The interpretation of d is analogous to Gamma. 3. Somers' D is appropriate only when both variables lie on an ordinal scale. Value Minitab displays two values for D, one value for when the row variable is the dependent variable, and one value for when the column variable is the dependent variable. Percent Discordant 21.6 Gamma 0.352. Gini coefficient is a summary statistic that can also be known as Accuracy Ratio or Somers’D. Pairs 17690 c 0.617. Somers' D values range from -1 (all pairs disagree) to 1 (all pairs agree). Somer's D = 2 AUC - 1 or Somer's D = (Concordant Percent - Discordant Percent) / 100 It should be greater than 0.4. Somers’ D is also sometimes defined in terms of Kendall’s Tau: D(Y |X) = τ (X,Y)/ τ (X,X) Where: (X,Y) is a pair of bivariate random variables. (Henceforth, I will be addressing Somers’ D as the Gini coefficient) Somers' D Somers' D measures the strength and direction of the relationship between pairs of variables. Somers' D is computed as. Logistic Regression Model with a continuous predictor. Point 95% Wald Effect Estimate Confidence Limits width 1.644 1.347 2.007 Association of Predicted Probabilities and Observed Responses Percent Concordant 73.5 Somers’ D 0.485 Percent Discordant 25.0 Gamma 0.492 Percent Tied 1.5 Tau-a 0.224 Pairs 6882 c 0.742 predicted_ predicted_ Obs wcat cases yes prop prob satell As Gamma and the Taus, D is appropriate only when both variables lie on an ordinal scale. Two pairs (X_i, Y_i), (X_j, Y_j) are concordant if the ranks of both elements agree; that … Τ is Kendall’s Tau. (-1) being a perfect negative ordinal relationship and 1 a perfect ordinal relationship. Percent Tied 33.5 Tau-a 0.063. Implementation in the SAS system is described in [14]. ... Further, Somers’ d is used. Formulas for Somers' D(R|C) are obtained by interchanging the indices. In practice, a credit score model with Somers’ D of 0.4 is deemed to be good. rowSums(tab). D(C | R) = \frac{P-Q}{n^2 - ∑(n_i.^2)} where P equals twice the number of concordances and Q twice the number of discordances and n_i. We now look at a logistic regression model, but this time with a single continuous predictor (AGE). It measures the degree to which the model has better discrimination power than the model with random scores. Categorical data. Gini (Somer's D) It is a common measure for assessing predictive power of a credit risk model. Categorical variables are characterized by values which are cate gories. Its range lies [-1, 1]. I'm looking for an efficient python implementation of Somers'D, for which I need to compute the number of concordant, discordant and tied pairs between two random variables X and Y. Somers’ D takes on a value between (-1) and 1. with where The variance of the estimator under the null hypothesis that D(C|R) equals zero is computed as Refer to Somers (1962), Goodman and Kruskal (1979), and Liebetrau (1983). Percent Concordant 45.0 Somers' D 0.234. In the Association Statistics table that SAS provides as analysis output there is the Somers' D stat. Alternatively, if one X is larger than the other, it can be defined as the difference between the two corresponding conditional probabilities. Could you provide an Stack Exchange Network Stack Exchange network consists of 176 Q&A communities including Stack Overflow , the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. It has the range .