Ordinal Logistic Regression

Regression Table - Odds Ratio

  

One advantage of the logit link function is that it provides an estimate of the odds ratio for each predictor in the model. In ordinal logistic regression, Minitab calculates a cumulative odds ratio, which provides the odds for response values less than or equal to a given response value versus the response values greater than the given response value.

Example Output

Logistic Regression Table

                                                    Odds        95% CI

Predictor        Coef    SE Coef      Z      P     Ratio    Lower    Upper

Const(1)     -1.75308   0.241928  -7.25  0.000

Const(2)    -0.810849   0.189384  -4.28  0.000

Const(3)    -0.102543   0.175413  -0.58  0.559

Const(4)     0.381173   0.176127   2.16  0.030

Const(5)     0.981362   0.187390   5.24  0.000

Const(6)      1.72139   0.216391   7.95  0.000

Const(7)      2.42882   0.260417   9.33  0.000

RaceOdds   -0.0290097  0.0075384  -3.85  0.000      0.97     0.96     0.99

 

Log-likelihood = -403.053

Test that all slopes are zero: G = 18.687, DF = 1, P-Value = 0.000

Interpretation

For the horse racing data, the logit link was used. One interpretation of the odds ratios is:

·    For every one-unit increase in the predictor, RaceOdds, the chance of the horse finishing first versus finishing second through eighth is reduced by a multiple of 0.97. Stated another way, the estimate suggests a 3% decrease in the odds that the horse finishes first versus finishes second through eighth for every one-unit increase in the predictor RaceOdds.

·    The confidence interval of the odds ratio provides the range in which the odds ratio is expected to fall. In this example, you can be 95% confident that the odds ratio will be between 0.96 and 0.99.

 

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