This paper presents a definitive description of neural network methodology and provides an evaluation of its advantages and disadvantages relative to statistical procedures. The development of this rich class of models was inspired by the neural architecture of the human brain. These models mathematically emulate the neurophysical structure and decision making of the human brain, and, from a statistical perspective, are closely related to generalized linear models. Artificial neural networks are, however, nonlinear and use a different estimation procedure (feed forward and back propagation) than is used in traditional statistical models (least squares or maximum likelihood). Additionally, neural network models do not require the same restrictive assumptions about the relationship between the independent variables and dependent variable(s). Consequently, these models have already been very successfully applied in many diverse disciplines, including biology, psychology, statistics, mathematics, business, insurance, and computer science. We propose that neural networks will prove to be a valuable tool for marketers concerned with predicting consumer choice. We will demonstrate that neural networks provide superior predictions regarding consumer decision processes. In the context of modeling consumer judgment and decision making, for example, neural network models can offer significant improvement over traditional statistical methods because of their ability to capture nonlinear relationships associated with the use of noncompensatory decision rules. Our analysis reveals that neural networks have great potential for improving model predictions in nonlinear decision contexts without sacrificing performance in linear decision contexts. This paper provides a detailed introduction to neural networks that is understandable to both the academic researcher and the practitioner. This exposition is intended to provide both the intuition and the rigorous mathematical models needed for successful applications. In particular, a step-by-step outline of how to use the models is provided along with a discussion of the strengths and weaknesses of the model. We also address the robustness of the neural network models and discuss how far wrong you might go using neural network models versus traditional statistical methods. Herein we report the results of two studies. The first is a numerical simulation comparing the ability of neural networks with discriminant analysis and logistic regression at predicting choices made by decision rules that vary in complexity. This includes simulations involving two noncompensatory decision rules and one compensatory decision rule that involves attribute thresholds. In particular, we test a variant of the satisficing rule used by Johnson et al. (Johnson, Eric J., Robert J. Meyer, Sanjoy Ghose. 1989. When choice models fail: Compensatory models in negatively correlated environments. (August) 255–270.) that sets a lower bound threshold on all attribute values and a “latitude of acceptance” model that sets both a lower threshold and an upper threshold on attribute values, mimicking an “ideal point” model (Coombs and Avrunin [Coombs, Clyde H., George S. Avrunin. 1977. Single peaked functions and the theory of preference. 216–230.]). We also test a compensatory rule that equally weights attributes and judges the acceptability of an alternative based on the sum of its attribute values. Thus, the simulations include both a linear environment, in which traditional statistical models might be deemed appropriate, as well as a nonlinear environment where statistical models might not be appropriate. The complexity of the decision rules was varied to test for any potential degradation in model performance. For these simulated data it is shown that, in general, the neural network model outperforms the commonly used statistical procedures in terms of explained variance and out-of-sample predictive accuracy. An empirical study bridging the behavioral and statistical lines of research was also conducted. Here we examine the predictive relationship between retail store image variables and consumer patronage behavior. A direct comparison between a neural network model and the more commonly encountered techniques of discriminant analysis and factor analysis followed by logistic regression is presented. Again the results reveal that the neural network model outperformed the statistical procedures in terms of explained variance and out-of-sample predictive accuracy. We conclude that neural network models offer superior predictive capabilities over traditional statistical methods in predicting consumer choice in nonlinear and linear settings.