Comments on “the measurement of factorial indeterminacy”

Guttman's index of indeterminacy (2² – 1) measures the potential amount of uncertainty in picking the right alternative interpretation for a factor. When alternative solutions for a factor are equally likely to be correct, then the squared multiple correlation ² for predicting the factor from the observed variables is the average correlation _AB between independently selected alternative solutionsA andB, while var ( _AB )=(1 – ²)²/s, wheres is the dimensionality of the space in which unpredicted components of alternative solutions are to be found. When alternative solutions for the factor are not equally likely to be chosen, ² is the lower bound for E( _AB ); however, E( _AB ) need not be a modal value in the distribution of _AB . Guttman's index and E( _AB ) measure different aspects of the same indeterminacy problem.     

Correlation and prediction in ordinal test theory

Based on the test theory model for ordinal measurements proposed by Schulman and Haden, the present paper considers correlations between tests, attenuation, regressions involving true and observed scores, and prediction of test reliability.The population correlation between tests is shown to be related to the expected sample correlation for samples of sizen ₁ andn ₂. Errors of estimation, measurement and prediction are found to be similar to their counterparts in interval test theory, while attenuation is identical to its counterpart. The bias in estimating population reliability from sample data is compared for Kendall's tau and Spearman's rho.The author wishes to thank the referees for their helpful comments on an earlier draft of this paper, and in particular, for the suggested alternative methods of establishing some of the presented results.     

Fitting and testing carroll's weighted unfolding model for preferences

A quadratic programming algorithm is presented for fitting Carroll's weighted unfolding model for preferences to known multidimensional scale values. The algorithm can be applied directly to pairwise preferences; it permits nonnegativity constraints on subject weights; and it provides a means of testing various preference model hypotheses. While basically metric, it can be combined with Kruskal's monotone regression to fit ordinal data. Monte Carlo results show that (a) adequacy of true preference recovery depends on the number of data points and the amount of error, and (b) the proportion of data variance accounted for by the model sometimes only approximately reflects true recovery.This study is based on a doctoral dissertation submitted to the University of Illinois at Urbana-Champaign. The author wishes to thank the members of his dissertation committee—Lawrence E. Jones, Chairman, Charles Lewis, Stephen Golding, Ledyard Tucker, and Nancy Wiggins—for their helpful comments.     

Anorexia and conditioned taste aversions in the rat

The present study examined whether or not certain anorexic agents produced flavor aversions. Rats showed comparable anorexia when injected with lithium chloride, ammonium sulfate, arginine·HCl, and d-glucose. Only lithium chloride produced a flavor aversion to either a novel liquid or food. Only arginine was found to interfere with the formation or recall of an association. The effects of the other chemicals were discussed in terms of the relationship between anorexia and induced sickness.     

Fixed-interval punishment of running in hamsters

Four hamsters received brief electric shocks contingent upon running in a wheel. The fixed interval between shocks was varied systematically from 0 to 60 sec. Time spent running was directly related to the length of the fixed interval, while running speed remained roughly constant. Running depended on the fixed interval between shocks in the same way as bar-pressing maintained by food reinforcement, despite the fact that running was not established with nor maintained by explicit reinforcement.     

Startbox-goalbox confinement durations as determinants of self-punitive behavior

Two levels of confinement duration (5 or 60 sec) in either startbox or goalbox were factorially combined with presence or absence of shock during extinction of a runway escape response in a self-punitive paradigm under a spaced-trials procedure. All groups were equated for amount and temporal spacing of handling before and after each trial. Shocked rats were more resistant to extinction than nonshocked rats only when startbox confinement was short. When startbox confinement was long, shock facilitated extinction. Long goalbox confinement enhanced running speed for shocked rats, but only in the presence of shock. It was suggested that duration of startbox confinement affects strength of conditioned fear, with long confinement leading to its extinction.     

