Criterion-related construct validity

Established results on latent variable models are applied to the study of the validity of a psychological test. When the test predicts a criterion by measuring a unidimensional latent construct, not only must the total score predict the criterion, but the joint distribution of criterion scores and item responses must exhibit a certain pattern. The presence of this population pattern may be tested with sample data using the stratified Wilcoxon rank sum test. Often, criterion information is available only for selected examinees, for instance, those who are admitted or hired. Three cases are discussed: (i) selection at random, (ii) selection based on the current test, and (iii) selection based on other measures of the latent construct. Discriminant validity is also discussed.This work was supported in part by Grant SES-87-01890 from the Measurement Methods and Data Improvement Program of the U.S. National Science Foundation.     

Functional classes and equivalence relations

Three adult subjects were taught a set of two-choice simultaneous discriminations, with three positive and three negative stimuli; all possible combinations of positive and negative stimuli yielded nine different pairs. The discriminations were repeatedly reversed and rereversed, the former positive stimuli becoming negative and the former negative stimuli becoming positive. With all subjects, a reversal of the contingencies for one pair of stimuli became sufficient to change their responses to all of the other pairs. The reversals had produced functional stimulus classes. Then, all subjects showed conditional discriminations emerging between members of a functional class; given a sample from one class and comparisons from both classes, they selected the comparison that was in the same class as the sample. Next, 2 of the subjects showed that the within-class conditional relations possessed the symmetric and transitive properties of equivalence relations; after having been taught to relate new stimuli to existing class members, the subjects then matched other class members to the new stimuli. Subsequent tests of two-choice discriminations showed that the conditional discriminations had transferred functional class membership to the new stimuli. The 3rd subject, who did not show equivalence relations among functional class members, was also found to have lost the within-class conditional relations after the equivalence tests.     

Effects of ratio reinforcement schedules on discrimination performance by Japanese monkeys

In Experiment 1, Japanese monkeys were trained on three conditional position-discrimination problems with colors as the conditional cues. Within each session, each problem was presented for two blocks of ten reinforcements; correct responses were reinforced under continuous-reinforcement, fixed-ratio 5, and variable-ratio 5 schedules, each assigned to one of the three problems. The assignment of schedules to problems was rotated a total of three times (15 sessions per assignment) after 30 sessions of acquisition training. Accuracy of discrimination increased to a moderate level with fewer trials under CRF than under ratio schedules. In contrast, the two ratio schedules, fixed and variable, were more effective in maintaining accurate discrimination than was CRF. With further training, as asymptotes were reached, accuracy was less affected by the schedule differences. These results demonstrated an interaction between the effects of reinforcement schedules and the level of acquisition. In Experiment 2, ratio sizes were gradually increased to 30. Discrimination accuracy was maintained until the ratio reached 20; ratio 30 strained the performance. Under FR conditions, accuracy increased as correct choice responses cumulated after reinforcement.     

Symmetry and transitivity of conditional relations in monkeys (Cebus apella) and pigeons (Columba livia)

In Experiment 1 six monkeys were tested with discriminative relations that were backward relative to their training in a 0-second conditional (“symbolic”) matching procedure. Although there was some indication of backward associations, the evidence was generally weak, and statistical evaluations did not reach conventional significance levels. Unlike children, who show backward associations to the point of symmetry, monkeys and pigeons display at best only weak and transient backward associations. In Experiment 2 associative transitivity was assessed across two sets of conditional matching tasks. All four monkeys tested demonstrated strong transitivity. In contrast, in Experiment 3 there was no evidence of transitivity in three pigeons tested under conditions closely comparable to those of Experiment 2. These results may identify some key features of interspecies differences and contribute to analyses of serial learning in animals.     

Stimulus class membership established via stimulus-reinforcer relations

In an arbitrary matching-to-sample procedure, two mentally retarded subjects learned conditional discriminations with two sets of stimuli. Each set included a spoken name (N1 or N2), an object (O1 or O2), and a printed symbol (S1 or S2). One subject selected conditionally (a) O1 upon N1, and O2 upon N2, and (b) S1 upon O1, and S2 upon O2. The other subject selected conditionally (a) S1 upon N1, and S2 upon N2, and (b) O1 upon S1, and O2 upon S2. For both subjects, selections of O1 and S1 produced one type of food, F1; selections of O2 and S2 produced a different type of food, F2. Both subjects also learned identity-matching performances, selecting O1, O2, S1, S2, F1, and F2 conditionally upon those stimuli as samples; F1 followed selections of O1, S1, and F1; F2 followed selections of O2, S2, and F2. Matching performances consistent with stimulus class formation involving the names, objects, symbols, and foods were demonstrated on probe trials, even though these performances had not been taught explicitly. Next, new objects, X1 and X2, were presented on identity-matching trials, producing F1 and F2, respectively. Without further training, X1 was selected conditionally upon N1, S1, and O1, and X2 was selected upon N2, S2, and O2. When the contingencies were changed so that selections of X1 and X2 were now followed by F2 and F1, respectively, X2 was selected conditionally upon N1, S1, and O1, and X1 was selected upon N2, S2, and O2. Class membership of X1 and X2 had apparently changed. This study provides evidence that reinforcers may become members of stimulus classes, and that new stimuli may become class members through relations with reinforcers.     

