I'm doing a regression on an ordinal variable, mmRS (3 months modified rankin scale, from 0-6). The ultimate goal is to do a multivariate ordinal regression. To avoid potential multi-collinearity, I planned to include variables only if they're with P<0.05 in univariate ordinal regression on the response variable. However 5 variables violated the proportional odd assumption with a significant test statistic on omodel.
According to Prof. Williams' useful teaching handout, gologit2 was applied. Now there appeared 2 situations.
1. Stata returned "All explanatory variables meet the pl assumption". This is a bit confusing since it is contradictory to the previous omodel result. Which one should i believe in? Or is it because proportional linear assumption is slightly different from proportional odds assumption? If that's the case can I adopt the OR which is equal across all mmRS levels as the common odds ratio for this variable?
An example code is as follows,
Code:
. omodel logit mmRS BaseRe if ant==1 Iteration 0: log likelihood = -261.72604 Iteration 1: log likelihood = -258.35881 Iteration 2: log likelihood = -258.34627 Iteration 3: log likelihood = -258.34627 Ordered logit estimates Number of obs = 136 LR chi2(1) = 6.76 Prob > chi2 = 0.0093 Log likelihood = -258.34627 Pseudo R2 = 0.0129 ------------------------------------------------------------------------------ mmRS | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- BaseRe | -1.430288 .5616626 -2.55 0.011 -2.531126 -.3294493 -------------+---------------------------------------------------------------- _cut1 | -2.185063 .2797802 (Ancillary parameters) _cut2 | -1.241382 .2091272 _cut3 | -.5477618 .1846715 _cut4 | -.0596471 .1792077 _cut5 | .4729539 .1838555 _cut6 | 1.224096 .2122543 ------------------------------------------------------------------------------ Approximate likelihood-ratio test of proportionality of odds across response categories: chi2(3) = 13.44 Prob > chi2 = 0.0038
Code:
gologit2 mmRS BaseRe if ant==1, auto lrforce ------------------------------------------------------------------------------ Testing parallel lines assumption using the .05 level of significance... Step 1: Constraints for parallel lines imposed for BaseRe (P Value = 0.1543) Step 2: All explanatory variables meet the pl assumption Wald test of parallel lines assumption for the final model: ( 1) [0]BaseRe - [1]BaseRe = 0 ( 2) [0]BaseRe - [2]BaseRe = 0 ( 3) [0]BaseRe - [3]BaseRe = 0 ( 4) [0]BaseRe - [4]BaseRe = 0 ( 5) [0]BaseRe - [5]BaseRe = 0 chi2( 5) = 8.03 Prob > chi2 = 0.1543 An insignificant test statistic indicates that the final model does not violate the proportional odds/ parallel lines assumption If you re-estimate this exact same model with gologit2, instead of autofit you can save time by using the parameter pl(BaseRe) ------------------------------------------------------------------------------ Generalized Ordered Logit Estimates Number of obs = 136 LR chi2(1) = 6.76 Prob > chi2 = 0.0093 Log likelihood = -258.34627 Pseudo R2 = 0.0129 ( 1) [0]BaseRe - [1]BaseRe = 0 ( 2) [1]BaseRe - [2]BaseRe = 0 ( 3) [2]BaseRe - [3]BaseRe = 0 ( 4) [3]BaseRe - [4]BaseRe = 0 ( 5) [4]BaseRe - [5]BaseRe = 0 ------------------------------------------------------------------------------ mmRS | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- 0 | BaseRe | -1.430288 .561663 -2.55 0.011 -2.531127 -.3294485 _cons | 2.185063 .2797802 7.81 0.000 1.636704 2.733422 -------------+---------------------------------------------------------------- 1 | BaseRe | -1.430288 .561663 -2.55 0.011 -2.531127 -.3294485 _cons | 1.241382 .2091273 5.94 0.000 .8315002 1.651264 -------------+---------------------------------------------------------------- 2 | BaseRe | -1.430288 .561663 -2.55 0.011 -2.531127 -.3294485 _cons | .5477619 .1846715 2.97 0.003 .1858123 .9097115 -------------+---------------------------------------------------------------- 3 | BaseRe | -1.430288 .561663 -2.55 0.011 -2.531127 -.3294485 _cons | .0596471 .1792078 0.33 0.739 -.2915937 .4108879 -------------+---------------------------------------------------------------- 4 | BaseRe | -1.430288 .561663 -2.55 0.011 -2.531127 -.3294485 _cons | -.4729539 .1838556 -2.57 0.010 -.8333043 -.1126036 -------------+---------------------------------------------------------------- 5 | BaseRe | -1.430288 .561663 -2.55 0.011 -2.531127 -.3294485 _cons | -1.224096 .2122543 -5.77 0.000 -1.640107 -.8080856 ------------------------------------------------------------------------------
I understand this binary variable is doomed to violate the proportional odds assumption, as none of the patients with sICHECASSII in our sample has mmRS less than 3 which also suggests its significant association with the response variable. Is there any chance to demonstrate its significance in an ordinal regression model?
