The Matrix Distributions node takes an Input Correlation Matrix and uses the Correlation values between each row and column to generate a set of correlated Customer Distributions. Additional Customer Distributions from the Input Attributes List can also be added to the Output Customer Distributions Matrix.

Each output Customer Distribution column will have a Mean and Standard Deviation (SD) set according to either the Configuration Dialog, or overridden by the 'Mean' and 'SD' columns in the Input Attribute List. By default, Unit Distributions having a Mean of 0.0 and a Standard Deviation of 1.0 will be generated. Each row in the set of Output Customer Distributions corresponds to a Feature 'Part-Worth' value or Product 'Willingness To Pay' (WTP) value for a Virtual Customer.

An upstream Differentiation Horizontal node, or Correlation Pairs to Matrix node, or Similarity Matrix node can produce an Output Product Correlation Matrix. This can be treated as the Input Correlation Matrix to this Matrix Distributions node.

The Output Customer Distributions from this Matrix Distributions node can become part of a Customer Willingness To Pay Matrix (WTP Matrix) for a set of Products. The Input WTP Matrix can feed a downstream Market Simulation node or a Market Tuning node.

Both the Input Attribute List and the Input Correlation Matrix is optional. If no inputs are provided, then the Matrix Distributions node will generate a single Customer Distribution with a Mean and SD set according to the Configuration Dialog. If just the Input Attribute List is provided, then the Default Correlation from the Configuration Dialog will set the level of Correlation between each of the Distributions. If just the Input Correlation Matrix is provided, then each Output Correlation will have a Mean and SD set according to the defaults in the Configuration Dialog.

**More Help:** Examples and sample workflows can be found at the Scientific Strategy website: www.scientificstrategy.com.

- Number of Customers
- The number of Virtual Customers to be generated by the Matrix Distributions node. Each Virtual Customer will be represented by a separate row in the Output Customer Distributions Matrix.
- Default Mean
- The default Mean for all Distributions in the Output Customer Distributions table. This default Mean will be applied to all Customer Distributions found in both the Input Attribute List and the Input Correlation Matrix. The default Mean value can be overridden by a 'Mean' column in the Input Attribute List. A Unit Distribution will have a Mean = 0.0 and Standard Deviation (SD) = 1.0.
- Default SD
- The default Standard Deviation (SD) for all Distributions in the Output Customer Distributions table. This default SD will be applied to all Customer Distributions found in both the Input Attribute List and the Input Correlation Matrix. The default Standard Deviation value can be overridden by a 'SD' column in the Input Attribute List. A Unit Distribution will have a Mean = 0.0 and Standard Deviation (SD) = 1.0.
- Default Correlation
- The default Correlation for all Distributions in the Output Customer Distributions table. This default Correlation will be applied to all Customer Distributions found in the Input Attribute List and the Input Correlation Matrix. The default Correlation will be overridden by the row-column Correlation values found in the Input Correlation Matrix as long as both the [row][column] and [column][row] value are not missing. Uncorrelated Distributions will have a Correlation = 0.0, while perfect Correlation = 1.0.
- Attribute to Customer Distribution Column
- Attributes listed in the Input Attribute List can be added to the Output Customer Distributions table. The Product name, Feature name, or other column can be selected as the Attribute to add. The Customer Distributions for these Attributes will be set to have the Default Correlation from the Configuration Dialog unless the same Attribute name is found in the Input Correlation Matrix.
- Save Randomizing Seed
- A Randomizing Seed can be saved to ensure that the random Customer Distributions generated by this node are always generated in the same way. If a Matrix Distributions node is copied within a workflow then the user should ensure the Saved Randomizing Seed is changed or not saved - otherwise Customer Distributions that ought to be uncorrelated may be incorrectly generated. The 'New' button will generate a new Randomized Seed. Disable the CheckBox to generate a new Randomizing Seed each time the node is run.

