Statistics

Estimated Variance Covariance Matrix

The estimated covariance matrix is the inverse of the information matrix (negative of the expected Hessian) evaluated at the MLE values of the parameters.

Estimated Correlation Matrix

The estimated correlation matrix is the standardized version of the covariance matrix, that is, all entries are divided by the product of the standard deviations.

Gini Coefficient

Notation:

N = Total number of observations

Hosmer-Lemeshow (HL) Goodness of Fit Statistic

Note: The Hosmer-Lemeshow statistic is asymptotically distributed and follows a Χ² distribution with n-2 degrees of freedom.

Kolmogorov-Smirnov (KS) test

For all Good observations, predicted probability of Bad is computed, that is the relative frequency of bad cases in the bin a Good observation is placed. This process is repeated for all Bad observations. The KS test is then completed with the Good/Bad indicator as the group variable and the predicted probability of Bad as the response.

Significance level (p) approximation is based on the formula:

Lift Value

ROC - Area Under Curve (AUC)

ROC - Sensitivity

ROC - Specificity

Somers' D

If ties are present:

If ties are not present:

Wald Statistic

For continuous variables:

For categorical variables:

If ß_i is a vector of MLEs associated with m-1 dummy coded variables, and C is the asymptotic covariance matrix for ß_i, the Wald statistic is calculated as:

Note: Asymptotically distributed as a Χ² distribution with degrees of freedom equal to the number of parameters estimated and is analogous to the t-test in linear regression.

Wald Statistic - Standard Error

The standard error (SE) is the square root of the i^th diagonal entry of the inverse information matrix.