The Contrasts tab provides a mechanism for creating custom hypothesis tests. For example, compare different treatments or treatment combinations to see if the mean values are the same. Contrasts can only be computed using the fixed effect model terms set in the Model Specification field. For more on contrasts in the linear mixed effects model, see the “Contrasts” section.
The Fixed Effects Model Terms box lists all the fixed effect model terms specified in the Fixed Effects tab. Drag a term from the Fixed Effect Model Terms box to the Effect field to compute the contrasts for that term.
The conditions for using model terms as effect variables are:
If all values of the dependent variable are missing or excluded for an effect variable level, then that level of the effect variable is not used in the Contrast vector.
Effect variables can be either numeric or alphabetic but they cannot be both. If a column contains both numeric and alphabetic data, the column cannot be used as an effect variable when building contrasts.
Interactions can be used as contrasts only if the interaction is a model term.
Nested terms can be used as contrasts only if the nested term is a model term.
Drag a model term from the Fixed Effect Model Terms box to the Effect field.
To remove a model term, use the pointer to drag a model term from the Effect field back to the Fixed Effects Model Terms box.
In the Title field, type a title for the contrast.
The title is displayed in the Contrasts and Contrasts Coefficients worksheets.
In the Coefficients column, type the coefficient value for each level of the model term in the contrast.
Note: The coefficients for contrasts must sum to zero.
Add extra columns to enter multiple coefficients for each model term in the contrast.
In the Number of columns for contrast box, select the number of coefficient columns to use with each contrast (default is 1).
If multiple coefficient columns are selected, then Phoenix simultaneously tests the multiple linearly independent combinations of coefficients.
To set the degrees of freedom, check the User specified degrees of freedom box and type a value greater than one (1) in the field.
Note: Only select the User specified degrees of freedom option if the Phoenix engine does not seem to use the appropriate choices for the degrees of freedom.
The Univariate Confidence Intervals use an approximation for the t-value that is very accurate when the degrees of freedom value is at least five but loses accuracy as the degrees of freedom value approaches one. The degrees of freedom are the number of observations minus the number of parameters being estimated (not counting parameters that are within the singularity tolerance, i.e., nearly completely correlated).
Check the Show coefficients of contrasts box to display the actual coefficients used in the Contrasts Coefficients results worksheet.
In the Estimability Tolerance field, type a value for the zero vector.
The estimability tolerance value indicates the closeness of the zero vector before the Phoenix engine is used to make it estimable. The default value is 1E–05. Typically, this value does not need to be changed.
Press Add Contrast to add another contrast.
Each contrast is tested independently of other contrasts. Enter up to 100 contrasts.
Press Delete Contrast to delete a contrast.
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