### INTRODUCTION

### MATERIALS AND METHODS

*β*

_{0}is a constant,

*h*

*(*

_{km}*X*

_{v}_{(}

_{k,m}_{)}) is the basis function in which

*v*(

*k*,

*m*) is the index of the predictor used in the

*m*th component of the

*k*th product,

*K*

*is the parameter limiting the order of interaction.*

_{m}*N*is the number of training cases,

*y*

*is the observed value of the dependent variable, ŷ is the predicted value of the dependent variable,*

_{i}*C*(

*M*) is the penalty function for the complexity of the model containing

*M*basis functions.

*a priori*probability of case membership in one of the calving difficulty classes was estimated from the training data based on Bayes’ theorem according to the following equation:

*y*is the value of the dependent variable (two or three classes of calving difficulty),

*x*

*is the value of the*

_{j}*j*th predictor conditionally independent from the remaining ones given the class,

*n*is the number of independent predictors.

*a posteriori*probability:

*z*

_{1}

*and*

_{i}*z*

_{2}

*are the values of the classification functions for the ith case in the first and second class of calving difficulty, respectively (for the two-class system),*

_{i}*a*

_{10}and

*a*

_{20}are the intercepts of the classification functions for the first and second class, respectively,

*a*

_{1}

*and*

_{j}*a*

_{2}

*are the weights of the*

_{j}*j*th predictor for the first and second class, respectively.

*a priori*probability of class membership was estimated from the training data.

*Y*is the dependent variable (calving difficulty class),

*X*

_{1},..,

*X*

_{n}are predictors,

*a*

_{0},

*a*

_{j}are regression coefficients,

*n*is the number of predictors.

### RESULTS

### Model quality for the two-class classification system

^{2}(399.33) for MLP1 (Table 2).

^{2}(70.24) for MARS (Table 2).

### Model quality for the three-class classification system

^{2}value (1,104.91) for MARS (Table 2).

^{2}(870.53) for MLP1 (Table 2).

### The most influential predictors

### Detection performance for the two-class classification system

*a posteriori*probability of true positives (P[PSTP]) (0.8158) for NBC and the greatest

*a posteriori*probability of true negatives (P[PSTN]) (0.9162) for MLP1; however, no significant differences in the values of the former occurred. The receiver operating characteristic (ROC) curve analysis revealed that all classifiers had very similar areas under the curve (AUC) (0.86 to 0.87) (Figure 1).

### Detection performance for the three-class classification system

### DISCUSSION

### Model quality

^{2}were also used for all the models. Their lower values indicated a better model.

^{2}value for the two-class system indicating a good fit to the training data, although its AIC and BIC were higher than those for LR due to the greater complexity of the neural model. We observed the lowest values of these criteria in the three-class system for NBC, which indicated its superior quality in comparison with other models, although the smallest G

^{2}was characteristic of MARS.

^{2}value indicating its good fit to the data, however, GDA had the lowest values of AIC and BIC due to its lower complexity compared with the MLP1 model. In the two-class classification system, we recorded the lowest values of AIC and BIC for MLP1 and the smallest G

^{2}for MARS, which shows that MLP1 was quite effective in predicting dystocia despite its relatively high complexity.