Design Points (Vertices & Centroids) for Constrained Surfaces and Mixtures - Quick Tab

Standard Designs for Mixture Experiments

Select the Quick tab of the Design Points (Vertices & Centroids) for Constrained Surfaces and Mixtures dialog to access options to specify whether you want to find the vertex and centroid points for a mixture experiment or for a response surface experiment and to specify the Initial factor constraints, specifically, the low and high factor settings; and Specify additional constraints.

Type of design

The selection of either the Response surface or Mixture design option button determines whether Statistica generates vertex and centroid points for a response surface or a constrained mixture region.

Response surface

If the Response surface option button is selected, Statistica generates vertex and centroid points for a regular response surface region.

Mixture design

If the Mixture design option button is selected, Statistica generates vertex and centroid points for a constrained mixture region.

Number of factors

Enter a value in the Number of factors box to specify the respective number of factors for the design.

Initial factor constraints (highs & lows)

Click the Initial factor constraints (highs & lows) button to display the Initial High/Low Constraints for Factors spreadsheet containing the initial factor constraints, that is, their minimum and maximum values. If the Type of design (see above) is set to Mixture design, the spreadsheet will also show the mixture Total. Enter here the factor minima and maxima, and, for mixture designs, the mixture total. To accept the values, click the OK button. When processing the constraints, the computations performed by Statistica are performed in the highest possible floating-point precision. However, if the minima and maxima for different factors are of completely different magnitudes, it is recommended that you rescale the factors to make them compatible in size. Extreme differences in the orders of magnitude for different factors may cause round-off problems when a large number of constraints are processed (see also the Options tab). See also General User Entry Spreadsheet.

Specify the additional constraints

Click the Specify the additional constraints button to display the Enter the parameters of the general linear constraint spreadsheet, in which you specify the additional linear constraints. Unless the current design is a mixture design, you usually should specify additional constraints (additional constraints can, of course, also be specified for mixture designs). The logic of linear constraints, and how to convert various types of constraints into the linear form, is discussed in the Introductory Overview. Specify in this spreadsheet the (linear) weights that define the respective linear constraints. Note that you do not have to specify 0's (zeros) explicitly; if you leave a cell blank then Statistica interprets the entry as a zero. To accept the entries in the spreadsheet, click the OK button.

Compute

The option selected in the Compute group box determines whether Statistica will compute vertex points only or also centroids.

Vertices only (no centroids)

If the Vertices only (no centroids) option button is selected, Statistica only computes the vertex points. Because the computation of lower-dimensional centroid points can require a significant amount of time, in particular when there are many vertices and you request to compute centroids of many orders (see below), it is recommended to first always compute the vertices only for the constrained region of interest. This allows you to "size-up" the problem, and to make a realistic choice concerning the number of centroids to compute.

Vertices and overall centroid only

If the Vertices and overall centroid only option button is selected, Statistica computes the vertex points and the overall centroid. The determination of the overall centroid point usually requires little extra computing time.

Vertices and N-dimensional centroids

If the Vertices and N-dimensional centroids option button is selected, Statistica computes the centroids for the number of dimensions entered in the For dim. N through boxes below the option button.

For dim. N through.

Enter in the For dim. N through boxes the dimensions values for which to compute centroids. For example, if you select dimensions 1 through 1, then centroid points are computed for all pairs of vertex points (i.e., for the "1-dimensional lines connecting" the pairs of points); if you select 1 through 2, then centroid points are computed for all pairs of vertex points, and for all triplets of vertex points, and so on. Note that the For dim. N through boxes are only available when the Vertices and N-dimensional centroids option button is selected.