Select the options for Ordinal Logistic Regression

Minitab provides three link functions, which let you fit a broad variety of ordinal response models. A link function is the inverse of a distribution function. You want to choose a link function that results in a good fit to your data. Examine the goodness-of-fit statistics in the output to compare how well the model fits your data using different link functions. You can also choose link functions for historical reasons or because they have a special meaning in your discipline. For more information, go to What is a link function?.

• Logit: By default, Minitab uses the logit link function because it provides the most natural interpretation of the estimated coefficients and it provides estimates of the odds ratios.
• Normit/Probit: Use the normit link function, which assumes that there is an underlying variable that follows a normal distribution that is classified into categories. For example, you assume that pesticide resistance is an unmeasurable characteristic of an insect that follows a normal distribution. However, instead of recording pesticide resistance, you classify insects into ordinal categories of how long they survived after exposure to the pesticide.
• Gompit/Complementary log-log: Use the gompit function, which is the inverse of the Gompertz distribution function. If the logit or normit functions do not fit the data, the gompit function can sometimes provide an adequate fit because the gompit function is asymmetric.

You can change the reference event for the response and the reference level for any factor. Changing the reference event or level does not affect the overall significance, but it can make the results more meaningful. For more information, go to Interpreting estimated coefficients in ordinal logistic regression.

Order of the response values

Enter the order of the response values from lowest to highest if you want to change reference event. (Text and date/time levels must be enclosed in quotation marks.) By default, Minitab sets the following reference events based on the data type:

• For numeric variables, the reference event is the largest numeric value.
• For date/time variables, the reference event is the most recent date/time.
• For text variables, the reference event is the last in alphabetical order.

Reference level (enter categorical predictor followed by level)

Enter the categorical predictor followed by the reference level if you want to change the default level. (Text and date/time levels must be enclosed in quotation marks.) By default, Minitab sets the following reference levels based on the data type:

• For numeric predictors, the reference level is the smallest numeric value.
• For date/time predictors, the reference level is the earliest date/time.
• For text factors, the reference level is first in alphabetical order.

You can enter values for estimated coefficients for several scenarios. For example, you may want to provide starting estimates so that the algorithm converges to a solution, or you may want to validate a model with an independent sample. For more information, go to Entering initial values for estimated coefficients.

Starting estimates for algorithm

Enter the column containing the initial values for model parameters. Specify initial values for model parameters or parameter estimates for a validation model.

Estimates for validation model

Enter the column containing the estimated model parameters. Minitab will then fit the validation model.