# Interpreting the estimated coefficients in nominal logistic regression

The interpretation of the estimated coefficients depends upon the designated reference event for the response and the reference level for each predictor. The estimated coefficient associated with a predictor represents the change in the particular logit for each unit change in the predictor, assuming that all other predictors are held constant. A one unit change in a factor refers to a comparison of a factor level to the reference factor level.

If there are k distinct response values, Minitab estimates k-1 sets of estimated coefficients. These are the estimated differences in log odds or logits of levels of the response variable relative to the reference event. Each set contains a constant and coefficients for the factors and the covariates. Note that these sets of parameter estimates give nonparallel lines for the response value. The interpretation of the parameter estimates is as follows:
• The coefficient of a predictor (factor or covariate) is the estimated change in the log of P(response level)/ P(reference event) for each unit change in the predictor, assuming the other predictors remain constant.
• The 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(response level)/P(reference event) for a certain factor level compared to the reference level. The odds ratios at different values of the covariate can be constructed relative to zero. In the covariate case, it may be more meaningful to interpret the odds and not the odds ratio. 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 parameter estimates, you can change the reference event or reference levels in the Options subdialog box.

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