The major assumptions of frustration theory (Amsel, 1958) were incorporated in the model. This resulted in a mathematical model (DMOD) that can account for not only trial-by-trial changes and asymptotic values in over 30 simple appetitive learning situations but also the preference for predictable rewards (observing response). The equation used to calculate changes in associative strength is the Rescorla-Wagner modification of the Bush and Mostellef (1955) linear operator: AV = aft (X -V). AV is the change in associative strength on a given trial; a is the salience of the stimulus; ft is a learning rate parameter; X is the size of the reward; V-is the total associative strength conditioned to all-stimuli present. When the reward is larger than expected (X is larger than V), an approach strength is conditioned (V AP ). Based on the two major assumptions of frustration theory, it is assumed that two additional V values can be conditioned. Smaller than expected rewards condition an avoidance strength (V AV , when X is smaller than V AP ), and positive goal events,in the presence of VA V condition courage (Vcc, countereonditioning). Behavior is determinedly the total V value that is assumed to be equal to the summation of the three V values (Vr = VAP + VAV + V cc ). Computer simulations have aided in accurately analyzing the model's predictions in appetitive learning situations.In the first part of the paper, the background, formulation, and assumptions of DMOD are summarized. DMOD'S analyses".-of simple learning situations are reviewed next (i.e., continuous reinforcement [GRF] acquisition, overshadowing, blocking, partial and varied reinforcement acquisition, simple discrimination learning, configural learning and negative patterning, the negative contrast effect, partial reinforcement extinction, elation and reacquisition effects, escape properties of aversive nonreward, effects of alcohol and amobarbital sodium in simple learning situations, overlearning extinction and reversal effects, the small trials partial reinforcement extinction effect; the initial nonreward extinction effect, delay of reinforcement, secondary reinforcement). Predictions in more complex choice situations are then reported, including the preference for predictable reward (the^ observing response) and the variables shown to influence the size of the preference (reward magnitude, drive level, proportion of reinforced trials). DMOD'S counterintuitive predictions for observing-response studies with supporting data are also presented. DMOD'S analysis of observing-response acquisition shows that predictable nonreward is less aversive than unpredictable nonreward. Because much empirical support for this analysis is available, the implication is clear: Transform unpredictable situations into predictable ones to reduce the aversiveness of situations in which nonreward or failure is unavoidable. We hope that by providing access to the computer program of the model, researchers in the area of learning and people working in applied fields will use com...

The computer simulation/mathematical model called DMOD, which can simulate over 35 different phenomena in appetitive discrete-trial and simple free-operant situations, has been extended to include aversive di~rete-trial situations. Learning (V) is calculated using a three-parameter equation .1V = a{j(A -V) (see Daly & Daly, 1982;Rescorla & Wagner, 1972). The equation is applied to three possible goal events in the appetitive (e.g., food)case and to three in the aversive (e.g., shock) case. The original goal event can be present, absent, or reintroduced; in the appetitive situation, these events condition approach (Vap), avoidance (Vav), and courage (Vee), respectively. In the aversive situation, the events condition avoidance (Vav*), approach (Vap*), and cowardice (Vcc*), respectively. The model was developed in simple learning situations and subsequently was applied to complex situations. It can account for such diverse phenomena as contrast effects after reward shifts, greater persistence following partial than following continuous reinforcement, and a preference for predictable appetitive and predictable aversive events. Application of the aversive version of the model to "reward" shifts is described.Our goal is to develop a computer simulation/mathematical model of learning that is as simple as possible with as much breadth as possible. The model, called DMOD (Daly MODification of the Rescorla-Wagner Model), is simple because learning is calculated with one simple equation using three parameters. It is applied to diverse situations by assuming that there are a number of different goal events possible, each of which conditions either approach or avoidance of the goal. It was originally developed to account for appetitive, discrete-trial experiments, and can currently account for behavior in over 30 different paradigms (see Daly & Daly, 1982). DMOD was then extended to simulate the effect of simple schedules of reinforcement in free-operant experiments (Daly & Daly, 1984b). Our purpose is to outline the extension of DMOD to the aversive case and to show its application in a complicated experimental situation. To understand the rationale behind the extension, however, it is neces- sary to review development of the model in the appetitive case and the rules we follow for development of DMOD. SELECTION OF PHENOMENA TO BE SIMULATEDWe believe that the initial goal of a new model is to be able to account for well-established and replicable phenomena. We feel that it is dangerous to develop a model around recently discovered phenomena, because the boundary conditions under which they can be obtained and the variables influencing them are unknown. The purpose of a theory, however, is not only to integrate existing replicable data, but also to correctly predict new results. The primary phenomenon we use to test predictions of the appetitive version of DMOD is acquisition of a preference for predictable reward. The model made some interesting predictions concerning when a preference for the unpredictable reward situati...

