Ordinal Regression/Parallel Lines Test

[Vik Rubenfeld]

I'm doing a new Ordinal Regression with a DV that has 5 categories ("Significantly Better" to "Significantly Worse").  I have 7 explanatory variables with 5 categories each, and 15 explanatory variables with 2 categories ("Yes" and "No") each.

PLUM CQIA7 BY CQIA5_1 CQIA5_2 CQIA5_3 CQIA5_4 CQIA5_5 CQIA5_6 CQIA5_7 CQIA6_1 CQIA6_4 CQIA6_5 

    CQIA6_6 CQIA6_7 CQIA6_8 CQIA6_9 CQIA6_10 CQIA6_11 CQIA6_12 CQIA6_13 CQIA6_16 CQIA6_17 CQIA6_18 

    CQIA6_19

  /CRITERIA=CIN(95) DELTA(0) LCONVERGE(0) MXITER(100) MXSTEP(5) PCONVERGE(1.0E-6) SINGULAR(1.0E-8)

  /LINK=LOGIT

  /PRINT=FIT PARAMETER SUMMARY TPARALLEL

  /SAVE=PREDCAT.

In the results, the parallel lines test is passed; it is not significant. Many coefficients are significant and the predicted category is precisely correct in 60% of the cases in the test data set.

David Garson discusses some instances in which it may be permissible to proceed even if the parallel lines test is significant.

The parallel lines assumption, also called the "proportionality of odds" assumption, is critical to ordinal regression. Ordinal regression computes multiple thresholds, which are the intercepts times -1 (discussed below), but only one set of effect coefficients (b's, which are the slopes of the effects).   There is one prediction equation for each threshold and it is assumed the slopes are identical, meaning the lines will be parallel, separated by the magnitude of the thresholds.

...Discounting the test is a common strategy if, on visual inspection, the b coefficients seem similar because the lines may well be sufficiently parallel (at a minimum, do not cross) for substantive interpretation even though not sufficiently parallel to pass the parallel lines test (Williams, 2006: 66). 

Garson, G. David (2012-05-08). Ordinal Regression (Statistical Associates "Blue Book" Series) (Kindle Locations 370-378). Statistical Associates Publishers. Kindle Edition. (emphasis added)

I would like to understand more about this.  Here are coefficients from these results, which pass that parallel lines test:

                                                   Parameter Estimates

                                                                        95% Confidence Interval

                       Estimate      Std. Error    Wald          dfSig. Lower Bound         Upper Bound

Threshold[CQIA7 = 1]           -5.472         0.922        35.255 1    0              -7.278     -3.666

         [CQIA7 = 2]           -2.355         0.877         7.215 1####               -4.074     -0.637

         [CQIA7 = 3]            2.182         0.843         6.704 1 0.01                0.53      3.833

         [CQIA7 = 4]             3.67         1.033        12.625 1    0               1.646      5.695

Location [CQIA5_1=1]           -2.562         1.169         4.803 1####               -4.854     -0.271

         [CQIA5_1=2]           -1.515         1.075         1.985 1####               -3.622      0.593

         [CQIA5_1=3]           -0.754         1.027         0.539 1####               -2.767      1.259

         [CQIA5_1=4]           -0.746         1.029         0.527 1####               -2.762      1.269

         [CQIA5_1=5]   0a            .             .              0.    .                   .

         [CQIA5_2=1]            -1.54         1.176         1.717 1 0.19              -3.844      0.764

         [CQIA5_2=2]           -0.991          1.15         0.743 1####               -3.245      1.262

         [CQIA5_2=3]           -1.012         1.115         0.823 1####               -3.198      1.174

         [CQIA5_2=4]           -0.613         1.205         0.259 1####               -2.975       1.75

         [CQIA5_2=5]   0a            .             .              0.    .                   .

         [CQIA5_3=1]           -0.361         0.962         0.141 1####               -2.246      1.525

         [CQIA5_3=2]           -0.112         0.907         0.015 1####               -1.889      1.665

         [CQIA5_3=3]            0.289         0.863         0.113 1####               -1.402       1.98

         [CQIA5_3=4]            0.288         0.862         0.111 1####               -1.402      1.977

         [CQIA5_3=5]   0a            .             .              0.    .                   .

         [CQIA5_4=1]            0.827         1.132         0.533 1####               -1.392      3.046

         [CQIA5_4=2]            0.816         0.979         0.694 1####               -1.103      2.734

         [CQIA5_4=3]            0.941         0.934         1.015 1####                -0.89      2.771

         [CQIA5_4=4]            0.912         0.898          1.03 1 0.31              -0.849      2.672

         [CQIA5_4=5]   0a            .             .              0.    .                   .

         [CQIA5_5=1]           -2.556         0.951         7.229 1####                -4.42     -0.693

         [CQIA5_5=2]            -2.84         0.864        10.815 1####               -4.533     -1.148

         [CQIA5_5=3]           -2.356         0.812          8.41 1####               -3.948     -0.764

         [CQIA5_5=4]            -1.62         0.775         4.373 1####               -3.139     -0.102

         [CQIA5_5=5]   0a            .             .              0.    .                   .

[more....]

Looking over this, I don't yet see any b coefficients that seem similar. What am I missing?

Thanks very much in advance to all for any info.

Best,

-Vik