Content deleted Content added
→As a set of independent binary regressions: Reduced pointless verbosity Tags: Mobile edit Mobile web edit |
|||
Line 219:
It is also possible to formulate multinomial logistic regression as a latent variable model, following the [[Logistic regression#As a two-way latent-variable model|two-way latent variable model]] described for binary logistic regression. This formulation is common in the theory of [[discrete choice]] models, and makes it easier to compare multinomial logistic regression to the related [[multinomial probit]] model, as well as to extend it to more complex models.
Imagine that, for each data point ''i'' and possible outcome ''k=1,2,...,K'', there is a continuous [[latent variable]] ''Y''<sub>''i,k''</sub><sup>''*''</sup> (i.e. an unobserved [[random variable]]) that is distributed as follows:
: <math>
| |||