Design & Analysis of Mixture Experiments - Analyze Design Tab
Select the Analyze design tab of the Design & Analysis of Mixture Experiments dialog to access options to specify the independent variables (factors or components of the experiment) and the list of dependent variables. Note that for mixture designs the sum of the component values must be equal to a constant. If you entered approximate component values into the data file (e.g., 0.33 in order to denote the component value 1/3, i.e., one-third) then you may have to adjust the Tolerance value (see below). This value (which is not to be confused with the tolerance value in Multiple Regression) is used when reading the data to determine whether the component values add up to a constant ± tolerance. However, regardless of the setting of the Tolerance value, STATISTICA always further adjusts the component values so that they sum to a constant exactly (given the machine precision for double-precision float numbers).
- Variables
- Click the Variables button to display the standard variable selection dialog, in which you specify the dependent variables of interest and the independent variable list (list of factors or components in the design). Note that for a valid mixture design, the component values for all cases (runs) in the experiment must sum to a constant (the mixture total).
Note: Multiple dependent variables and missing data. When more than one dependent variable is specified, then, when reading the data, STATISTICA performs casewise deletion of missing data. Thus, a case or run will be excluded from the analysis if it has missing data for any of the dependent variables specified for the analysis.
Recode factor values (pseudo-components) from. Ordinarily, when analyzing standard mixture designs, you want to rescale the original factor values so that the low and high factor settings for each factor (for a standard simplex design) are transformed to 0 and +1, respectively. Specifically, during the analysis, the component settings are customarily recoded to so-called pseudo-components so that (see also Cornell, 1990a, Chapter 3; or the Introductory Overview):
xi' = (xi - Li)/(Total-L)
Here, x'i stands for the i'th pseudo-component, xi stands for the original component value, Li stands for the lower constraint (limit) for the i'th component, L stands for the sum of all lower constraints (limits) for all components in the design, and Total stands for the mixture total. This transformation makes the coefficients for different factors comparable in size (see the Analysis of a Mixture Experiment dialog; however, remember that regardless of scaling, the results dialog also always allows you to review the regression coefficients for the original factor settings). The options in the Recode factor values (pseudo-components) from group box determine how the values for each factor are rescaled, that is, how the Li values (and L) in the formula shown above are determined.
- Automatically determined factor min/max values
- If the Automatically determined factor min/max values option button is selected, then, when you click the OK button (after you have selected the variables), STATISTICA automatically determines the values for Li and the mixture total from the values found in the data file. Specifically, Li will be set equal to the respective factor minimum found for the i'th independent variable (component) in the data file, and the mixture total will be taken from the sum of the component values for the first valid case (with non-missing data).
- User-defined values (high/low factor values)
- Select the User-defined values option button, or click the adjacent
button, to display the
Specifications for Mixture Variables spreadsheet, where you can enter the low and high values for each factor as well as the mixture total. To accept the values entered, click the OK button. While reading the data, all runs with component values that fall outside the Low and High Value boundaries for the respective factors will be ignored. Note that the entries in this spreadsheet must be consistent, i.e., allow for the construction of a standard mixture design. If some of the components are specified to have lower-bound restrictions, then STATISTICA (after you click the OK button) automatically adjusts the factor High values. This spreadsheet and the adjustment of component highs and lows is described in the context of the
Design of a Mixture Experiment dialog. See also the General User Entry Spreadsheet. Refer to the Introductory Overview for a discussion of pseudo-components.
- Tolerance value
- The value in the Tolerance value box is used by STATISTICA while reading the data to verify that the component values for each run sum to a constant ± tolerance (the mixture total, plus or minus the tolerance value). (This value is not to be confused with the tolerance value in Multiple Regression.) If you entered approximate component values into the data file (e.g., 0.33 in order to denote the component value 1/3, i.e., one-third) then you may have to adjust the Tolerance value. Note that, regardless of the setting of the Tolerance value, STATISTICA always further adjusts the component values (while reading the data) so that they sum to a constant exactly (given the machine precision for double-precision float numbers).