Methods for Ordinal Logistic Regression

Find definitions and interpretation guidance for the Method table.

In This Topic

Link function
Response information
Factor information

Link function

A link function maps the interval (0, 1) onto the whole real line. This guarantees that the predicted probability of an event using the model produces a number between 0 and 1. Minitab provides three link functions:

Logit
Normit (probit)
Gompit (complementary log-log)

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.

One advantage of the logit link function is that it provides an estimate of the odds ratio for each predictor in the model.

Response information

Minitab displays this information about the response:

Variable: Name of the response variable
Value: Levels of the response variable
Count: Number of observations at each level of the response variable
Total: Number of nonmissing observations

Interpretation

Use the response information to examine how much data are in the analysis. Larger random samples with many occurrences of each level usually provide more accurate inferences about the population.

Factor information

The factor information table displays the factors in the design, the numbers of levels, and the values of the levels. Factors can assume only a limited number of possible values, known as factor levels. Factor levels can be text or numeric. Numeric factors use a few controlled values in the experiment, even though many values are possible.

Interpretation

Use the factor information table to see the number of levels in the analysis. For example, a quality analyst plans to study factors that could affect plastic strength during the manufacturing process. The analyst includes Additive. Additive is a categorical variable which can be type A or type B.

Factor Information

Factor	Levels	Values
Additive	2	A, B

Factors can be crossed or nested. Two factors are crossed when each level of one factor occurs in combination with each level of the other factor. Two factors are nested when a set of the levels for one factor appear at only one level of a second factor. For example, if a design contains machine and operator, these factors are crossed if all operators use all machines. However, operator is nested in machine if each machine has a different set of operators.

In the factor information table, parentheses indicate nested factors. For example, Standard(Appraiser) indicates that Standard is nested within Appraiser. In this context, the nesting indicates that each appraiser has their own set of standard parts. The factor levels of a nested factor are repeated for each level of nesting, which increases the number of levels for the nested factor. In this example, each appraiser has 5 standards, but because standard is nested in appraiser, standard has 20 different levels.

Factor Information

Factor	Levels	Values
Standard(Appraiser)	20	1(Amanda), 2(Amanda), 3(Amanda), 4(Amanda), 5(Amanda), 1(Britt), 2(Britt), 3(Britt), 4(Britt), 5(Britt), 1(Eric), 2(Eric), 3(Eric), 4(Eric), 5(Eric), 1(Mike), 2(Mike), 3(Mike), 4(Mike), 5(Mike)
Appraiser	4	Amanda, Britt, Eric, Mike

For more information on factors, go to Factors and factor levels, What are factors, crossed factors, and nested factors?, and What is the difference between fixed and random factors?.