# Methods in Analyze Binary Response for Factorial Design

Select the method or formula of your choice.

## Factor/covariate pattern

Describes a single set of factor/covariate values in a data set. Minitab calculates event probabilities, residuals, and other diagnostic measures for each factor/covariate pattern.

For example, if a data set includes the factors gender and race and the covariate age, the combination of these predictors may contain as many different covariate patterns as subjects. If a data set only includes the factors race and sex, each coded at two levels, there are only four possible factor/covariate patterns. If you enter your data as frequencies, or as successes, trials, or failures, each row contains one factor/covariate pattern.

## Design matrix

Minitab uses the same approach to the design matrix as used in general linear model (GLM), which uses regression to fit the model you specify. First Minitab creates a design matrix from the factors and the model that you specify. The columns of this matrix, called X, represent the terms in the model.

The design matrix has n rows, where n = number of observations and columns that correspond to the terms in the model. The columns for the terms have the following order in the design matrix:
1. Constant
2. Covariates
3. Blocks
4. Factors
5. Interactions
These types of terms have 1 column each in the design matrix:
• Constant
• Covariate
• Continuous factor

For blocks, the number of columns is one less than the number of blocks.

### Categorical factors and interactions in 2-level designs

In a 2-level design, the term for a categorical factor has 1 column. Any interaction terms also have 1 column.

### Categorical factors in general factorial designs

In a general factorial design, categorical factors can have multiple columns. The number of columns is 1 less than the number of levels. Suppose A is a factor with 4 levels. Then it has 3 degrees of freedom and its block contains 3 columns. Let these columns be A1, A2, A3. Each row is coded as one of the following:
Level of A A1 A2 A3
1 1 0 0
2 0 1 0
3 0 0 1
4 -1 -1 -1

### Interactions in general factorial designs

To calculate the columns for an interaction term, multiply the corresponding columns for the factors in the interaction. For example, suppose factor A has 6 levels, C has 3 levels, D has 4 levels. Then the term A * C * D has 5 x 2 x 3 = 30 columns. To obtain the levels, multiply each column for A by each for C, by each for D.

### Whole plot columns in split-plot designs

###### Note

Minitab does not analyze split-plot designs with a binary response.

For a split-plot design, Minitab uses 2 versions of the design matrix. One version is the same matrix used for any 2-level factorial design. The other matrix includes a block of columns that represent whole plots. Calculation, for example, of the whole plot error term uses this second version of the design matrix. The columns for whole plots follow the columns for the hard-to-change factors and interactions that involve only hard-to-change factors.

By using this site you agree to the use of cookies for analytics and personalized content.  Read our policy