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Choice in a self-control paradigm with human subjects: Effects of changeover delay duration
LEARNING
AND
MOTIVATION
18, 421-438 (1987)
Choice in a Self-Control Paradigm with Human Subjects: Effects of Changeover Delay Duration GEORGE R. KING AND A. W. LOGUE State University of New York at Stony Brook The present experiment examined the choices of human subjects as a function of changeover delay (COD) duration. A self-control paradigm was used; subjects chose between larger, more delayed and smaller, less delayed reinforcers. The COD durations were 1 s, I5 s, and 30 s. The results indicated that at the I-s COD, the subjects distributed their responses approximately equally between the two response alternatives. However, at the 15-s and 30-s COD durations, the subjects tended to demonstrate virtually exclusive preference for the larger, more delayed reinforcer. Furthermore, increasing the COD duration significantly increased the subjects’ sensitivity to variation in reinforcer delay. Increasing the COD duration also increased the subjects’ sensitivity to reinforcer amount, but this effect was not significant. The results are qualitatively consistent with an interpretation that the subjects followed a strategy which attempted to maximize overall amount of reinforcement. 0 1987 Academic Press, Inc.
Self-control can be defined as the choice of a larger, more delayed reinforcer over a smaller, less delayed reinforcer (Ainslie, 1974; Eisenberger, Masterson, & Lowman, 1982; Grosch & Neuringer, 1981; Rachlin & Green, 1972). Similarly, the opposite of self-control can be defined as impulsiveness, the choice of a smaller, less delayed reinforcer over a larger, more delayed reinforcer. Within a self-control paradigm, a subject should always choose the larger, more delayed reinforcer in order to maximize total received reinforcement, given equal rates of reinforcement for both alternatives. A version of the original matching law (Herrnstein, 1970) has provided The research reported here was supported by NSF Grant BNS-8416302, principal investigator A. W. Logue. Some of the data reported here were presented at the Annual Meeting of the Association for Behavior Analysis in Milwaukee, WI, June 1986. Comments by J. Higa, J. Hinson, and F. K. McSweeney on a previous version of this paper are greatly appreciated. Requests for reprints should be sent to A. W. Logue, Department of Psychology, State University of New York, Stony Brook, NY 11794. 421 0023-9690187 $3.00 Copyright 0 1987 by Academic Press, Inc. All rights of reproduction in any form reserved.
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an adequate description of pigeons’ choices between reinforcers of different amounts and delays in a self-control paradigm (Ainslie & Hermstein, 1981; Green, Fisher, Perlow, & Sherman, 1981). According to this law,
(2)=($?)
(1)
where B, and B, represent the number of choices for reinforcers obtained from the left and right response alternatives, respectively, and A,, A,, D,, D, represent the amounts (sizes) and delays of the left and right reinforcers, respectively. Logue, Rodriguez, Pena-Correal, and Mauro (1984) proposed the following equation (similar to Baum’s, 1974, generalized matching law) to model individual differences in sensitivity to reinforcer amount and delay, and describe subjects’ choices when reinforcer amount and delay are varied:
(2) = (~)““(g””
(2)
where B,, B,, A,, A,, D,, and D, are defined as in Eq. (l), and sA and SD represent sensitivity to reinforcer amount and reinforcer delay, respectively. The Logue et al. modification provided a better description of their and others’ results (Ainslie & Herrnstein, 1981; Green et al., 1981; Mazur & Logue, 1978) than did the original matching law in investigations of self-control with pigeons. Experimentally naive adult humans often show large discrepancies from matching when choosing between reinforcers of different amounts (Bangert, Green, Snyderman, & Turow, 1985; Logue, Pena-Cot-real, Rodriguez, & Kabela, 1986; Wurster & Griffiths, 1979). For example, in Logue et al. (1986, Experiments 2, 3, 4, and 5), subjects consistently chose more of the larger reinforcers than predicted by the original matching law. However, an inadequate changeover delay (COD) may have been used in the Logue et al. study. A COD specifies a minimum period that must elapse after a changeover response from making a response on one alternative to making it on the other atlternative, or after the first response following reinforcement, before a subsequent response can deliver a reinforcer. A COD is used to decrease the probability of reinforcement of response sequences involving responses on both alternatives (de Villiers, 1977; Herrnstein, 1961). Previous research indicates that matching on concurrent schedules of reinforcer frequency, with equal amounts and delays of reinforcement for both alternatives, improves with the introduction of a COD (Catania & Cutts, 1963; de Villiers & Millenson, 1972; Herrnstein, 1961; McSweeney, 1978; Shull & Pliskoff, 1967; Silberberg & Fantino, 1970). For example, McSweeney (1978) varied the COD duration from 0 to
CHANGEOVER
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423
