Nominal Logistic Regression

Logistic Regression Table - Nominal Logistic Model

  

Nominal logistic regression examines the relationship between one or more predictors and a nominal response.

The nominal logistic equation treats each nominal outcome separately. The logistic regression equation is comprised of multiple logit functions, one for each value of the response minus one. Each equation has a unique slope for the predictors. These equations evaluate how the probability of observing a particular nominal outcome relative to the probability of observing the reference outcome changes as the predictor variables change.

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, because there are 8 values in the response information table, there are 7 logit equations.

·    Logit 1 is formed using the coefficients for Constant (-0.919125) and Odds (0.143745) in the logit equation. This logit equation compares the probability of the horse finishing last to the probability of a horse finishing first for a given value of RaceOdds. The positive coefficient for RaceOdds implies that the higher the odds, the higher the probability of finishing last instead of first.

·    Logit 2 is formed using the coefficients for Constant (-2.11912) and Odds (0.184382) in the logit equation. This logit equation compares the probability of the horse finishing seventh to the probability of a horse finishing first for a given value of RaceOdds. The positive coefficient for RaceOdds implies that the higher the odds, the higher the probability of finishing seventh instead of first.

·    Logit 3 is formed using the coefficients for Constant (-1.14562) and Odds (0.159653) in the logit equation. This logit equation compares the probability of the horse finishing sixth to the probability of a horse finishing first for a given value of RaceOdds. The positive coefficient for RaceOdds implies that the higher the odds, the higher the probability of finishing sixth instead of first.

·    Logit 4 is formed using the coefficients for Constant (-0.839914) and Odds (0.137946) in the logit equation. This logit equation compares the probability of the horse finishing fifth to the probability of a horse finishing first for a given value of RaceOdds. The positive coefficient for RaceOdds implies that the higher the odds, the higher the probability of finishing fifth instead of first.

·    Logit 5 is formed using the coefficients for Constant (-1.11708) and Odds (0.143264) in the logit equation. This logit equation compares the probability of the horse finishing fourth to the probability of a horse finishing first for a given value of RaceOdds. The positive coefficient for RaceOdds implies that the higher the odds, the high the probability of finishing fourth instead of first.

·    Logit 6 is formed using the coefficients for Constant (-0.571955) and Odds (0.117747) in the logit equation. This logit equation compares the probability of the horse finishing third to the probability of a horse finishing first for a given value of RaceOdds. The positive coefficient for RaceOdds implies that the higher the odds, the higher the probability of finishing third instead of first.

·    Logit 7 is formed using the coefficients for Constant (-0.243669 and Odds (0.0635537) in the logit equation. This logit equation compares the probability of the horse finishing second to the probability of a horse finishing first for a given value of RaceOdds. The positive coefficient for RaceOdds implies that the higher the odds, the higher the probability of finishing second instead of first.