An individual difference model for the multidimensional analysis of preference data

A model for the analysis of paired comparison data is presented which combines features of the BTL-model with features of the Unfolding model. The model is metric, mathematically tractable, and has an exact algebraic solution. Since it is multidimensional and allows for individual differences, it is thought to be more realistic for some choice situations than either the Thurstone model or the BTL-model. No claim is made that the present model will be appropriate for all conceivable choice situations. Rather, it is argued that the fact that it is explicitly falsifiable is a point in its favor.This work was supported by a grant of the United States Public Health Service (1 R03 MH19139 01 MSM) and a David Ross (XR) grant of the Purdue Research Foundation (PRF 2132), both of which are gratefully acknowledged. We also owe thanks to Dr. Terry Cooper, whose careful scrutiny of an earlier draft of this paper allowed us to reduce the number of errors from n to n-1.     

Some new results on factor indeterminacy

Some relations between maximum likelihood factor analysis and factor indeterminacy are discussed. Bounds are derived for the minimum average correlation between equivalent sets of correlated factors which depend on the latent roots of the factor intercorrelation matrix . Empirical examples are presented to illustrate some of the theory and indicate the extent to which it can be expected to be relevant in practice.     

Some differences among figural aftereffects,apparent motion,and paracontrast*

It has been suggested that figural aftereffects, apparent motion, and paracontrast may be produced by very similar or equivalent processes. The empirical functions relating figural aftereffect to the duration of the inspection figure and the interfigural distance are significantly different from the corresponding apparent motion and paracontrast functions. The functions relating paracontrast to the interstimulus interval are significantly different from the corresponding figural-aftereffect and apparent-motion functions. Thus, it is unlikely that the processes underlying the three phenomena are the same. Researchers who attempt to study feature analyzers in the human visual system should consider using more than one dependent variable, since none of the three phenomena contains all of the available information. Within-Ss designs should be avoided because a strong response bias exists between figural-aftereffect and apparent-motion tasks.     

Some effects of interreinforcement time upon choice

Pigeons' responses were reinforced on two identical and concurrently available chain variable-interval-schedules. Unlike the typical concurrent chains procedure, both links were operative throughout, thus producing three types of concurrency: (1) concurrent initial links; (2) concurrent initial and terminal links; (3) concurrent terminal links. Choice proportions in each of these three states suggested that the pigeons were sensitive to momentary likelihoods of reinforcement: choice proportions for a schedule were higher when the schedule had been operative for some time, resulting in a higher probability of reinforcement. The study also showed that the relative rates of responding did not match the relative rates of reinforcement in any of the three states of concurrency. Instead, the choice proportions in both the concurrent initial and in the concurrent terminal links were intermediate between the scheduled and the obtained relative rates of reinforcement, while the choice proportions for a terminal link concurrent with an initial link consistently overmatched the relative interreinforcement times (and were typically 1.00). These data indicate that an accurate characterization of choice may not be obtained by considering only the relative interreinforcement interval where one interreinforcement interval is segmented into a chain. Instead, the organism's choice for a schedule will be substantially lowered by the chaining operation.     

Inverse relation between choice and local response rate with a schedule of response-produced blackouts

Pigeons were exposed to a two-key concurrent chains schedule in which identical frequencies and distributions of food presentations generated different response rates in the terminal links. An inverse relation between local rate of response in the terminal links and relative frequency of response in the initial links was observed. The high response rate was produced in one terminal link by a second-order schedule in which responding produced brief blackouts of the response key. Responding under the same schedule in the other terminal link did not produce blackouts. Under initial training and after spatial reversal of the terminal-link schedules, two of three pigeons had lower relative frequencies of response in the initial member of the chain with the higher terminal link response rate. The third pigeon showed no change in preference at reversal.     

Two temporal parameters of food postponement

Rats were trained to press a lever under schedules of food postponement. In the absence of lever presses, food was delivered periodically (food-food interval). Responses initiated a second interval (response-food interval) that was reset by each additional response. Performance was first studied at different response-food intervals with the food-food interval fixed at 30 or 60 sec, or 10 min. Response-food intervals were examined in ascending order and then recovery was studied at shorter intervals. Finally, the food-food interval was manipulated with response-food interval fixed at 30 sec. At food-food intervals of 30 and 60 sec, responding first increased and then decreased as the response-food interval increased. At the 10-min food-food interval, responding decreased with increasing response-food interval. In general, very low rates of responding occurred when the response-food interval was 60 sec or more and when it equalled or exceeded the food-food interval. However, responding was maintained in one animal when the food-food interval was decreased from 120 to 15 sec with the response-food interval at 30 sec. Results, in terms of several dependent variables, are compared with data on shock avoidance. Effects of response-independent and response-produced food and shock are discussed.     

A yoked-chamber comparison of concurrent and multiple schedules

Pigeons were exposed to alternative pairs of variable-interval schedules correlated with red and green lights on one key (the food key). In one experimental chamber, responses on a white key (the changeover key) changed the color of the food key and initiated a 2-sec changeover delay. Pigeons in a second chamber obtained food by pecking on a colored key whenever the pigeons in the first (concurrent) chamber had obtained food for a peck on that key color. There was no changeover key in the second (multiple) chamber: changeover responses in the first chamber alternated the schedules and colors in both chambers. The pigeons in both chambers emitted the same proportion of responses on each of the variable-interval schedules, and mastered discrimination reversals at the same rate. The pigeons differed only in their absolute response rates, which were greater under the concurrent schedules. In a second experiment, changes in key color occurred automatically, with different proportions of time allocated to the two variable-interval schedules. Matching of relative response frequency to relative reinforcement frequency was affected by the relative amounts of time in each component, by rate of changeovers, and by manipulations of the variable-interval scheduling.