Seth Roberts

How persuasive is a good fit? A comment on theory testing

Quantitative theories with free parameters often gain credence when they closely fit data. This is a mistake. A good fit reveals nothing about the flexibility of the theory (how much it cannot fit), the variability of the data (how firmly the data rule out what the theory cannot fit), or the likelihood of other outcomes (perhaps the theory could have fit any plausible result), and a reader needs all 3 pieces of information to decide how much the fit should increase belief in the theory. The use of good fits as evidence is not supported by philosophers of science nor by the history of psychology; there seem to be no examples of a theory supported mainly by good fits that has led to demonstrable progress. A better way to test a theory with free parameters is to determine how the theory constrains possible outcomes (i.e., what it predicts), assess how firmly actual outcomes agree with those constraints, and determine if plausible alternative outcomes would have been inconsistent with the theory, allowing for the variability of the data.

Cross-modal use of an internal clock.

Four experiments used time-discrimination procedures with rats to ask if light and sound are timed by the same internal clock and if measured durations of light and sound are stored in the same memory. Experiment 1 used a choice procedure and a cross-modal transfer-of-training design. Rats were trained to press one lever after a 1-sec signal, another lever after a 4-sec signal. At first, the signal was light (or sound); when performance was accurate, the signal was changed ot sound (or light). There was transfer of the time discrimination across modalities: To some extent, the rats treated the new signal (sound) as if it were the old signal (light). The rest of the experiments used the peak procedure, which is similar to a discrete-trials fixed-interval procedure. With the peak procedure, response rate reaches a maximum in the middle of the trial; the time of the maximum (peak time) is a measure of the clock and temporal memory. Experiment 2 found that changing the time of food during light (or sound) changed peak time during sound (or light). In Experiments 3 and 4, intervals of light (or sound) were followed by intervals of sound (or light). The interval of light decreased the peak time measured from the start to the interval of sound, whether the two intervals were adjacent (Experiment 3) or separated by 5 sec (Experiment 3). Experiments 1 and 2 suggest that measured durations of light and sound are stored by the same memory; Experiments 3 and 4 suggest that light and sound are timed by the same clock.

Exploring the domain of the cerebellar timing system

Abstract The ability of an animal to process temporal information has adaptive significance across different temporal ranges. The ability to encode and utilize temporal information allows an animal to predict and anticipate events. However, the time scales vary widely. The predictable event might be based on information that changes over relatively long periods such as a year or a day, or over periods comprising much shorter durations, events that change within a few minutes or milliseconds. Are there a single set of neural mechanisms that are essential for representing temporal information over these different scales? Despite the fact that numerous neural structures have been linked to successful performance on a variety of timing tasks, this question has received relatively little attention. In this chapter, we will focus on the role of the cerebellum in a variety of timing tasks. We will review the hypothesis that the cerebellum can be conceptualized as a relatively task-independent timing mechanism. An important feature of this hypothesis is that the range of the cerebellar timing system is assumed to be relatively restricted. Specifically, we assume that the cerebellum is capable of representing temporal information ranging from a few milliseconds to an upper bound of a few seconds. What remains unclear is whether the cerebellum is involved on tasks spanning longer durations. Cognitive processes such as attention and memory become clearly important here, and indeed, may dominate performance for longer intervals. The animal literature points to non-cerebellar structures as playing a critical role in these tasks and we will provide a brief review of this work. Finally, we will present the preliminary results from two experiments designed to directly test the hypothesis that the cerebellums temporal capabilities are limited to relatively short durations.

Control of variation by reward probability

Two bar-press experiments with rats tested the rule that reducing expectation of reward increases the variation from which reward selects. Experiment 1 used a discrete-trial random-interval schedule, with trials signaled by light or sound. One signal always ended with reward; the other signal ended with reward less often. The 2 signals were randomly mixed. Bar-press duration (how long the bar was held down) varied more during the signal with the lower probability of reward. Experiment 2 closely resembled Experiment 1 but used a random-ratio schedule rather than a random-interval schedule. Again, bar-press duration varied more during the signal with the lower probability of reward. The results support the rule--the first well-controlled comparisons to do so.

Self-experimentation as a source of new ideas: Ten examples about sleep, mood, health, and weight

Little is known about how to generate plausible new scientific ideas. So it is noteworthy that 12 years of self-experimentation led to the discovery of several surprising cause-effect relationships and suggested a new theory of weight control, an unusually high rate of new ideas. The cause-effect relationships were: (1) Seeing faces in the morning on television decreased mood in the evening (> 10 hrs later) and improved mood the next day (> 24 hrs later), yet had no detectable effect before that (0-10 hrs later). The effect was strongest if the faces were life-sized and at a conversational distance. Travel across time zones reduced the effect for a few weeks. (2) Standing 8 hours per day reduced early awakening and made sleep more restorative, even though more standing was associated with less sleep. (3) Morning light (1 hr/day) reduced early awakening and made sleep more restorative. (4) Breakfast increased early awakening. (5) Standing and morning light together eliminated colds (upper respiratory tract infections) for more than 5 years. (6) Drinking lots of water, eating low-glycemic-index foods, and eating sushi each caused a modest weight loss. (7) Drinking unflavored fructose water caused a large weight loss that has lasted more than 1 year. While losing weight, hunger was much less than usual. Unflavored sucrose water had a similar effect. The new theory of weight control, which helped discover this effect, assumes that flavors associated with calories raise the body-fat set point: The stronger the association, the greater the increase. Between meals the set point declines. Self-experimentation lasting months or years seems to be a good way to generate plausible new ideas.

