Intertrial-interval effects on sensitivity (A') and response bias (B") in a temporal discrimination by rats.

Killeen and Fetterman's (1988) behavioral theory of animal timing predicts that decreases in the rate of reinforcement should produce decreases in the sensitivity (A') of temporal discriminations and a decrease in miss and correct rejection rates (decrease in bias toward "long" responses). Eight rats were trained on a 10- versus 0.1-s temporal discrimination with an intertrial interval of 5 s and were subsequently tested on probe days on the same discrimination with intertrial intervals of 1, 2.5, 5, 10, or 20 s. The rate of reinforcement declined for all animals as intertrial interval increased. Although sensitivity (A') decreased with increasing intertrial interval, all rats showed an increase in bias to make long responses.     

A comparison of generalized and modified sample biserial correlation estimators

In a recent paper, Bedrick derived the asymptotic distribution of Lord's modified sample biserial correlation estimator and studied its efficiency for bivariate normal populations. We present a more detailed examination of the properties of Lord's estimator and several competitors, including Brogden's estimator. We show that Lord's estimator is more efficient for three nonnormal distributions than a generalization of Pearson's sample biserial estimator. In addition, Lord's estimator is reasonably efficient relative to the maximum likelihood estimator for these distributions. These conclusions are consistent with Bedrick's results for the bivariate normal distribution. We also study the small sample bias and variance of Lord's estimator, and the coverage properties of several confidence interval estimates.The author would like to thank the referees for several suggestions that improved the paper.     

On robust estimation of effect size under semiparametric models

Estimation of effect size is of interest in many applied fields such as Psychology, Sociology and Education. However there are few nonparametric estimators of effect size proposed in the existing literature, and little is known about the distributional characteristics of these estimators. In this article, two estimators based on the sample quantiles are proposed and studied. The first one is the estimator suggested by Hedges and Olkin (see page 93 of Hedges & Olkin, 1985) for the situation where a treatment effect is evaluated against a control group (Case A). A modified version of the robust estimator by Hedges and Olkin is also proposed for the situation where two parallel treatments are compared (Case B). Large sample distributions of both estimators are derived. Their asymptotic relative efficiencies with respect to the normal maximum likelihood estimators under several common distributions are evaluated. The robust properties of the proposed estimators are discussed with respect to the sample-wise breakdown points proposed by Akritas (1991). Simulation studies are provided in which the performing characteristics of the proposed estimator are compared to that of the nonparametric estimators by Kraemer and Andrews (1982). Interval estimation of the effect sizes is also discussed. In an example, interval estimates for the data set in Kraemer and Andrews (1982) are calculated for both cases A and B.     

Weighted least squares fitting using ordinary least squares algorithms

A general approach for fitting a model to a data matrix by weighted least squares (WLS) is studied. This approach consists of iteratively performing (steps of) existing algorithms for ordinary least squares (OLS) fitting of the same model. The approach is based on minimizing a function that majorizes the WLS loss function. The generality of the approach implies that, for every model for which an OLS fitting algorithm is available, the present approach yields a WLS fitting algorithm. In the special case where the WLS weight matrix is binary, the approach reduces to missing data imputation.This research has been made possible by a fellowship from the Royal Netherlands Academy of Arts and Sciences to the author.     

THE ACCELERATED INTAKE: A METHOD FOR INCREASING INITIAL ATTENDANCE TO OUTPATIENT COCAINE TREATMENT

We examined whether offering an accelerated (same-day) versus a standard (1- to 7-day delay) intake appointment increased initial attendance at an outpatient cocaine treatment program. Significantly more of the subjects who were offered an accelerated intake (59%) attended than those who were given a standard intake (33%), χ² (2, N = 78) = 4.198, p < .05. The accelerated intake procedure appears to be useful for enhancing enrollment in outpatient addiction treatment.     

Concurrent choice: Effects of overall reinforcer rate and the temporal distribution of reinforcers

Six pigeons responded on a series of concurrent exponential variable-interval schedules, offering a within-subject comparison with previously published data from concurrent arithmetic variable-interval schedules. Both relative and overall reinforcer rates were varied between conditions. The generalized matching law described the data well, with undermatching much more frequent than strict matching. Time-allocation sensitivity consistently exceeded response-allocation sensitivity for both schedule types, and exponential-schedule sensitivity exceeded arithmetic-schedule sensitivity for both measures of choice. A further set of conditions using variable-interval schedules whose shortest interval was correlated with the mean interval, like arithmetic schedules, but that provided a constant conditional probability of reinforcement, like exponential schedules, produced sensitivities between those produced by conventional arithmetic and exponential schedules. Unlike previous arithmetic-schedule results, exponential sensitivity changed nonmonotonically with changes in overall reinforcer rate. The results clarify our knowledge of the effects of arithmetic and exponential schedules but confuse our understanding of the effects of overall reinforcer rate on concurrent choice.     