Observing responses maintained by conditional discriminative stimuli.

In a conditional discrimination procedure, pigeons' observing responses were analyzed to examine whether two color stimuli (blue or red), conditionally related to whether each of two line stimuli (vertical or horizontal) accompanied reinforcement or nonreinforcement, functioned as conditioned reinforcers. If a variable-interval (VI) 10-s requirement was fulfilled, an observing response produced onset of a color stimulus. A little later, a line stimulus was presented independently of responding, added to the color stimulus to form a compound stimulus. If 55 s elapsed with a response not having occurred either through 55 s or after the variable-interval 10-s had timed out, one of the color-line compound stimuli was presented independently of responding. To control for sensory reinforcement effects and for earlier entrance to the later link, a simple discrimination procedure also was conducted in which reinforcement was not correlated with the color stimuli but with the line stimuli only. As in the conditional discrimination, the observing response also could produce earlier presentation of blue or red. The observing response occurred more frequently during the conditional discrimination than during the simple discrimination. The results were related to different theoretical accounts of conditioned reinforcement, particularly the information hypothesis.     

Conditional relations by monkeys: Reflexivity, symmetry, and transitivity

Two cynomolgous macaques categorized six colors into two groups of three after conditional discrimination training (zero-delay symbolic match-to-sample). The procedures resulted in the establishment of relations among the elements of each set-relations that were not specifically trained and that can be characterized by the properties of reflexivity, symmetry, and transitivity. Each set of colors was related to a characteristic pattern of responding: One response pattern involved temporal duration (press and hold the response keys); the second response pattern entailed repeated pressing and releasing of the response keys (fixed ratio 8). Six combinations of two colors were trained, three combinations from each set. After discriminative performance stabilized for each monkey, they were tested with 10 additional color combinations, all of which differed from the training combinations. The conditional relations established between test combinations can be characterized as stimulus equivalence. The training procedures were analogous to the procedure of using category names, and have implications for understanding the function of language in the formation of equivalence classes.     

A note on the computation of the second-order derivatives of the elementary symmetric functions in the rasch model

Jansen (1984) gave explicit formulas for the computation of the second-order derivatives of the elementary symmetric functions. But they are only applicable to those pairs of items which have unequal parameters. It is shown here that for equal parameters similar explicit formulas do exist, too, facilitating the application of the Newton-Raphson procedure to estimate the parameters in the Rasch model and related models according to the conditional maximum likelihood principle.The author wishes to thank the reviewers for their helpful comments on an earlier draft of this paper.     

Transfer of matching-to-figure samples in the pigeon

Three pigeons were trained on a modified six-key matching-to-sample procedure. The third peck on the figure-sample key (which presented a bird, hand, face, beetle, rabbit, fish, flower, or red hue, as the sample) lighted only one comparison key. Every three additional pecks on the sample lighted another comparison key, up to a maximum of five keys. Pecks on keys of matching figures produced grain. Pecks on nonmatching keys (mismatches) turned off all lights on the comparison keys and repeated the trial. Three figures were used during acquisition. The birds learned to peck each sample until the matching comparison stimulus appeared on one of three comparison stimulus keys, and then to peck that key. Later, five novel stimuli, employed as both sample and comparison stimuli, and two additional matching keys were added. Each bird showed matching transfer to the novel samples. The data suggest that the birds may have learned the concept of figure matching rather than a series of two-component chains or discrete five-key discriminations.     

The effect of COVID-19 on home advantage in high- and low-stake situations: Evidence from the European national football competitions

The Covid-19 pandemic has significantly altered the way sporting events are observed. With the absence or limited presence of spectators in stadiums, the traditional advantage enjoyed by home teams has diminished considerably. This underscores the notion that the support of home fans can often be considered a key factor of the home advantage (HA) phenomenon, wherein teams perform better in front of their own supporters. However, the impact of reduced attendance on games with higher stakes, as opposed to low-stakes friendly matches, remains uncertain. In this study, we investigate the recently concluded European football championship (EURO 20), wherein several teams had the advantage of playing at home in high-stakes games with only one-third of the stadium capacity filled. Firstly, we demonstrate that the Covid-19 restrictions, leading to reduced fan attendance, resulted in a nearly 50% decrease in HA compared to the HA exhibited by the same teams during the qualification stage preceding EURO 20, even after accounting for team strength. Secondly, we show that while low-stakes friendly matches generally exhibit a smaller overall HA compared to high-stakes games, the absence of fans led to a similar reduction in HA during the low-stakes matches. Utilizing the recently developed Home Advantage Mediated (HAM) model (Bilalić, Gula, & Vaci, 2021, Scientific Reports, 21558), we were able to attribute the reduction in both high- and low-stakes games to poorer team performance, with no significant contribution from referee bias.