A nonlinear multiple logistic model and multiple regression analysis are described as a method for determining the weights for two-layer networks and are compared to error backpropagation. We also provide a method for constructing a three-layer network whose semilinear middle units are primarily provided to discriminate two categories. Experimental results on speaker-independent vowel recognition show that both multivariate methods provide stable weights with fewer iterations than backpropagation training started with random initial weights, but with slightly inferior performance. Backpropagation training with initial weights determined by a multiple logistic model after introduction of data distribution information gives a recognition rate of 98.2%, which is significantly better than average backpropagation with random initial weights.