Nominal Logistic Regression

Logistic Regression Table - P-Value

  

The p-values indicate whether or not an observed relationship is statistically significant. You need to:

1    Identify the p-value at the bottom of the regression table. This p-value tells you if there is a significant association between the response and at least one logit by testing whether all slopes are equal to zero.

2    Compare this p-value to your a-level. A commonly used a-level is 0.05.

-     If the p-value is less than or equal to the a-level, then the association is significant, and you can conclude that at least one predictor is significantly associated with the response.

-     If the p-value is greater than the a-level, then you can conclude that there is no significant association and the interpretation ends.

3    If you concluded in step 2 that there is at least one significant logit, for each logit function, identify the p-value for each term in the model. These p-values tell you, for a given logit, whether or not there is a statistically significant association between a particular predictor variable and the nominal response.

4    Compare the individual p-values to your a-level: If a p-value is less than or equal to the a-level you have selected, the association is significant.

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 p-value for testing all the slopes for RaceOdds equal zero is 0.000. Assume an a-level of 0.05. Because 0.000 is less than 0.05, you conclude that there is a significant relationship between the response variable Finish and the predictor variable Odds for at least one logit.

·    For logits 1, 2, 3, 4, 5, and 6, the p-values for RaceOdds are 0.009, 0.001, 0.003, 0.012, 0.010, and 0.035. Because all p-values are less than 0.05, you conclude that there is a significant relationship between the response variable Finish and the predictor variable RaceOdds for these logits.

·    For logit 7, the p-value for RaceOdds is 0.299. Because this p-value is greater than 0.05, there is not enough evidence to conclude that a significant relationship exists between the response variable Finish and the predictor variable RaceOdds.