Methods for Fit Poisson Model

Find definitions and interpretation guidance for the Method table.

In This Topic

Categorical predictor coding
Continuous predictor standardization
Link function
Validation

Categorical predictor coding

Minitab can use either the (0, 1) or (−1, 0, +1) coding scheme to include categorical variables in the model. The (0, 1) scheme is the default for regression and Cox regression analyses while the (−1, 0, +1) scheme is the default for ANOVA and DOE. The choice between these two schemes does not change the statistical significance of the categorical variables. However, the coding scheme does change the coefficients and how to interpret them.

Interpretation

Verify the coding scheme that is displayed to ensure that you performed the intended analysis. Interpret the coefficients for the categorical variables as follows:

With the (0, 1) coding scheme, each coefficient represents the difference between each level mean and the reference level mean. The coefficient for the reference level is not displayed in the Coefficients table.
With the (−1, 0,+1) coding scheme, each coefficient represents the difference between each level mean and the overall mean.

Continuous predictor standardization

If you chose to standardize the continuous predictors in your model, Minitab provides details about the method in the Continuous predictor standardization table.

Usually, you use standardization to center variables, to scale variables, or both. When you center variables, you reduce multicollinearity caused by polynomial terms and interaction terms, which improves the precision of the coefficient estimates. In most cases, when you scale variables, Minitab converts the different scales of the variables to a common scale, which lets you compare the size of the coefficients.

Interpretation

Use the standardization method table to verify that you performed the analysis as you intended. Depending on your choice for the method, you may have to change the interpretation of the coefficients as follows:

Specify low and high levels to code as -1 and +1: This method both centers and scales the variables. Each coefficient represents the expected change in the mean of the transformed response given that the predictor changes by 1 unit on the coded scale. For example, the coefficient represents the change in the mean of the transformed response when the predictor changes from 0 to +1.
Subtract the mean, then divide by the standard deviation: This method both centers and scales the variables. Each coefficient represents the expected change in the mean of the transformed response given that the predictor variable changes by 1 standard deviation.
Subtract the mean: This method centers the variables. Each coefficient represents the expected change in the mean of the transformed response given that the predictor changes by 1.
Divide by the standard deviation: This method scales the variables. Each coefficient represents the expected change in the mean of the transformed response given that the predictor variable changes by 1 standard deviation.
Subtract a specified value, then divide by another: Whether this method centers or scales the variables depends on the values that you specify. Each coefficient represents the expected change in the mean of the transformed response given that the predictor variable changes by the divisor. For example, if you divide by 4, the coefficient represents an increase of 4 in the original measurement scale.

The exact interpretation of the coefficients also depends on other aspects of the analysis, such as the link function.

Link function

Minitab provides three link functions:

Log link function
Square root link function
Identity link function

Interpretation

Use the link function to find a model that best fits your data. Use the goodness-of-fit statistics to compare fits using different link functions. Certain link functions can be used for historical reasons or because they have a special meaning in a discipline.

Validation

When you use a test data set, the table shows the percentage of the data that are in the test data set. When you use cross-validation, the table shows the number of folds. When you specify a column that specifies which observations are in the test data set or which observations are in each fold, then the table shows the title of the column.

Interpretation

Verify the validation method that is in the results to ensure that you performed the intended analysis.