# Interpreting estimated coefficients in ordinal logistic regression

The interpretation of the estimated coefficients depends on: the link function, reference event for the response, and reference levels for the predictor. The estimated coefficient associated with a predictor (factor or covariate) represents the change in the link function for each unit change in the predictor, assuming all other predictors are held constant. A unit change in a factor refers to a comparison of a factor level to the reference factor level.

The logit link provides the most natural interpretation of the estimated coefficients and is therefore the default link in Minitab. A summary of the interpretation follows:
• The odds of an event are the ratio of P(event) to P(not event). The estimated coefficient of a predictor (factor or covariate) is the estimated change in the log of P(event)/P(not event) for each unit change in the predictor, assuming the other predictors remain constant.
• The estimated coefficient can also be used to calculate the odds ratio, or the ratio between two odds. Exponentiating the estimated coefficient of a factor yields the ratio of P(event)/P(not event) for a certain factor level compared to the reference factor level. The odds ratios at different values of the covariate represent a 1-unit change in the covariate. Note that a coefficient of zero or an odds ratio of one both imply the same thing-the factor or covariate has no effect.

To change how you view the estimated coefficients, you can change the event or reference levels in the Options subdialog box. For example, if your response was coded Low, Medium, and High, the default reference event would be Medium because it is last in alphabetical order. In most cases, using High as the reference event would make the results more meaningful.