Nominal logistic regression estimates the probability of choosing one of the response levels as a smooth function of the x factor. The fitted probabilities must be between 0 and 1, and must sum to 1 across the response levels for a given factor value.

In a logistic probability plot, the y-axis represents probability. For k response levels, k - 1 smooth curves partition the total probability (which equals 1) among the response levels. The fitting principle for a logistic regression minimizes the sum of the negative natural logarithms of the probabilities fitted to the response events that occur (that is, maximum likelihood).