Nominal Logistic Regression

Regression Table - Odds Ratio

  

In nominal logistic regression, for each logit function, there is an odds ratio for each covariate. If the covariate is a categorical variable, there is an odds ratio for the number of categories minus one. This is because a unique parameter is calculated for each covariate for each value of the response except for the reference event.

Example Output

Logistic Regression Table

                                                     Odds     95% CI

Predictor            Coef    SE Coef      Z      P  Ratio  Lower  Upper

Logit 1: (8/1)

Constant        -0.919125   0.446453  -2.06  0.040

RaceOdds         0.143745  0.0549665   2.62  0.009   1.15   1.04   1.29

 

Logit 2: (7/1)

Constant         -2.11912   0.523139  -4.05  0.000

RaceOdds         0.184382  0.0548107   3.36  0.001   1.20   1.08   1.34

 

Logit 3: (6/1)

Constant         -1.14562   0.451970  -2.53  0.011

RaceOdds         0.159653  0.0546516   2.92  0.003   1.17   1.05   1.31

 

Logit 4: (5/1)

Constant        -0.839914   0.444873  -1.89  0.059

RaceOdds         0.137946  0.0551381   2.50  0.012   1.15   1.03   1.28

 

Logit 5: (4/1)

Constant         -1.11708   0.463681  -2.41  0.016

RaceOdds         0.143264  0.0553128   2.59  0.010   1.15   1.04   1.29

 

Logit 6: (3/1)

Constant        -0.571955   0.439702  -1.30  0.193

RaceOdds         0.117747  0.0559315   2.11  0.035   1.12   1.01   1.26

 

Logit 7: (2/1)

Constant        -0.243669   0.453674  -0.54  0.591

RaceOdds        0.0635537  0.0612533   1.04  0.299   1.07   0.95   1.20

 

Log-likelihood = -389.629

Test that all slopes are zero: G = 45.535, DF = 7, P-Value = 0.000

Interpretation

For the horse racing data, the odds ratios can be interpreted as:

·    Logit 1: For every one unit increase in RaceOdds, the odds for finishing last are 1.15 times greater than the odds for finishing first.

·    Logit 2: For every one unit increase in RaceOdds, the odds for finishing seventh are 1.20 times greater than the odds for finishing first.

·    Logit 3: For every one unit increase in RaceOdds, the odds for finishing sixth are 1.17 times greater than the odds for finishing first.

·    Logit 4: For every one unit increase in RaceOdds, the odds for finishing fifth are 1.15 times greater than the odds for finishing first.

·    Logit 5: For every one unit increase in RaceOdds, the odds for finishing fourth are 1.15 times greater than the odds for finishing first.

·    Logit 6: For every one unit increase in RaceOdds, the odds for finishing third are 1.12 times greater than the odds for finishing first.

·    Logit 7: For every one unit increase in RaceOdds, the odds for finishing second are 1.07 times greater than the odds for finishing first.