that improves on predictive accuracy by splitting the estimation/classification prob-
lems into two steps. In the first step, the two group sample consists of healthy firms
on the one hand and unsound and vulnerable companies on the other. “Vulnerable”
companies are those that are not at the point being considered “Unsound” but are bor-
derline cases. The second step was to develop another discriminant analysis model to
classify the vulnerable companies on the one hand and the unsound companies on the
other. Estimation of the model was done based on data three years prior to distress
and tested on original and control (hold-out) sample for one and three years prior.
The results of the tests of the two models are as shown in Exhibit 10.6.
(b) Neural Networks. Neural networks consist of a potentially large number of el-
ementary processing units. Every unit is interconnected with other units and each is
able to perform relatively simple calculations. The processing behavior of the net-
work is derived from the collective behavior of the units each of which is capable of
altering its responses to stimuli from the external environment as well as from the
other neurons with which it is linked. Obviously, the change of response is the learn-
ing process that the NN goes through as revisions are introduced to the weightings
that drive the response. Neural networks can range in complexity from the simple
single-layer network to multilayer networks. In general, the more complex the net-
work, the greater is the promise that it will have a genuine capacity to solve a prob-
lem, but also greater is the difficulty associated with understanding its sometimes
anomalous behavior. And, more complex networks take longer to train.
The Altman et al. (1994) experiment with neural network progressed through four
steps:
1.Attempt to replicate the scores generated by multiple discriminant analysis
using ratios different from those used in discriminant analysis. The objective in10 • 24 BUSINESS FAILURE CLASSIFICATION MODELSF1 Discriminant Model Results
Test Period Healthy Firms Unsound FirmsEstimation sample (404
companies in each group)
Estimation period T-3 90.3% 86.4%
Control period T-1 92.8 96.5
Holdout sample (150 companies
in each group) T-1 90.3 95.1
F2 Discriminant Model Results
Test Period Healthy Firms Unsound FirmsEstimation sample (404
companies in each group)
Estimation period T-3 99.0% 60.1%
Control period T-1 97.8 82.7
Holdout sample (150 companies
in each group) T-1 96.8 81.0
Exhibit 10.6. Test Results.