A new mathematical model of the role of reward and aversive nonreward in appetitive learning situations can successfully account for over 30 appetitive learning phenomena (see Daly & Daly, 1982). Due to the interest shown in the computer program used to simulate predictions of the model (called DMOD), we include here: (1) a copy of the program written in MICROSOFT BASIC (modifiable for similar BASIC languages used on machines such as the Apple II and TR8-80); (2) a description of the model; (3) instructions on how to conduct simulations; and (4) three simulation examples. The same program may be used to simulate predictions of the Rescorla and Wagner (1972) model in both primary and secondary reinforcement experiments.A recently developed mathematical model of appetitive learning called DMOD can account for over 30 basic learning phenomena (Daly & Daly, 1982). It can simulate such basic phenomena as acquisition on a continuous or partial reinforcement schedule, blocking, and discrimination learning, as well as several paradoxical reward effects, such as the partial reinforcement acquisition and extinction effects, depression and elation effects, overlearning extinction and reversal effects, and complex phenomena such as secondary or conditioned reinforcement and acquisition of a preference for predictable over unpredictable rewards ("observing response").Due to the interest shown in the computer program and the number of requests for help in using it, we include in this paper a brief description of the model, a manual on how to conduct simulations, and a listing of the computer program, written in MICROSOFT BASIC. The program is written to be transported with minor modifications to machines using similar BASIC languages, such as those used on the Apple II and TRS-80 Model III microcomputers. DESCRIPTION OF DMODDMOD was developed to account for both trial-bytrial changes and asymptotic levelsofbehavior in discretetrial, appetitive learning situations. It is assumed that there are three important goal events possible that organisms learn about in appetitive learning situations. If a positive reward, such as food for a hungry organism, is present, the organism learns to approach the goal. If the organism has learned to expect food and no food is present, the organism learns to avoid the goal because nonreward in the presence of an expectancy for reward is considered an aversive goal event (see Amsel, 1958, and Daly, 1974, on frustration theory). If a food reward occurs after the organism has learned to expect aversive nonreward, the organism learns to approach the goal despite the expectation of the aversive event (see Amsel, 1958, on counterconditioning).The Rescorla-Wagner (1972) modification of the linear operator equation (Bush & Mosteller, 1955) is used to calculate the approach (VAP), avoidance (VAv). and counterconditioning (VCe) gradients: /).V = a (3(X -V). The symbols represent the following: V-strength of the gradient due to prior learning; V-sum of the gradient strengths of all stimuli present [...

Unfortunately our world does not always reward us when we expect it, and we must learn to deal with nonreward. How do these experiences influence our behaviors and how can we use them to help us? In Frustration Theory: An Analysis ofDispositional Learning and Memory (1992), Abram Arosel has answered these questions; he has summarized over 40 years of exciting research and the development of an elegant theory. He has also reviewed recent applications of frustration theory in such areas as fetal alcohol syndrome and attention deficit-hyperactivity disorders. In this invited commentary, we briefly summarize a mathematical model of frustration theory (called DMOD) and review simulations of the model that highlight the importance of the assumptions based on frustration theory (e.g., aversiveness of unexpected nonreward, counterconditioning). We also review assumptions (e.g., unlearning, passive and active "inhibition," decline in aversiveness of expected nonreward) that are required if one is to simulate intuitive and counterintuitive phenomena. 311Unfortunately, we are not always rewarded. How we learn to deal with aversive nonreward has a major impact on our success and happiness. The field of psychology has been very fortunate to include the work of Abram Amsel, who has provided us with a large database that shows the importance of nonreward. He has also developed a comprehensive theory that integrates the research results and gives us the power to make predictions. His book Frustration Theory: An Analysis of Dispositional Learning and Memory (1992), which we have been asked to comment on, is a beautiful summary of over 40 years of research and theory development. The book begins with a summary of behavioral consequences of nonreward in adult and immature rats and then reviews the effects of brain lesions and in utero exposure to alcohol. The book ends with applications offrustration theory to children with attention deficit-hyperactivity disorders.In this commentary, we briefly review a mathematical model offrustration theory (called DMOD) and describe results of simulations that highlight the importance of nonreward as well as the importance of reintroduction of rewards.