Specify coding for factors and covariates for Fit General Linear Model

Coding for factors

To perform the analysis, Minitab needs to recode the factors using one of two methods. Consider changing the method based on whether you want to compare the levels of the factor to the overall mean or the mean of a reference level. The coding scheme does not change the test of the overall effect of the factor. For more information, go to Interpreting categorical predictors.

• (-1, 0, +1): Choose to estimate the difference between each level mean and the overall mean.
• (1, 0): Choose to estimate the difference between each level mean and the reference level's mean. If you choose the (1, 0) coding scheme, the reference level table becomes active in the dialog box.

Reference level table

Factor

Shows all the names of the factors in your model. This column does not take any input.

Reference level

Minitab compares the means of the non-reference level to the reference level. Changing the reference level does not affect the overall significance, but it can make the coefficients more meaningful to interpret.

For factors with 1, 0 coding, by default, Minitab sets the following reference levels based on the data type:

• For numeric factors, the reference level is the level with the least numeric value.
• For date/time factors, the reference level is the level with the earliest date/time.
• For text factors, the reference level is the level that is first in value order, which is alphabetical order, by default.

Standardizing the covariates can improve the interpretation of the model for specific conditions. You can standardize the covariates using the following methods:

• Center the covariates by subtracting the mean: This method helps reduce multicollinearity, which improves the precision of the coefficient estimates. This method is helpful when your model contains highly correlated predictors due to higher-order terms and interaction terms. Each coefficient represents the expected change in the response given a one unit change in the predictor, using the original measurement scale.
• Standardize the covariates by dividing with their corresponding standard deviations. This method allows you to compare the size of the coefficients because they use a comparable scale. This approach is helpful when you want to know which covariates have a larger effect, while controlling for differences in scale. However, each coefficient represents the expected change in the response given a change of one standard deviation in the covariate.

Use one of the following methods to standardize the covariates:

• Do not standardize: Use your original data for the covariates.
• Specify low and high levels to code as -1 and +1: Use to both center the covariates and to place them on a comparable scale. All data values that fall between the low and high values that you specify are transformed to fall between −1 and +1. In the table, enter low and high values or use the default minimum and maximum values in the sample.

  Covariate

  Shows the names of all the covariates in your model. This column does not take any input.

  Low

  Enter a value to code as −1. The default is the minimum value in the sample.

  High

  Enter a value to code as +1. The default is the maximum value in the sample.

• Subtract the mean, then divide by the standard deviation: Use to both center the covariates and to place them on a comparable scale.
• Subtract the mean: Use to center the covariates.
• Divide by the standard deviation: Use a comparable scale for all covariates.
• Subtract a specified value, then divide by another: Specify other values rather than using the mean and standard deviation estimates from the sample.

  Covariate

  Shows the names of all the covariates in your model. This column does not take any input.

  Subtract

  Enter the value to subtract from each covariate.

  Divide By

  Enter the value that Minitab uses to divide the result of the subtraction.