Multinomial logistic regression: Difference between revisions

Content deleted Content added
m Linear predictor: imply that x₀ = 1 by definition.
m As a set of independent binary regressions: Clarify that k = 0 is not included.
Line 63:
 
: <math>
\ln \frac{\Pr(Y_i=k)}{\Pr(Y_i=K)} \,=\, \boldsymbol\beta_k \cdot \mathbf{X}_i, \;\;\;\;,\;\;1\leq k < K
</math>.
 
Line 71:
 
: <math>
\Pr(Y_i=k) \,=\, {\Pr(Y_i=K)}\;e^{\boldsymbol\beta_k \cdot \mathbf{X}_i}, \;\;\;\;,\;\;1\leq k < K
</math>
 
Line 86:
 
:<math>
\Pr(Y_i=k) = \frac{e^{\boldsymbol\beta_k \cdot \mathbf{X}_i}}{1 + \sum_{j=1}^{K-1} e^{\boldsymbol\beta_j \cdot \mathbf{X}_i}}, \;\;\;\;,\;\;1\leq k < K
</math>.