Estimation of the hypothesis hierarchy in probabilistic inference tasks*

Is there a hierarchical order among the hypotheses about functional rules in probabilistic inference tasks, i.e. what is the construction and the procedure of the “hypothesis sampling mechanism” employed by the subjects in this kind of task? According to the hypothesis sampling model initially proposed by Brehmer (1974) there should be a hierarchical order among the hypotheses in the subject's hypothesis pools. The procedures of hypothesis sampling and testing ought to follow this strict data independent order (see e.g. Sniezek, 1986; Brehmer, 1987). Knez (1991a, b) showed, however, that this assumption may be incorrect. As a follow up to these results the question regarding the construction of the subject's hypothesis pools was reapproached in the present study. The results indicated a consistency with the hierarchical assumption (Brehmer, 1974) only regarding the relation between the linear and nonlinear rules but not within these types of rules.     

Human choice in "counterintuitive" situations: fixed- versus progressive-ratio schedules.

College undergraduates were given repeated opportunities to choose between a fixed-ratio and a progressive-ratio schedule of reinforcement. Completions of a progressive-ratio schedule produced points (exchangeable for money) and incremented that response requirement by 20 responses with each consecutive choice. In the reset condition, completion of a fixed ratio produced the same number of points and also reset the progressive ratio back to its initial value. In the no-reset condition, the progressive ratio continued to increase by increments of 20 throughout the session with each successive selection of this schedule, irrespective of fixed-ratio choices. Subjects' schedule choices were sensitive to parametric manipulations of the size of the fixed-ratio schedule and were consistent with predictions made on the basis of minimizing the number of responses emitted per point earned, which is a principle of most optimality theories. Also, the present results suggest that if data from human performances are to be compared with results for other species, humans should be exposed to schedules of reinforcement for long periods of time, as is commonly done with nonhuman subjects.     

Choice between fixed-interval schedules: Graded versus step-like choice functions

Pigeons chose between two fixed-interval schedules of food reinforcement. A single peck on one of two lighted keys started the fixed-interval schedule correlated with that key. The schedule had to be completed before the next choice opportunity. The durations of the fixed intervals were varied over conditions from 15 s to 40 s. To maximize the rate of reinforcement, the pigeons had to choose exclusively the shorter of the two schedules. Nevertheless, choice was not all-or-none. Instead, relative choice, and the rates of producing the fixed intervals, varied in a graded fashion with the disparity between the two schedules. Choice ratios under this procedure (single response to choose) were highly sensitive to the ratios of the fixed-interval schedules.     

Choice and behavioral patterning

Ten pigeons pecked left and right keys in a discrete-trials experiment in which access to food was contingent upon changeovers to the right key after particular runs of left-key pecks. In each of three sets of conditions, two run lengths were reinforced according to a concurrent variable-interval schedule: reinforcement followed runs of either 1 or 2, 1 or 4, or 2 or 4 left-key pecks preceding changeovers. The intertrial interval separating successive pecks was varied from .5 to 10.0 sec, and the relative frequency of reinforcement for the shorter of the two reinforced runs was varied from 0 to .75. The contingencies established local behavioral patterning that roughly approximated that required for reinforcement. For a fixed pair of reinforced run lengths, preference for the shorter of the two frequently increased as the intertrial interval increased and therefore as the minimum temporal durations of both reinforced runs increased. Preference for the shorter of the two also increased as its corresponding relative frequency of reinforcement increased. Both of these effects on preference were qualitatively similar to corresponding effects in previous research with two different kinds of reinforced behavioral patterns, interresponse times and interchangeover times. In all these experiments, analytical units were found in the temporal patterns of behavior, not in the behavior immediately contiguous with a reinforcer. It is suggested that a particular local temporal pattern of behavior is established to the extent to which it is repeatedly remembered when reinforcers are delivered, regardless of whether the delivery of a reinforcer is explicitly contingent upon that pattern.     