**Input Attribute List**: (optional) The set of additional Products, Features, or other Attributes to add to the Output Customer Distributions Matrix. The Customer Distributions for these Attributes will be correlated according to the Input Correlation Matrix or the Default Correlation value found in the Configuration Dialog. The Input Attribute List should include the following columns:**Product**(string): (optional) Unique Product Name or Product ID. The Products listed in this column can be added to the Output Customer Distributions table if the user selects this as the 'Attribute to Customer Distribution Column' in the Configuration Dialog. Attribute names can match the column-row names in the Input Correlation Matrix to override the default Mean and SD. The 'No Sale' Product will pass through to the 'Output Attribute List' but no Customer Distribution will be generated.**Feature**(string): (optional) Name of the Feature associated with the Product. The Features listed in this column can be added to the Output Customer Distributions table if the user selects this as the 'Attribute to Customer Distribution Column' in the Configuration Dialog. If the user wishes to add Customer Distributions named using a [Product].[Feature] format then this column will need to be manually added by the user upstream of the Input Attribute List.**Mean**(double): (optional) The Mean of the part-worth values to generate in the Customer Distribution for the Product, Feature, or Attribute. If this Mean value is missing then the default Mean value (initially 0.0) from the Configuration Dialog will be used instead. 'Average', 'Value', 'WTP', 'A', and 'Start' can also be used as column names.**SD**(double): (optional) The Standard Deviation (SD) of the part-worth values to generate in the Customer Distribution for the Product Feature. If this SD value is missing then the default SD value (initially 1.0) from the Configuration Dialog will be used instead. 'Variance', 'Diversity', 'Range', 'B', and 'End' can also be used as column names.**Price**(double): (optional) Price of the Product. This value will have no impact on the generation of the Output Customer Distributions, but may be conveniently passed downstream to a Market Simulation node.**Cost**(double): (optional) Cost of the Product or Feature. This value will have no impact on the generation of the Output Customer Distributions, but may be conveniently passed downstream to a Market Simulation node. The Cost cannot be negative.**Quantity**(integer): (optional) Quantity Sold of the Product. This value will have no impact on the generation of the Output Customer Distributions, but may be conveniently passed downstream to a Market Simulation node. The Input Quantity Sold would typically be compared against the Output Quantity Sold predicted by a Market Simulation node for testing and tuning.**Conformity**(double): (optional) The degree of Conformity the Attribute has from the norm (range limited to between +1.0 and 0.0). When the optional 'Input Correlation Matrix' has not been connected, then the Conformity will be multiplied by the 'Default Correlation' from the Configuration Dialog to create the Correlation Matrix between Products. To set the Correlations to be equal to the Conformity values, set the 'Default Correlation' to equal 1.0. When two Attributes have different Conformity values, their mutual Correlation is set to the minimum Conformity. When the optional 'Input Correlation Matrix' has been connected, then the Attribute Conformity values will modify those Input Correlations. Conformity = 1.0 (default) means that the Input Correlation is not changed. Conformity = 0.0 changes the Attribute's Correlation so that it is vastly different and unpredictable from the norm.

**Input Correlation Matrix**: (optional) The set of correlations that define the relationship between the Output Customer Distributions. The Input Correlation Matrix must be symmetrical such that the number of data rows match the number of columns. Each row Distribution Name should be unique and correspond to a column of the same name. These Customer Distribution names can also match the Attribute names from the Input Attributes List - useful when setting custom Mean / SD values for each Customer Distribution. The Input Correlation Matrix should include the following columns:**Distribution**(string): The name of the correlated Customer Distribution to generate. This name should correspond to a column of the same name in the same Correlation Matrix. The Distribution column can have any name. If multiple string columns are found then the first column is treated as the Distribution name column and the other string columns are ignored. If no string columns are found then the RowID column is treated as the Distribution name column.**Correlation Values**(double): The correlation value between each Distribution row and each Distribution column. As the Correlation Matrix is expected to be symmetrical, each row-column value must be the same as each column-row value. Left-Lower or Right-Upper triangle matrices can also be used. The diagonal values should all be equal to 1.0.

**Output Attribute List**: The set of Products, Features, or other Attributes added to the Output Customer Distributions Matrix. These Attributes are directly passed-through from the Input Attribute List as a convenience to downstream nodes. For example, the Input Attribute List can include details about the 'Price' of Products or 'Cost' of Features. In addition, the Output Attribute List will contain these columns:**Mean**: The Mean of the part-worth values in the Output Customer Distribution Matrix for the Product, Feature, or Attribute. The Mean is either set in the Configuration Dialog or overridden in the Input Attribute List. The relative difference of the Means between related Attributes reflects the primary degree of Vertical Differentiation between each.**SD**: The Standard Deviation (SD) of the part-worth values in the Output Customer Distribution Matrix for the Product Attribute. The SD is either set in the Configuration Dialog or overridden in the Input Attribute List. A Product lacking Vertical Differentiation (that is, having a low Mean) can still attract Customers if it has a relatively high SD, or if it has Horizontal Differentiation (that is, its Customer Distribution is uncorrelated) relative to other Products.

**Output Customer Distributions**(double): The set of correlated Customer Distributions for each Distribution column in the Input Correlation Matrix by each Virtual Customer row. Additional Customer Distribution columns will be added for each unique Attribute found in the Input Attribute List. The total number of Virtual Available Customers is equal to the number of rows in the Output Customer Distributions Matrix.

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