Construct Model Effects

This section describes the options that you can use to facilitate entering effects into your model. Examples of how these options can be used to obtain specific types of models are given in Examples of Model Specifications and Their Model Fits.

Add

Adds effects to the model. These effects can either be added directly from the Select Columns list or they can be selected in that list and modified using Macros or Attributes. Effects can also be created and added, or modified, using Cross and Nest. The modeling types of the variables involved in the effect, as well as any Attribute assigned to the effect, determine how that effect is treated in the model.

Note: To remove an effect from the Construct Model Effects list, double-click the effect, or select it and click Remove or press the Backspace or Delete key.

Cross

Creates interaction or polynomial effects. Select two or more variables in the Select Columns list and click Cross. Or, select one or more variables in the Select Columns list and one or more effects in the Construct Model Effects list and click Cross.

See Statistical Details, for a discussion of how crossed effects are parameterized and coded.

Note: You can construct effects that combine up to ten columns as crossed and nested.

Example of Crossed Effects

Suppose that a product coating requires a dye to be applied. Both Dye pH and Dye Concentration are suspected to have an effect on the coating color. To understand their effects, you design an experiment where Dye pH and Dye Concentration are each set at a high and low level. It is possible that the effect of Dye pH on the color is more pronounced at the high level of Dye Concentration than at its low level. This is known as an interaction. To model this possible interaction, you include the crossed term, Dye pH * Dye Concentration, in the Construct Model Effects list. This enables JMP to test for an interaction.

Nest

Creates nested effects. If the levels of one effect (B) occur only within a single level of another effect (A), then B is said to be nested within A. The notation B[A], which is read as “B nested within A,” is typically used. Note that nesting defines a hierarchical relationship. A is called the outside effect and B is called the inside effect. Nested terms must be categorical.

Note: The nesting terms must be specified in order from outer to inner. For example, if B is nested within A, and C is nested within B, then the model is specified as follows: A, B[A], C[B,A] (or, equivalently, A, B[A], C[A,B]). You can construct effects that combine up to ten columns as crossed and nested.

Example of Nested Effects

As an illustration of nesting, consider the math teachers in each of two schools. One school has three math teachers; the other school has two math teachers. Each teacher in each school teaches two or three classes consisting of non-overlapping groups of students. In this example, classes (C) are nested within teachers (B), and teachers (B) are nested within schools (A). Enter these effects in the Fit Model launch window as follows:

Add both A and B to the Construct Model Effects panel.

In the Construct Model Effects panel, click B.

In the Select Columns list, click A.

Click Nest. This converts B to the effect B[A].

Add C to the Construct Model Effects panel and click on it.

Select A and B in the Select Columns list.

Click Nest. The converts C to the effect C[A, B].

Macros

In the Macros list, select options to automatically generate the effects for commonly used models and enter them into the Construct Model Effects list:

Full Factorial

Creates all main effects and interactions for the columns selected in the Select Columns list. These are entered in an order that is based on the order in which the main effects are listed in the Select Columns list. For an alternate ordering, see Factorial Sorted, in this table.

Factorial to Degree

Creates all main effects, but only interactions up to a specified degree (order). Specify the degree in the Degree box beneath the Macros button.

Factorial Sorted

Creates the same set of effects as the Full Factorial option but lists them in order of degree. All main effects are listed first, followed by all two-way interactions, then all three-way interactions, and so on.

Response Surface

Creates main effects, two-way interactions, and quadratic terms. The selected main effects are given the response surface attribute, denoted RS. When the RS attribute is applied to main effects and the Standard Least Squares personality is selected, a Response Surface report is provided. This report gives information about critical values and the shape of the response surface.

See also Response Surface Effect in Attributes and Response Surface Designs in the Design of Experiments Guide.

Mixture Response Surface

Creates main effects and two-way interactions. Main effects have the response surface (RS) and mixture (Mixture) attributes. In the Standard Least Squares personality, the Mixture attribute causes a mixture model to be fit. The RS attribute creates a Response Surface report that is specific to mixture models.

See also Mixture Effect in Attributes and Response Surface Designs in the Design of Experiments Guide.