Code:
. omodel logit mmRS sICHE if ant==1 Iteration 0: log likelihood = -252.1589 Iteration 1: log likelihood = -242.2106 Iteration 2: log likelihood = -242.12639 Iteration 3: log likelihood = -242.12627 Ordered logit estimates Number of obs = 131 LR chi2(1) = 20.07 Prob > chi2 = 0.0000 Log likelihood = -242.12627 Pseudo R2 = 0.0398 ------------------------------------------------------------------------------ mmRS | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- sICHECASSII | 2.376835 .5758406 4.13 0.000 1.248209 3.505462 -------------+---------------------------------------------------------------- _cut1 | -1.846412 .2693475 (Ancillary parameters) _cut2 | -.9389729 .2059614 _cut3 | -.2637609 .1873559 _cut4 | .2710231 .1871226 _cut5 | .8204586 .1994106 _cut6 | 1.690714 .2473567 ------------------------------------------------------------------------------ Approximate likelihood-ratio test of proportionality of odds across response categories: chi2(3) = 12.25 Prob > chi2 = 0.0066
Code:
. gologit2 mmRS sICHE if ant==1, auto lrforce ------------------------------------------------------------------------------ Testing parallel lines assumption using the .05 level of significance... Step 1: Constraints for parallel lines are not imposed for sICHECASSII (P Value = 0.00281) If you re-estimate this exact same model with gologit2, instead of autofit you can save time by using the parameter npl ------------------------------------------------------------------------------ Generalized Ordered Logit Estimates Number of obs = 131 LR chi2(4) = 24.19 Prob > chi2 = 0.0001 Log likelihood = -240.0651 Pseudo R2 = 0.0480 ------------------------------------------------------------------------------ mmRS | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- 0 | sICHECASSII | 0 (omitted) _cons | 1.832589 .2692591 6.81 0.000 1.304851 2.360327 -------------+---------------------------------------------------------------- 1 | sICHECASSII | 0 (omitted) _cons | .9223383 .2057949 4.48 0.000 .5189876 1.325689 -------------+---------------------------------------------------------------- 2 | sICHECASSII | 15.59655 708.8611 0.02 0.982 -1373.746 1404.939 _cons | .2425618 .1870634 1.30 0.195 -.1240757 .6091993 -------------+---------------------------------------------------------------- 3 | sICHECASSII | 2.114213 .782297 2.70 0.007 .5809388 3.647487 _cons | -.2425638 .1870636 -1.30 0.195 -.6092016 .1240741 -------------+---------------------------------------------------------------- 4 | sICHECASSII | 2.184546 .6759847 3.23 0.001 .8596406 3.509452 _cons | -.7985196 .2006948 -3.98 0.000 -1.191874 -.405165 -------------+---------------------------------------------------------------- 5 | sICHECASSII | 2.387373 .6047541 3.95 0.000 1.202076 3.572669 _cons | -1.694644 .256442 -6.61 0.000 -2.197261 -1.192027 ------------------------------------------------------------------------------ WARNING! 15 in-sample cases have an outcome with a predicted probability that is less than 0. See the gologit2 help section on Warning Messages for more information.
PS. I've been appreciating the forum for months but this is my first try of posting my own unsolved question. Sorry if my attempt of elucidating the question tends out to be tedious and lengthy 🤣
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