Rats learn the relationship between responding and environmental events: An expansion of the learned helplessness hypothesis

Previous research has shown that preexposure to inescapable shock interferes with subsequent acquisition of escape responding, while pretraining with escapable shock facilitates subsequent acquisition of a different escape response. It has also been demonstrated that interference and facilitation persist when the aversive event is changed between the two phases of training. The present experiment extended these findings, showing generalized learning from an appetitive to an aversive situation. Six groups of rats received the following treatment in the presence of discriminative stimuli: One group was trained to nose press for food, a second to chain pull for food, and a third to chain pull to escape or avoid shock. Two groups received either signalled free food or inescapable shock, and a naive control group received no pretreatment. All groups were then tested in a nose-press escape-avoidance situation. The three groups with prior response training acquired responding most rapidly, and at the same rate. The naive controls acquired responding slowly, and the two groups with response-independent histories did not acquire responding during the 5 days of training. It was concluded that rats learn the relationship between responding and environmental events and that such learning strongly influences subsequent learning.     

Dimensional stimulus control following brief wavelength training

Pigeons with extensive training pecking a key illuminated by a white line then had brief training with the key illuminated by 555 nanometers. This was immediately followed by a wavelength generalization test in extinction. Dimensional stimulus control about the training wavelength increased with the duration and number of reinforcements given on variable-interval 30-sec and variable-interval 10-sec schedules in Experiment I. In Experiment II, dimensional stimulus control was obtained after only 4 min of wavelength training from birds with prior and independent discrimination training. Experiment III provided groups equated in number of reinforcers with groups in Experiment I and two 8-min duration groups. Analyses, which included results from both Experiments I and III, showed that dimensional stimulus control increased: (a) more rapidly as a function of the duration of variable-interval 10-sec than variable-interval 30-sec reinforcement; (b) at the same rate across variable-interval reinforcement schedules, as a function of the number of reinforcers available during brief wavelength training.     

A comparison of the key-peck and treadle-press operants in the pigeon: differential-reinforcement-of-low-rate schedule of reinforcement

Key pecking and treadle pressing in pigeons were compared under concurrent (key-treadle) and single-operant differential-reinforcement-of-low-rate schedules of food reinforcement ranging from 5 to 60 sec (concurrent procedure) or 5 to 120 sec (single-operant procedure). Under both procedures, the two operants followed the same general law: decreasing response rate and reinforcement rate and increasing number of responses per reinforcement as a function of increasing schedule interval. High correlations were found between key pecking and treadle pressing for the measures of response rate, reinforcement rate, and responses per reinforcement. Regression equations allowed the prediction of treadle pressing from key pecking. More bursting occurred in responding to the key, and key pecking showed a more precise temporal discrimination than treadle pressing. A test for sequential dependencies between key and treadle responses showed significant dependencies not only under the concurrent procedure but also in data created artificially by merging key and treadle sequences from different pigeons under the concurrent procedure and from the same pigeon under the single-operant procedure. It seems likely that the sequential dependencies found were due to the independent action of the schedule on each operant and that behavioral dependencies did not occur with the concurrent training procedure. The key-peck operant does not appear to have any special qualities that preclude its use in discovering general laws of behavior, at least under the differential-reinforcement-of-low-rate schedule. The usefulness of the key peck in other situations requires direct experimental study.     

Short-term retention of response outcome as a determinant of serial reversal learning

The correlation between short-term retention of the outcome of the preceding response and overall learning proficiency was investigated for serial reversal learning. Pigeons were trained to asymptote on a serial reversal problem and then were presented a percentage reinforcement schedule where only some correct trials were rewarded. Nonrewarded correct trials were treated exactly as incorrect trials. The difference in error probability following the two types of correct trials was then used as a measure of short-term retention. When intertrial intervals (ITI) were short (6 sec), substantial differences occurred. When the ITI's were increased, the difference in accuracy declined regularly to no difference at an ITI of 60 sec. This demonstration of a short-term retention gradient, coupled with the finding that overall reversal learning was much better with the shorter ITI's, suggests that a primary mechanism of improvement in serial reversal learning is the acquisition of a conditional discrimination based on the outcome of the preceding response.