Pattern Substitution Analysis

This type of analysis fills in the missing values of the explained attribute depending on the values of explanatory attributes based on the existing classification.

NOTE. For method calculation, selected data must contain at least one attribute and two observations, excluding titles. If data source is:
     • Regular report. Title is the first row in the selected range.
     • Workbook. Titles are series names.
     • Express report, dashboard, data table. Titles are column headers.

Select the missing data substitution method in the drop-down list:

Decision Tree. Based on the data this method builds a hierarchical tree of rules where each object corresponds to a single node that provides a decision. The rule is a logical structure that looks like "if … then …". This method operates on categorical values.

NOTE. To increase performance and speed up saving of values obtained using this method, make sure that the table, to which data will be saved, contains primary index. To determine a primary index, select the primary index checkbox in index properties.

Logistic Regression. This method is applied if the user needs to predict whether an event will occur based on a number of characteristics. For example, if the user needs to forecast whether a patient has a disease based on gender and age. The column to be analyzed must contain binary data.
Back-Propagation Network. The method uses the back-propagation neural network for missing data substitution. This network uses a training algorithm, in which the error is propagated from the output layer to the input one, that is, in the opposite direction of signal propagation with the normal functioning of the network. The method operates on numeric values.
Decision Tree Ensembles. The method uses results obtained by various decision trees or one decision tree, but built by different parameters. The trees form an ensemble, and a final collective decision is found out.

Select the table column, in which it is required to substitute missing data, in the drop-down list. If attribute for analysis does not contain missing data, an information message appears.

NOTE. The selected attribute can be binary for the Logistic Regression method.

Select the checkboxes of the factors used to substitute the missing data in the analyzed column:

To select all factors, click the Select All button.
To deselect all factors, click the Deselect All button.

NOTE. The selected factors must contain some data.

To edit an attribute for analysis or selected factor influencing the analyzed attribute, click the Edit button located next to the drop-down menu with values of the dependent variable or next to the list of factors influencing the dependent variable. The Edit Attribute dialog box opens.

NOTE. Editing of the analyzed attribute or the selected factor that affects the analyzed attribute is available only in the desktop application. The Back-Propagation Network method enables editing only the attribute to analyze.

NOTE. It is available only for the Logistic Regression method.

Pattern substitution errors can be minimized by means of selecting cutoff point, that is, threshold value of probability that divides data into groups.

Analyzed attribute can have only two values. In the course of analysis, value of attribute is formed depending on probability value. If the probability is greater than the threshold value, value of the analyzed attribute belongs to one group, otherwise it belongs to another group. The optimal threshold value is "0.50".

NOTE. This option is available only for the Decision Tree Ensembles method.

To select an algorithm for building decision tree ensembles, use the Algorithm drop-down list. The number of available settings depends on the selected algorithm.

Available algorithms:

Gradient Boosting. Algorithm is a gradual optimization of loss function using gradient descent method. Algorithm parameters:

Maximum Number of Tree Levels. The value is in the range [1; <number of observations>]. The default value - 7.
Minimum Number of Observations. The value is in the range: [1; <number of observations> - 1]. The default value - 25.
Learning Rate. It enables the user to control weight correction value at each iteration. The value is in the range: (0; 1]. The default value - 0.1.
Number of Iterations. The value is in the range: [1; 2147483647]. The default value - 100.

Random Forest. Ensemble (committee) of decision trees is used to build decision rules. Objects are classified by means of voting: each tree of the created tree assigns the considered object to one of the categories. The category that scores the most of votes wins. Algorithm parameters:

Maximum Number of Tree Levels. The value is in the range [1; <number of observations>]. The default value - 7.
Minimum Number of Observations. The value is in the range: [1; <number of observations> - 1]. The default value - 25.
Number of Trees in Random Forest. The value is in the range: [1; 2147483647]. The default value - 100.
Number of Factors in Tree. The value is in the range: [1; <number of factors>]. The default value - 4.
Learning Sample Proportion. The value is in the range: (0; 1]. The default value - 0.7.

Cross-validation is a method of classification quality assessment.

To set up cross-validation:

Select the Cross-Validation checkbox. By default the checkbox is selected.
Select cross-validation method and set it parameters:

Leave-One-Out Cross-Validation. A separate value is used as a test set, other observations from source data are used for training. Training and checking the predicted value is repeated as many times as there is the number of objects with the known classification in the sample. The method does not contain additional parameters.
Repeated Random Sub-Sampling Cross-Validation. Source data is randomly split into a training set and a test set.
Set additional method parameters:

Training Set Size. Use the slider or the value editor to determine training set size. Parameter value may be from 1% to 99%. The default value is 70%.

Number of Repetitions. Use the value editor to determine the number of validation procedure repetitions. Parameter value may be from 1 to 231-1. The default value is 10.

K-Fold Cross-Validation. The method is set by default. Source data is split into K of equal-sized folds: one fold is used for testing, others K-1 for training. The procedure is repeated K times, each fold is used once as a test set. This results in K results, one for each fold, resulting accuracy assessment is an averaged value by all folds.
Set additional method parameter:

Number of Folds. Use the value editor to set value of the K parameter that determines the number of parts, into which source data must be split. Parameter value may be from 1 to the number of observations. The default value is 5.

The analysis results can be saved to a file, printed or inserted on the regular report sheet. For details see the Working with Analysis Results section.

The following tabs are displayed for the Pattern Substitution analysis on the Analysis Result page:

The tab displays data of the attribute to analyze. Missing data that is substituted by pattern is highlighted with color.

The tab is displayed only for the Decision Tree substitution method.

The tab contains a list of rules of influence on analyzed attribute values:

The tab is displayed only for the Logistic Regression substitution method.

The tab contains assessment of factor coefficients and general model characteristics.

The tab is displayed only for the Gradient Boosting algorithm in the Decision Tree Ensembles method.

The tab contains a list of rules of influence on analyzed attribute values:

The tab is displayed only for the Random Forest algorithm in the Decision Tree Ensembles method.

The tab contains a list of rules of influence on analyzed attribute values:

The tab displays the following tables:

The table that describes prediction and classification quality of object categories.
The table containing variable data.

The tab is displayed for the Logistic Regression and Decision Tree Ensembles filling methods in case of variable binary dependency.

The tab displays a ROC curve and its characteristics:

Area under curve.
Standard error.
Asymptotic confidence interval (lower and upper bounds).

Example of ROC curve: