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This study uses two artificial neural networks (ANNs), categorical learning/instar ANNs and probabilistic (PNN) ANNs, suitable for classification and prediction type issues, and compares them to traditional multivariate discriminant analysis (MDA) and logit to examine financial distress one to three years prior to failure. The results indicate that traditional MDA and logit perform best with the lowest overall error rates. However, when the relative error costs are considered, the ANNs perform better than traditional logit or MDA. Also, as the time period moves farther away from the eventual failure date, ANNs perform more accurately and with lower relative error costs than logit or MDA. This supports the conclusion that for auditors and other evaluators interested in early warning techniques, categorical learning network and probabilistic ANNs would be useful.  1997 John Wiley & Sons, Ltd. Intell. Sys. Acc. Fin. Mgmt. 6: 235–248, 1997. No. of Figures: 0. No. of Tables: 5. No. of References: 45. INTRODUCTION and evaluate financial distress models using two popular standard statistical techniques, logit and Multiple Discriminant Analysis The increase in bank failures since the 1980s has renewed the interest of researchers in the (MDA) (Sinkey, 1975; Altman et al., 1977; Ohlson, 1980; Jones, 1987; Gilbert et al., 1990). Howsafety of the banking system and in bank financial distress models (Hooks, 1992). Prior ever, the use of both logit and MDA requires the data and models to comply with certain studies indicate that researchers generally test assumptions, e.g. distribution assumptions, noncollinearity assumptions. When data or *Correspondence to: Ram Sriram, Georgia State Unimodel deviate from these assumptions, both versity, College of Business Administration, Atlanta, GA 30302-4050, USA. logit and MDA provide suboptimal solutions CCC 1055-615X/97/030235-14$17.50 Received January 1996  1997 John Wiley & Sons, Ltd. Revised June 1996 INTELLIGENT SYSTEMS IN ACCOUNTING, FINANCE AND MANAGEMENT VOL. 6: 235–248 (1997) (Altman et al., 1977; Pinches and Trieschmann, alternative ANNs, categorical learning neural networks and probabilistic neural networks 1977; Ohlson, 1980; Hamer, 1983). Unlike logit and MDA, Artificial Neural Networks (ANNs), (suitable for classification and prediction-type problems). After making a few modifications a type of artificial intelligence, are less stringent about data assumptions, a priori model specifito the categorical learning neural network, the study compares the performances of the ANNs cation or knowledge about probability distributions. For these reasons, researchers find to the benchmark performances of traditional MDA and logit models. The primary objective ANNs to be a useful alternative to traditional logit or MDA to evaluate financial distress is test whether these ANNs are capable of increased classification and prediction accuracy models (Bell et al., 1990; Hansen and Messier, 1991; Chung and Tam, 1992; Liang et al., 1992; and whether they are better as early warning tools for predicting bankruptcies than traTam and Kiang, 1992; Salchenberger, 1993; Coats and Fant, 1993; Fanning and Cogger, ditional statistical techniques. 1994; Brockett et al., 1994; Boritz et al., 1995; Boritz and Kennedy, 1995; Etheridge and Sriram, 1996). ARTIFICIAL NEURAL NETWORKS The commercial software market offers several ANN models such as backpropagation, The commercial ANN software package used in this study is NeuralWorks Professional II/Plus. Boltzman machine, categorical learning, probabilistic learning, and Bayesian probabilistic netThe software has 27 built-in ANN models and allows modifications to the models by the user. works, useful for financial distress evaluation or for other classification and prediction probBecause the purpose is classification and prediction, this study focused only on those ANN lems. These commercial ANN models differ in their algorithms and training approaches. For models that are suitable for classification and prediction issues. After testing various models business researchers who examined classification and prediction type problems, backproand after making several modifications to the various ANN models, the study finally identpagation ANNs have been the frequent choice (Barniv and Raveh, 1989; Frydman, et al., 1985; ified two ANN models, categorical learning networks and probabilistic neural networks, as the Braun and Chandler, 1987; Parker and Abramowics, 1989; Raghupathi et al., 1991, Boritz et most suitable. The study observed categorical learning network to improve in performance al., 1995). However, because of certain characteristics in their algorithm and training, backthe most when its output processing elements were modified with the instar learning laws. propagation ANNs are not always suitable for every type of classification and prediction probThese two ANN models are discussed further. lem (Klimasauskas, 1994; Jang and Lai, 1994). For example, backpropagation ANNs use errorCategorical