The option newton sets the Newton-Raphson algorithm as the method for finding the maximum of the likelihood function. The Hessian (the matrix of partial derivatives of the second order), which is used in the Newton-Raphson algorithm is approximated by the BHHH estimator (see Berndt et al. (1974)).

The vector of model parameters is estimated by the maximization of the logarithm of the likelihood function (the notation is introduced in the Method Description section):

Finding this maximum is equivalent to finding the critical points of the likelihood function, i.e. to solving a system of n (or n+1 if INTERCEPT = TRUE) equations

The option fisher sets the Fisher scoring algorithm (compare with the Lawless Singhal algorithm in Hosmer and Lemeshow (1989) page 129) as the method for estimating model parameters using the iterative formula:

where X is the matrix of observations,

The option logit sets the logit link function, i.e. the model will have the following form:

The option probit sets the probit link function, i.e. the model will have the following form:

where is the cumulative distribution function of the standard normal distribution.

Specifies the true a priori probability for the positive category (selected by setting the Positive Target Category) occurrence in the given population. This option is useful for choice-based samples, when the positive category frequency in build data differs from a-priori probability. If Positive Category Apriori is not set, the proportion from the sample is taken. If Positive Target Category is not set, the first category in the specified order will be the default positive category.

Specifies the order, in which target categories will appear in the model. The default value is alphabetical, which means appearance in the order of ascending numerical values or alphabetical categorical values. The value alphabeticalDesc means descending order. The value dataOrder means the order in which categories appear in the input data table.

The value of the Standard Coefficient of the variable (or attribute) is equal to:

where s_k is the total sample standard deviation for the k-th explanatory variable and

.

The value of the Wald statistics the variable (or attribute) is equal to:

where and H is the Hessian of the likelihood function evaluated at the point

the percentage of pairs of observations for which the model-estimated probability of an observation with a positive response is greater than the probability of an observation with a negative response. The probabilities are calculated using the following formula:

The value of the deviance statistic, measuring the goodness of fit of the model, is calculated using the following formula:

And

In the case when the observations are divided into M groups the formula for is more complex (see also Hosmer and Lemeshow 1989, p.146).

This statistic is defined as:

where is the Concordant, and is the Discordant.

This statistic, measuring the goodness of fit of the model, is calculated using the formula:

where denotes the number of test groups (see the option Hosmer-Lemeshow Groups), is the number of observations in the k-th group, denotes the number of observations in the k-th group with a positive response (i.e. observations for which the event, whose probability of occurrence we want to predict, has occurred) and

denotes the average predicted probability for the k-th group.

This statistic is defined as:

where stands for the number of Concordant pairs, stands for the number of Discordant pairs and N is the number of observations.

The Likelihood Ratio statistic is defined as:

If the indicator variables are binary (zero-one) then the likelihood of the saturated model is equal to 1 and the equation above can be simplified.

This is the p-value of the Wald statistic for the attribute. If the attribute is not significant the statistic has approximately the chi-square distribution with one degree of freedom.

The area of the region under the plot of the Receiver Operating Characteristic (ROC) function is equal to:

where stands for the Concordant and stands for the Discordant.

This statistic is defined as:

where

and L(0) denote the likelihoods of the estimated model and the model containing only the intercept, respectively.

The value of the Wald statistics is calculated as:

where H(a) stands for the Hessian of the likelihood function evaluated at the point .

The correlation matrix for coefficient estimators is calculated as

where are the -th elements of the covariance matrix of the parameter estimators.

Correlation between attributes is calculated in standard way.

The covariance matrix of the parameter estimators is calculated as

where is the Hessian matrix of the parameter estimators.

There are two base lifts, first is calculated for train data (always calculated), and the second one is calculated for validation data (if validation data is determined for build task). Except these two base lifts there are also auxiliary lifts which are calculated for transitional models. Transitional model is derived from the main model, and is built by removing one of variables. Auxiliary lifts can be determined respectively for train and validation data.

The auxiliary lifts are accessible in two places: in modelStatistics, where each lift can be visualized separately, and in the Lifts tab, where the lifts for the training data set and validating data set (if used) are displayed on the same chart. By clicking on the selected model variables (or group of variables- dependent on Group Mode setting in Variable Selection Settings) the user can display the appropriate auxiliary lifts on the chart. This provides the means for straightforward comparison of the main and transitional models.