -.0159553 .0533639
student | .7294596 .185481 3.93 0.000 .3659235 1.092996
unemp | .2874827 .2435057 1.18 0.238 -.1897796 .764745
foreign_bakgrnd | .0259353 .0095523 2.72 0.007 .0072131 .0446576
tax | -.0011078 .0067755 -0.16 0.870 -.0143875 .0121719
total_unemp | -.0617319 .0238923 -2.58 0.010 -.10856 -.0149038
welfare | .0026904 .0484414 0.06 0.956 -.0922529 .0976337
----------------+----------------------------------------------------------------
/cut1 | .6259649 .7343175 -.813271 2.065201
/cut2 | 1.721342 .724796 .3007678 3.141916
/cut3 | 2.781114 .7424679 1.325904 4.236325
/cut4 | 3.80011 .7355121 2.358533 5.241687
Mlogit
Code:
mlogit refugee gender age educ income student unemp foreign_bakgrnd tax total_unemp welfare if raised_swe==1 & mom==1 & dad==1 & f
> 80a==1 & citizen==1, cluster (kommun)
Iteration 0: log pseudolikelihood = -3262.2904
Iteration 1: log pseudolikelihood = -3118.6774
Iteration 2: log pseudolikelihood = -3114.8747
Iteration 3: log pseudolikelihood = -3114.8613
Iteration 4: log pseudolikelihood = -3114.8613
Multinomial logistic regression Number of obs = 2035
Wald chi2(40) = 1788.08
Prob > chi2 = 0.0000
Log pseudolikelihood = -3114.8613 Pseudo R2 = 0.0452
(Std. Err. adjusted for 50 clusters in kommun)
--------------------------------------------------------------------------------------
| Robust
refugee | Coef. Std. Err. z P>|z| [95% Conf. Interval]
---------------------+----------------------------------------------------------------
_Very_Good |
gender | -.394604 .1127504 -3.50 0.000 -.6155907 -.1736173
age | -.010347 .0045848 -2.26 0.024 -.019333 -.001361
educ | -.3645869 .0721144 -5.06 0.000 -.5059286 -.2232452
income | -.0522729 .0287455 -1.82 0.069 -.108613 .0040672
student | -.4549115 .3531302 -1.29 0.198 -1.147034 .2372111
unemp | .0304258 .3571199 0.09 0.932 -.6695163 .7303679
foreign_bakgrnd | .0016004 .0099909 0.16 0.873 -.0179815 .0211823
tax | .0018852 .0105668 0.18 0.858 -.0188254 .0225957
total_unemp | .0154779 .0351648 0.44 0.660 -.0534439 .0843997
welfare | .0490317 .0599628 0.82 0.414 -.0684932 .1665565
_cons | 1.632298 1.059698 1.54 0.123 -.4446714 3.709268
---------------------+----------------------------------------------------------------
Fairly_Good |
gender | -.0450976 .121754 -0.37 0.711 -.2837311 .1935359
age | -.0067947 .0046264 -1.47 0.142 -.0158623 .0022729
educ | -.2249964 .0519674 -4.33 0.000 -.3268507 -.1231422
income | -.0199047 .0257654 -0.77 0.440 -.070404 .0305945
student | -.2329129 .3298539 -0.71 0.480 -.8794146 .4135888
unemp | -.4127772 .4627189 -0.89 0.372 -1.31969 .4941352
foreign_bakgrnd | -.0044638 .0106793 -0.42 0.676 -.0253949 .0164672
tax | .0096151 .0088208 1.09 0.276 -.0076734 .0269036
total_unemp | .006274 .0330595 0.19 0.849 -.0585215 .0710695
welfare | .0407527 .0541683 0.75 0.452 -.0654151 .1469206
_cons | -.0608351 .9518732 -0.06 0.949 -1.926472 1.804802
---------------------+----------------------------------------------------------------
Neither_good_nor_bad | (base outcome)
---------------------+----------------------------------------------------------------
Fairly_bad |
gender | -.0628752 .1013472 -0.62 0.535 -.2615122 .1357617
age | .0040965 .0060997 0.67 0.502 -.0078586 .0160516
educ | .2815299 .084509 3.33 0.001 .1158953 .4471646