Effect of Reward Probability on Spatial and Temporal Variation

Gharib, Derby, and Roberts (2001) proposed that reducing reward expectation increases variation of response form. We tested this rule in a new situation and asked if it also applied to variation of response location and timing. In 2 discrete-trial experiments, pigeons pecked colored circles for food. The circles were of 6 possible colors, each associated with a different probability of reward. Reducing reward expectation did not affect peck duration (a measure of form) but did increase horizontal variation of peck location and interpeck-interval variation. The effect of reward probability on the standard deviation of interpeck intervals was clearer (larger t value) than its effect on mean interpeck interval. Two datasets from rats had similar interresponse-interval effects.

Evidence for distinct serial processes in animals: The multiplicative-factors method

The assumption that responses are controlled by distinct serially arranged processes was used by Sternberg (1969a) to explain the result, observed in many human experiments, that two factors have additive effects on reaction time (RT). With slight changes, Sternberg’s explanation of additive factors with RT also explains the result, observed in animal experiments, that two factors have multiplicative effects on response rate. This article describes and interprets 17 examples of multiplicative factors from response-rate experiments with rats, pigeons, and goldfish, as well as some other animal evidence for distinct serial processes. The examples suggest and/or support new and old ideas about generalization, attention, timing, learning, motivation, and response production. Most important, the animal evidence makes the case for distinct serial processes considerably stronger. Since the procedures used in the two sets of experiments (human and animal) have little in common, distinct serial processes may control behavior in a very wide range of situations.

What starts an internal clock

Five experiments with rats investigated under what conditions a stimulus is timed by the internal clock used in time-discrimination procedures. In Experiments 1-4, we trained rats to time one stimulus (e.g., light) and then asked whether they timed a stimulus from another modality (e.g., sound). The second stimulus was treated in three ways: exposed (presented alone), paired with food, and extinguished. Experiments 1 and 2 used the peak procedure, similar to a discrete-trial fixed-interval schedule, and paired the treated stimulus with food using instrumental training; Experiments 3 and 4 used a psychophysical choice procedure and paired the treated stimulus with food using classical conditioning. All four experiments found that there was cross-modal transfer of the time discrimination after pairing, but not after exposure or extinction. This suggests that the rats internal clock timed the treated stimulus after pairing, but not after exposure or extinction. Experiment 5 tested a theory of extinction based on the results of Experiments 1-4; the results suggested that the decline of responding observed in extinction is not due to changes in timing. The main conclusion is that the internal clock apparently times stimuli with signal value (associative strength) and does not time stimuli without signal value.

The unreasonable effectiveness of my self-experimentation.

Over 12 years, my self-experimentation found new and useful ways to improve sleep, mood, health, and weight. Why did it work so well? First, my position was unusual. I had the subject-matter knowledge of an insider, the freedom of an outsider, and the motivation of a person with the problem. I did not need to publish regularly. I did not want to display status via my research. Second, I used a powerful tool. Self-experimentation about the brain can test ideas much more easily (by a factor of about 500,000) than conventional research about other parts of the body. When you gather data, you sample from a power-law-like distribution of progress. Most data helps a little; a tiny fraction of data helps a lot. My subject-matter knowledge and methodological skills (e.g., in data analysis) improved the distribution from which I sampled (i.e., increased the average amount of progress per sample). Self-experimentation allowed me to sample from it much more often than conventional research. Another reason my self-experimentation was unusually effective is that, unlike professional science, it resembled the exploration of our ancestors, including foragers, hobbyists, and artisans.

Variation of bar-press duration: Where do new responses come from?

Instrumental learning involves both variation and selection: variation of what the animal does, and selection by reward from among the variation. Four experiments with rats suggested a rule about how variation is controlled by recent events. Experiment 1 used the peak procedure. Measurements of bar-press durations showed a sharp increase in mean duration after the time that food was sometimes given. The increase was triggered by the omission of expected food. Our first explanation of the increase was that it was a frustration effect. Experiment 2 tested this explanation with a procedure in which the first response of a trial usually produced food, ending the trial. In Experiment 2, unlike Experiment 1, omission of expected food did not produce a large increase in bar-press duration, which cast doubt on the frustration explanation. Experiments 3 and 4 tested an alternative explanation: a decrease in expectation of reward increases variation. Both used two signals associated with different probabilities of reward. Bar presses were more variable in duration during the signal with the lower probability of reward, supporting this alternative. These experiments show how variation can be studied with ordinary equipment and responses.