Polynomial to Degree

Creates main effects and polynomial terms up to a specified degree. Specify the degree in the Degree box beneath the Macros button.

Scheffé Cubic

Creates main effects, interactions, and Scheffé cubic terms, which are useful in specifying response surfaces for mixture experiments. This macro creates a complete cubic model.

When you fit a third-degree polynomial model to a mixture, you must not introduce even-powered terms, for example, X1*X1*X2, because they are not estimable. However, it turns out that a complete polynomial specification of the surface can include terms of the form X1*X2*(X1 – X2), which are called Scheffé cubic terms.

Scheffé cubic terms are also included if you enter a 3 in the Degree box and then select the Mixture Response Surface macro command.

Grouped Regressors

Creates a single effect for up to 10 continuous factors that are treated as one effect in various parts of the report. You can add or remove the grouped effect in the Effect Summary. There is one leverage plot and one effect test for each group effect, rather than individual plots and tests for each factor in the group. This can be useful if your data table contains indicator columns that represent levels of a categorical effect.

Note: Non-continuous factors included in a group of regressors are not included in the analysis.

Attributes

In the Attributes list, select attributes that you can assign to an effect selected in the Construct Model Effects list.

Random Effect

Assigns the Random attribute to an effect. For details about random effects, see Specifying Random Effects and Fitting Method in Standard Least Squares Report and Options.

Response Surface Effect

Assigns the RS attribute to an effect. Note that the relevant model terms must be included in the Construct Model Effects list. The Response Surface option in the Macros list automatically generates these terms and assigns the RS attribute to the main effects. To obtain the Response Surface report, interaction and polynomial terms do not need to have the RS attribute assigned to them. You need only assign this attribute to main effects.

LogVariance Effect

Assigns the LogVariance attribute to an effect. This attribute indicates that the effect is to be included in a model of the variance of the response.

To include an effect in models for both the mean and variance of the response, you must specify the effect twice. In the tabbed interface, it must appear on both the Mean Effects and Variance Effects tabs. Otherwise, you can enter it twice on the Mean Effects tab, once without the LogVariance Effect attribute and once with the LogVariance Effect attribute.

Mixture Effect

Assigns the Mixture attribute to main effects. This is used to specify the main effects involved in the mixture. Note that the Mixture Response Surface option in the Macros list automatically assigns the mixture attribute to selected effects, and provides a Response Surface report when possible.

Excluded Effect

Assigns the Excluded attribute to an effect. This excludes the effect from the model fit. However, the effect is used to group observations for lack-of-fit tests. In the Standard Least Squares personality, a table of least square means is provided for this effect.

Knotted Spline Effect

Assigns the Knotted attribute to a continuous main effect. This implicitly adds cubic splines for the effect to the model specification. See Knotted Spline Effect.

Knotted Spline Effect

Knotted splines are used to fit a response Y using a flexible function of a predictor. Consider the single predictor X. When the Knotted Spline Effect is assigned to X, and k knots are specified, then k - 2 additional effects are implicitly added to the set of predictors. Each of these effects is a piecewise cubic polynomial spline whose segments are defined by the knots. See Stone and Koo (1985).

The number of splines is determined by the number of knots, which you are asked to specify. The coefficients associated with the splines are estimated based on the method used by the personality.

The placement of knots follows guidance given in the literature. In particular, if there are 100 or fewer points, the first and last knots are the fifth smallest and largest points, respectively. Otherwise, the first and last knots are placed at the 0.05 and 0.95 quantiles for 5 or fewer knots, or the 0.025 and 0.975 quantiles for more than 5 knots. The default number of knots is 5 for more than 30 observations, and 3 for fewer than 30 observations.

Note: Knotted splines are implemented only for main-effect continuous terms.

Transform

The Transform options transform selected Y columns or main effects that are selected in the Construct Model Effects text box.

Note: You can also transform a column by right-clicking it in the Select Columns list and selecting Transform. A reference to the transformed column appears in the Select Columns list. You can then use the column in the Fit Model window as you would any data table column. See the Transform Columns in the Using JMP book for details.

None

Removes any Transform options that have been applied.

Log

Applies the natural logarithm transformation to the selected variable.

Sqrt

Applies the square root of the values of the selected variable.