Download Interpreting the results

Ordinal Logistic Regression: OrdinalYears versus Adj_Forty
Link Function: Logit
Response Information
Variable
OrdinalYears
Value
0
1
2
Total
Count
9
10
11
30
Logistic Regression Table
Predictor
Const(1)
Const(2)
Adj_Forty
Coef
-3.66970
-2.25094
0.0292074
SE Coef
3.35366
3.30836
0.0342799
Z
-1.09
-0.68
0.85
P
0.274
0.496
0.394
Odds
Ratio
1.03
95% CI
Lower Upper
0.96
1.10
Log-Likelihood = -32.529
Test that all slopes are zero: G = 0.659, DF = 1, P-Value = 0.417
Goodness-of-Fit Tests
Method
Pearson
Deviance
Chi-Square
60.2893
65.0573
DF
57
57
P
0.358
0.217
Measures of Association:
(Between the Response Variable and Predicted Probabilities)
Pairs
Concordant
Discordant
Ties
Total
Number
170
125
4
299
Percent
56.9
41.8
1.3
100.0
Summary Measures
Somers' D
Goodman-Kruskal Gamma
Kendall's Tau-a
0.15
0.15
0.10
Interpreting the results
Response Information displays the number of observations that fall into each of the response
categories, and the number of missing observations. The ordered response values, from lowest to
highest, are shown. Here, we use the default coding scheme which orders the values from lowest
to highest: 0 is zero years in NFL, 1 = more than zero but not more than 3 years, and 2 = more
than three years.
Logistic Regression Table shows the estimated coefficients, standard error of the coefficients, zvalues, and p-values. When you use the logit link function, you see the calculated odds ratio, and
a 95% confidence interval for the odds ratio.
 The values labeled Const(1) and Const(2) are estimated intercepts for the logits of the
cumulative probabilities of survival for 0 years, and for 0 to 3 years, respectively. Because the
cumulative probability for the last response value is 1, there is not need to estimate an intercept
for more than 3 years.
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 There is one estimated coefficient for each covariate, which gives parallel lines for the factor
levels. Here, the estimated coefficient for the single covariate, Adj_Forty, is 0.0292, with a pvalue of 0.394. The p-value indicates that for most -levels, there is insufficient evidence to
conclude that the adjusted forty time affects years in NFL. The positive coefficient, and an odds
ratio that is greater than one indicates that higher adjusted forty times tend to be associated with
lower values of NFL years. Specifically, a one-unit increase in adjusted forty time results in a 3%
increase in the odds that a player serves 0 years versus greater than 3 years and that the player
serves less than or equal to 3 years versus greater than 3 years.
 Next displayed is the last Log-Likelihood from the maximum likelihood iterations along with
the statistic G. This statistic tests the null hypothesis that all the coefficients associated with
predictors equal zero versus at least one coefficient is not zero. In this example, G = 0.659 with a
p-value of 0.417, indicating that there is insufficient evidence to conclude that at the estimated
coefficient is different from zero.
Goodness-of-Fit Tests displays both Pearson and deviance goodness-of-fit tests. In our example,
the p-value for the Pearson test is 0.358, and the p-value for the deviance test is 0.217, indicating
that there is insufficient evidence to claim that the model does not fit the data adequately. If the pvalue is less than your selected -level, the test rejects the null hypothesis that the model fits the
data adequately.
Measures of Association display a table of the number and percentage of concordant, discordant
and tied pairs, and common rank correlation statistics. These values measure the association
between the observed responses and the predicted probabilities.
 The table of concordant and discordant pairs and tied pairs is calculated by pairing the
observations with different response values. Here, we have nine 0's, ten 1's, and eleven 2's,
resulting in 9 x 10 + 9 x 11 + 10 x 11 = 299 pairs of different response values. For pairs involving
the lowest coded response value (the 01 and 02 value pairs in the example), a pair is
concordant if the cumulative probability up to the lowest response value (here 0) is greater for the
observation with the lowest value. This works similarly for other value pairs. For pairs involving
responses coded as 1 and 2 in our example, a pair is concordant if the cumulative probability up
to 1 is greater for the observation coded as 1. The pair is discordant if the opposite is true. The
pair is tied if the cumulative probabilities are equal. In our example, 56.9% of pairs are
concordant, 41.8% are discordant, and 1.3% are ties. You can use these values as a comparative
measure of prediction. For example, you can use them in evaluating predictors and different link
functions.
 Somers' D, Goodman-Kruskal Gamma, and Kendall's Tau-a are summaries of the table of
concordant and discordant pairs. The numbers have the same numerator: the number of
concordant pairs minus the number of discordant pairs. The denominators are the total number of
pairs with Somers' D, the total number of pairs excepting ties with Goodman-Kruskal Gamma,
and the number of all possible observation pairs for Kendall's Tau-a. These measures most likely
lie between 0 and 1 where larger values indicate a better predictive ability of the model.
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