Interaction Effects

 

Relationships between the Target variable and the characteristics used in the analysis are often not as simple as multiplicative factor relationships. Sometimes the relationship of the target variable to a specific characteristic depends on the value of a separate characteristic. The Interaction Effects utility allows the user to investigate interaction effects and provides ways for handling them. To go straight to the information on handling interaction effects, see the Add Interaction Effect Fields section.

 

After completing an analysis run, select the yellow braid button on the menu bar,  to investigate interactions.

 

A pop-up window will then open, allowing you to view the following across individual or all characteristics:

 

Interaction Statistic

Actual / Modeled

Exposure

Modeled Target

Residual

 

Interaction Statistic

 

The interaction statistic is designed to identify situations where consistent deviations from the strict multiplicative relationship are observed. It relies on the deviation of actual from modeled results, the level of credibility associated, and the scale of the observation.

 

The calculation is performed at the intersection of a value/bin for a specific characteristic with a value/bin of another characteristic. It is then aggregated at various levels depending on the view selected by the user. This summarized statistic can be viewed at three levels.

 

1.Each Characteristic vs. each other Characteristic

2.One Characteristic's values/bins vs. each other Characteristic

3.One Characteristic's values/bins vs. another Characteristic's values/bins

 

The interaction statistics are displayed within the matrix defined by the user. To define the matrix columns and rows, the user selects from the drop downs boxes in the top left hand corner of the Interaction Effects window. 

 

Selecting 'All Characteristics' in the drop-down box labeled 'Row' results in each of the selected characteristics from the model becoming the labels down the left hand side of the matrix. Selecting a particular characteristic from the analysis from the 'Column' drop-down box, results in the different values/bins that characteristic takes becoming the labels across the top of the matrix.

 

 

The user can also get to a specific characteristic by a specific characteristic view by double clicking on the number in the cell that intersects the two desired characteristics when it is in the 'All Characteristics' by 'All Characteristics' view.

 

 

How the Interaction Statistic is calculated:

 

 

 

The final two terms in the above equation are necessary to adjust the modeled amount to full Credibility. Otherwise what we are observing is often dominated by the overall difference between modeled and actual that results from assigning less than 100% credibility to what is observed. This is not an interaction effect, and so we attempt to exclude it here.

 

** The subscript 'i' describes the data for the records with the value 'i' for the row characteristic

** The subscript 'j' describes the data for the records with the value 'j' for the column characteristic

** The subscript 'ij' describes the data for the records with the value 'i' for the row characteristic and the value 'j' for the column characteristic.

 

 

Using an example:

 

 

(The values of the grouped characteristic Char3 have been labeled with 'Bin 1', 'Bin 2', etc. for reference purposes.)

 

Consider specifically, the cell highlighted in blue, where:

 

Char1 = 'A'

Char3 = 'Bin 1'

 

In the formulation of the two equations above, the subscript 'i' refers to 'Bin 1', and 'j' refers to 'A'.

 

 

 

 is the total exposure of the records where Char 3 = 'Bin 1' and Char 1 = 'A'

 is the modeled target of the records where Char 3 = 'Bin 1' and Char 1 = 'A'

 is the actual target of the records where Char 3 = 'Bin 1' and Char 1 = 'A'

 

Ultimately, a larger interaction statistic suggests possible interaction between the two bins or characteristics. 

 

 

The following four data computations can only be calculated in a 'Bins v. Bins' manner.

 

Actual/Modeled

This matrix displays the ratio .

 

Exposure

This matrix displays the breakdown of the total Exposure in the data set. Each cell represents the sum of the Exposure for all records that have the combination of bins specified by the row and column. For example, referring to the screen shot below, the value '1,303' represents the sum of the Exposure for records with the value 'A' for the Char1 characteristic and the value 'X' for the Char2 characteristic.

 

 

Modeled Target

This matrix displays, .

 

Residual

 

 

Interpreting the Statistics

 

To analyze the Actual/Modeled screen, look for patterns within the matrix for numeric Grouped Characteristics and look for extreme values for categorical characteristics (Generic Characteristic).