Discriminative properties of briefly presented stimuli

In Experiment I, pigeons' responses produced food according to a fixed-interval schedule while responses on the key also produced brief stimuli according to a variable-interval schedule. Each brief stimulus reset the fixed interval. Thus, a brief stimulus occurred irregularly but a fixed minimum time separated the occurrence of food from a brief stimulus. Pauses followed brief stimuli and were followed by an accelerated response rate until another brief stimulus or food occurred. In Experiment II, four control procedures were examined. (1) Brief-stimulus presentations were omitted, producing a loss of response patterning. (2) A second-order schedule was studied with fixed-interval components. This schedule produced patterning following brief stimuli similar in kind and degree to that found in Experiment I. (3) A conjoint schedule was arranged in which food was no longer separated from the stimulus by a fixed time; pauses following the stimulus no longer resulted. (4) A brief food reinforcer replaced the brief visual stimulus, resulting in a constant response rate with no pausing following the brief food stimulus. The results suggest that the brief-stimulus effects were due to discriminative functions produced by the fixed temporal relation separating the stimulus from food.     

Undermatching on concurrent variable-interval schedules and the power law.

The phenomenon of undermatching on concurrent variable-interval schedules is shown to be derivable by transforming the individual interreinforcement intervals of each variable-interval schedule and averaging the transformed values to produce an "estimate" of the rate of reinforcement the schedules deliver. If the transformation is based on a power function with a fractional exponent, such as is found in many studies of temporal control in animals, matching response rations to the ratios of these estimated rates of reinforcement yields undermatching. If the concurrent variable-interval schedules are arranged such that the individual intervals in each schedule have a constant proportionality (a procedure found in many commonly used variable-interval schedules) the slope of the line relating logarithms of response ratios and of programmed reinforcement ratios is identical to the exponent of the power transformation applied to the individual time intervals in the variable-interval schedules. In other cases this simple relation does not hold but the degree of undermatching is greater the lower the value of the exponent of the power function. This account of undermatching predicts values similar to those typically observed.     

A COMPARISON OF INDIRECT MEASURES FOR LONG-DURATION BEHAVIORS1

A computer program was developed to simulate long-duration behavior. The program generated data by using two time-series models linked together by a covariance parameter. By varying the parameters of the program, the characteristics of the simulated behavior were altered, including the mean and variance of the durations of behavior, the mean and variance of the interresponse time, and the degree of relationship within and between durations of behavior and interresponse times. Four data-collection methods were applied to the simulated data: whole interval, partial interval, momentary time-sampling, and continuous measures. The accuracies of the first three recording measures were judged by comparing them to the continuous measure. The results indicated that only the momentary time-sampling approach yielded unbiased results. The degree of bias for the whole and partial interval measures was a function of the ratio of the interval recording length to the sum of the mean duration of behavior and the mean interresponse time. Unfortunately, it was concluded that researchers cannot estimate the magnitudes of these latter two parameters for most behaviors of interest and, consequently, are unable to choose an appropriate interval length. Therefore, it was recommended that the use of interval recording approaches be greatly restricted and that momentary time-sampling be substituted where possible.     

ON THE INABILITY OF INTERVAL TIME SAMPLING TO REFLECT FREQUENCY OF OCCURRENCE DATA1

Interval time sampling yields the result, percentage of intervals scored. It is rudimentary to note that this measure per se does not constitute a response dimension. It is a useful behavioral measure, therefore, only to the extent that it accurately reflects the nature and degree of the fundamental dimensions from which it is drawn i.e., frequency and duration. The correspondence between scored intervals and response duration is fairly well understood (Journal of Applied Behavior Analysis, 1975, 8 , 463–469; 1977, 10 , 325–332). This study determined the correspondence between scored intervals and response frequency. Eleven, 30-minute experimental sessions that differed along the variables of frequency of occurrence and time per response (the average length of a response per session) were computer simulated. In the first group of four sessions, the frequencies were 45, 100, 150, and 300; in these sessions, all responses ranged from one to three seconds. In the second group of four sessions, the frequencies were 31, 61, 101, and 152; in these sessions, all responses ranged from three to nine seconds. In the last group of three sessions, the frequencies were 25, 34, and 50; here, all responses ranged from nine to 27 seconds. The response distribution within the above ranges was rectangular, with each whole second represented once. The responses were selected by a random number generator, and on each trial every number in the distribution had an equal probability of occurrence. These provisions produced a linear pattern of responding. The time per response in the three groups of sessions were 2, 6, and 18 seconds. For all sessions, event recordings were made and analyzed. The analysis consisted of using partial interval time sampling to determine the percentage of intervals scored; this total was subdivided into intervals containing (1) single responses, (2) multiple responses, (3) continuing responses, and (4) response initiations or terminations. The analysis was performed when the length of the observation interval was 5, 10, 20, 30, 60, and 120 seconds. An additional session drawn from a study that contained real-life data was subjected to this same analysis. The most significant results were derived by finding the ratio of scored intervals containing single responses to the total intervals scored. If every scored interval contained a single response, this ratio would equal 1.0; if no scored interval contained a single response, the ratio would be 0.0. It can be seen that this ratio is an objective expression of the validity of interval time sampling as a measure of response frequency. Of 66 data points (11 sessions × six observation lengths per session), only five were equal to or greater than 0.80. These five points were all found in just two sessions (f = 45, 100). A validity index of less than 0.50 was observed in 49 of the 66 points. Also, the validity index increased, peaked, and then decreased within sessions as the length of the observation interval was increased. The results from the real-life session were in close agreement with those obtained from the simulations. The importance of these and previous findings lies in the demonstration that changes in scored intervals need not represent true behavior change. The data indicate that there are many combinations of behavioral frequency and duration where interval time sampling cannot produce valid measurement results.