Learning Neural Networks correction rules to adjust the connection weights and their training is done in two Categorical learning networks typically include an input, a middle and an output layer. The stages: a forward pass for error estimation and a backward pass for modifying the weights heart of this network is a Kohonen (middle) layer. This Kohonen layer is self-organizing and (Kryzanowski and Galler, 1993). Generally, the researcher can set the learning rate. These traincan be used in classification tasks. The layer uses the concept of competition among the proing and error-correction approaches sometimes trap a backpropagation ANN in a local minicessing elements. That is, only the processing element with the weight vector closest to the mum of the error function. This was probably the reasons why some of the previous financial input vector generates an output signal; all other processing elements generate a zero. distress studies reported mixed classification and prediction accuracy rates for backpropagFurther, the processing element that generates the output signal and its immediate neighbors ation ANNs (Coats and Fant, 1993; Klersey and Dugan, 1995). Therefore, this study chooses two in the network learn by adjusting their weights Intell. Sys. Acc. Fin. Mgmt. 6: 235–248, 1997  1997 John Wiley & Sons, Ltd. 236 H.L. ETHERIDGE AND R.S. SRIRAM (Caudill, 1988). The competition among the proInstar Learning cessing elements is moderated by intra-layer In the 1950s and 1960s, Steven Grossberg (1982) connections. That is, each processing element applied Pavlov’s concepts of unconditioned outputs its activation and thus acts as an inhibiresponses and conditioned responses to neural tory input to all other processing elements, networks. He also used Hebb’s Law (Hebb, except its closest neighbors (Caudill, 1988). The 1949), a learning concept developed by the diseffect of a processing element’s activation tinguished psychologist Donald Hebb. Accorddecreases as it moves farther away from the ing to Hebb’s Law: processing element. The Kohonen layer distinguishes among If a neuron, A is repeatedly stimulated by classes in the following manner. During trainanother neuron, B, at times when neuron A ing, the processing element whose vector of is active (for whatever reason), then neuron weights is closest to the training vector A will become more sensitive to stimuli from (feedback) is declared the winner. If the winneuron B; the synaptic connection from B to ning processing element is in the same class as A will be more efficient. Thus, B will find it the feedback, its vector is moved toward the easier to stimulate A to produce an output training vector. If the winning processing in the future (Caudill, November 1988). element is not in the same class as the feedback, its vector is moved away from the training Grossberg used both Pavlov’s and Hebb’s convector. Consequently, during training the veccepts to develop the instar and outstar learning tors of the processing elements assigned to a approaches. Grossberg describes an instar as a specific class converge to a region associated processing element at the center of many with that class. As the training process proinwardly directed input signals and describes ceeds, the ‘neighborhood’ surrounding the winan outstar as a processing element at the center ning processing element takes the form of a of a large number of outwardly directed conslowly diminishing circle. The number of neighnections. According to this definition, a probors allowed to adjust their weights decreases cessing element in a network can be an instar to the point where only the winning processing as well as an outstar. element is allowed to adjust its weight (Caudill, Instar learning approach takes place when August 1988). In the next step, the training processing elements (instars) repond to external process continues as a new input set is stimuli and become more active when such presented. At this step, a new winning prostimuli are present and less active when the cessing element is chosen and the process constimuli are absent. Processing elements respond tinues as described. After completing training, quickly to the stimuli (learn) and lose the when an input vector is presented to the netresponse (forget) rapidly when the stimuli are work, the system calculates the distance of the removed. If an active instar is stimulated by input vector from the vectors of all processing another processing element, then the synapse elements. The processing element, whose vector associated with that particular processing is closest to the input vector, is declared the element learns. Instar learning approach also has a forgetting constant that determines the winner and the input vector is placed in the rate of decay of its input synapses. same class as the winning processing element. The categorical learning neural network supplied with the commercial software, by de

A comparison of the relative costs of financial distress models: artificial neural networks, logit and multivariate discriminant analysis