income | .0234315 .0260612 0.90 0.369 -.0276474 .0745105
student | .5616208 .2876051 1.95 0.051 -.002075 1.125316
unemp | .0937818 .3774915 0.25 0.804 -.646088 .8336516
foreign_bakgrnd | .0112605 .0156116 0.72 0.471 -.0193376 .0418586
tax | .0125842 .0084345 1.49 0.136 -.0039471 .0291155
total_unemp | -.0368523 .0329919 -1.12 0.264 -.1015153 .0278107
welfare | .0899803 .0785352 1.15 0.252 -.0639458 .2439064
_cons | -2.966431 .9481258 -3.13 0.002 -4.824723 -1.108139
---------------------+----------------------------------------------------------------
Very_bad |
gender | .2793758 .1481659 1.89 0.059 -.011024 .5697756
age | -.0066449 .0054863 -1.21 0.226 -.017398 .0041081
educ | .4074613 .0708812 5.75 0.000 .2685368 .5463859
income | -.0283097 .033077 -0.86 0.392 -.0931394 .0365201
student | .5167056 .3865466 1.34 0.181 -.2409118 1.274323
unemp | .3544362 .4450767 0.80 0.426 -.5178981 1.226771
foreign_bakgrnd | .0511379 .0121621 4.20 0.000 .0273007 .0749752
tax | -.0007457 .0101354 -0.07 0.941 -.0206107 .0191194
total_unemp | -.1032037 .0395097 -2.61 0.009 -.1806413 -.0257661
welfare | .0197273 .0590026 0.33 0.738 -.0959156 .1353702
_cons | -1.737012 1.161006 -1.50 0.135 -4.012543 .538519
--------------------------------------------------------------------------------------
Code:
brant
Brant test of parallel regression assumption
| chi2 p>chi2 df
-----------------+------------------------------
All | 50.52 0.011 30
-----------------+------------------------------
gender | 4.86 0.182 3
age | 8.33 0.040 3
educ | 2.06 0.561 3
income | 5.84 0.119 3
student | 1.57 0.666 3
unemp | 2.25 0.522 3
foreign_bakgrnd | 5.61 0.132 3
tax | 1.82 0.611 3
total_unemp | 1.29 0.732 3
welfare | 1.13 0.769 3
A significant test statistic provides evidence that the parallel
regression assumption has been violated.
Code:
oparallel, ic
Tests of the parallel regression assumption
| Chi2 df P>Chi2
-----------------+----------------------
Wolfe Gould | 44.44 30 0.043
Brant | 50.52 30 0.011
score | 47.37 30 0.023
likelihood ratio | 45.59 30 0.034
Wald | 48.76 30 0.017
Information criteria
| ologit gologit difference
------+------------------------------------
AIC | 6308.43 6322.84 -14.41
BIC | 6387.09 6570.05 -182.96
Code:
. fitstat, dif force
| Current Saved Difference
-------------------------+---------------------------------------
Log-likelihood |
Model | -3114.861 -3140.216 25.354
Intercept-only | -3262.290 -3262.290 0.000
-------------------------+---------------------------------------
Chi-square |
D (df=1991/2021/-30) | 6229.723 6280.431 -50.709
Wald (df=40/10/30) | 1788.084 313.196 1474.888
p-value | 0.000 0.000 0.010
-------------------------+---------------------------------------
R2 |
McFadden | 0.045 0.037 0.008
McFadden (adjusted) | 0.032 0.033 -0.001
Cox-Snell/ML | 0.135 0.113 0.022
Cragg-Uhler/Nagelkerke | 0.141 0.118 0.023
Count | 0.309 0.290 0.019
Count (adjusted) | 0.096 0.071 0.025
-------------------------+---------------------------------------
IC |
AIC | 6317.723 6308.431 9.291
AIC divided by N | 3.105 3.100 0.005
BIC (df=44/14/30) | 6564.926 6387.087 177.839
Note: Likelihood-ratio test assumes saved model nested in current model.
Difference of 177.839 in BIC provides very strong support for saved model.