Independence of response force and reinforcement rate on concurrent variable-interval schedule performance

Five pigeons were trained over 43 experimental conditions on a variety of concurrent variable-interval schedules on which the forces required on the response keys were varied. The results were well described by the generalized matching law with log reinforcement ratios and log force ratios exerting independent (noninteractive) effects on preference. A further analysis using the Akaike criterion, an information-theoretic measure of the efficiency of a model, showed that overall reinforcement rate and overall force requirement did not affect preference. Unlike reinforcement rate changes, force requirement increases did not change the response rate on the alternate key, and an extension of Herrnstein's absolute response rate function for force variation on a single variable-interval schedule is suggested.     

Memory for two stimulus-response items in pigeons

Six pigeons served in a discrete-trial experiment on short-term memory. Combinations of three key positions and two ordinal positions, yielding six possible sequences of stimulus-response pairs, were used as lists of items. A retention interval separated list presentation from the test phase in which two (for Group 1) or three (for Group 2) keys were illuminated with either red or green light. A reinforcer was delivered if a subject pecked the key of the first item on a red trial and the key of the second item on a green trial. When the retention interval was lengthened from one to five or nine seconds, a systematic loss of stimulus control resulted. Lengthening the interval between items from one to eight seconds had a much smaller effect for the birds in Group 1, whereas a systematic loss of stimulus control was found in red trials for the birds in Group 2. The functional relations between choice accuracy and delay provided an empirical basis for analysis of what relations among temporal events can become discriminative stimuli.     

Choice and the relative immediacy of reinforcement

The relative immediacy of reinforcement in concurrent-chain schedules was varied while the relative reduction in the overall average time to reinforcement associated with terminal-link entry was held constant. For each of four pigeons, choice did not vary with relative immediacy of reinforcement. Subsequently, choice by the same subjects was shown to be sensitive to relative reduction in average time to reinforcement.     

Parameterizing inequality constraints on unique variances in linear structural models

Current computer programs for analyzing linear structural models will apparently handle only two types of constraints: fixed parameters, and equality of parameters. An important constraint not handled is inequality; this is particularly crucial for preventing negative variance estimates. In this paper, a method is described for imposing several kinds of inequality constraints in models, without the necessity for having computer programs which explicitly allow such constraints. The examples discussed include the prevention of Heywood cases, extension to inequalities of parameters to be greater than a specified value, and imposing ordered inequalities. Work on this project was aided by the City University of New York—Professional Staff Congress Research Award Program Grant Number 13631.     

Eating and drinking: An economic analysis

Food-deprived rats were exposed to various schedules of food delivery; water-deprived rats were exposed to various schedules of water delivery. Eating and drinking were measured over sessions and at points throughout sessions. The symmetries and asymmetries of food and water consumption were explored in terms of: (1) substitutability of food versus water, and of food and water on the one hand versus leisure on the other, (2) constraints imposed by various schedules of food and water, and (3) the tendency of rats to maximize utility within the imposed constraints.     

Signal detection and matching: analyzing choice on concurrent variable-interval schedules.

Pigeons' pecks on a red key and a green key were followed by access to grain according to pairs of concurrent independent variable-interval schedules in a combined signal detection/matching law paradigm. Pecks on the red key were reinforced by the richer variable-interval schedule if a short-duration tone had been presented; pecks on the green key were reinforced by the richer variable-interval schedule if a long-duration tone had been presented. Pecks on the green key given a short-duration tone, or on the red key given a long-duration tone, were reinforced by the leaner variable-interval schedule. The data were analyzed according to both signal detection's and the matching law's separate measures of, first, the discrimination of the choices and, second, the bias to make one response or another. Increasing the difficulty of the tone-duration discrimination decreased both methods' measures of the discrimination of the choices and did not change both methods' measures of the bias to make one response or another. Changing the leaner variable-interval schedule so that it approached the richer variable-interval schedule decreased signal detection's measure of discrimination but left its measure of response bias and the matching law measures unchanged. Data collected only until a subject's first changeover response following presentation of a long or a short tone showed higher values for both methods' measures of discrimination, no change in signal detection's measure of response bias, and lower values for the matching law's measure of response bias. Relationships between the matching law's and signal detection's methods of analyzing choice are discussed. It is concluded that a signal detection analysis is more efficient for examining changes in the difficulty of a discrimination, whereas a matching law analysis is more effective for examining the effects of changes in relative reinforcer frequency.