20 s with pigeons responding on simple concurrent keypeck treadle-press schedules. She found that matching and the fit of the generalized matching law for concurrent schedules (Baum, 1974) improved when the COD duration was increased from 0 to 5 or 20 s, but that there was no consistent difference between the fits of the equation when the COD was increased from 5 to 20 s. Human subjects’ responding on concurrent schedules also seems sensitive to the imposition of a COD. Catania and Cutts (1963) used a concurrent variable interval extinction (cone VI ext) schedule to examine the effects of a COD on human choice behavior during a button pressing task. These researchers found that, without a COD present, superstitious response sequences developed involving responses to both alternatives. However, with the introduction of a COD between 2 and 15 s, responding on the extinction schedule was substantially reduced, and in some cases eliminated, thereby improving matching. Thus, the findings of Catania and Cutts (1963) indicate that, when humans respond on simple concurrent schedules, a COD has a similar effect on humans’ choice as it does on other organisms’ choice behavior. de Villiers (1977) has argued that for the matching relation to hold, a minimum COD duration must be in effect. The minimum COD value that produces matching seems to be species dependent, and must be empirically determined. Therefore prior failures to find matching with humans in a self-control paradigm, such as Logue et al. (1986), may be the result of the COD durations used in those experiments being too short (e.g., Logue et al., 1986, Experiments 2-5, used a 3-s COD). Previous findings have suggested that the criterion for ending a session may also affect matching in human subjects. The Logue et al. (1986) data suggested that their adult human subjects chose a greater number of the larger, more delayed reinforcers when sessions ended after 90 reinforcers than when sessions ended after 30 min, although the effect was not significant. It is not clear to what extent the Logue et al. use of a perhaps inadequate COD affected these findings. The present experiment examined humans’ choice behavior during a self-control paradigm as a function of COD duration. This experiment attempted to discern what effect increasing the COD duration would have on human subjects’ self-control behavior. The effects of COD duration have not previously been examined within a self-control paradigm, either with human or nonhuman subjects. The present experiment also attempted to determine if the fit of the generalized matching law for self-control (Eq. (2)) would improve, similar to McSweeney (1978), as the COD duration was increased. Finally, in the experiment described here, the criterion for determining session termination (session time or number of received reinforcers) was manipulated to determine if this procedural
424
KING AND LOGUE O@@ Lights
Counter 5
Left Disc
Button c3
0
Righ Disc cc
FIG. 1. Diagram of the aluminum panel used in the present experiment. The letters G, W, R indicate the colors green, white, and red, respectively.
variation would have any effect on subjects’ choice behavior when reinforcer amount and delay, as well as COD duration, were manipulated. METHOD Subjects The subjects were experimentally naive adult human females, numbered 1, 2, 3, 4, and 5. All of the subjects were enrolled at the State University of New York at Stony Brook. Subject 3 was a graduate student in astronomy; the other five subjects were undergraduates majoring in the humanities and social sciences. No subject was a psychology major. Apparatus The experiment was conducted in a small room, 3.1 x 3.4 m, that could be illuminated by a standard 60-W light bulb. One wall of the room contained a one-way mirror that allowed observation of the subject. The room contained a chair and a desk. The experimental apparatus was placed on the desk, which was located against one wall. The apparatus was a wooden box, 122 cm wide, 66 cm deep, and 81 cm high. The front of the apparatus was painted black. An aluminum panel (see Fig. l), 35 cm wide and 51 cm high, on the front of the apparatus, contained the experimental stimuli and the manipulandum, an aluminum rod. The rod, 1.6 cm in diameter, protruded 14 cm from the panel, and was mounted 4 cm from the bottom of the apparatus and equidistant from the sides. The rod could be pushed to
CHANGEOVER
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425
the left or the right and required a minimum force of 18.8 N to operate in either direction. One translucent Plexiglas disc, 3.8 cm in diameter, was located to each side of the rod. The left disc could be transilluminated green, and the right disc red. A hole, 2.5 cm in diameter, located 5 cm above the rod, allowed access to a black button, mounted 3.8 cm behind the surface of the panel. Button presses were effective only when a light, located below the button, was lit. A counter was located 11.8 cm above the hole. On the top front edge of the apparatus were three DBDSl 1 7.5-W light bulbs. The left light was green, the center light white, and the right light red. Located behind the three lights was a loudspeaker that emitted continuous white noise to mask extraneous noises. A PDP-8/A computer, located in another room, controlled the experimental stimuli and recorded responses using a SUPERSKED program. Procedure
During each session, subjects were escorted into the experimental chamber. They were given the following minimal instructions as to what they were to do during the experimental session: Please read carefully. Do not ask for additional instructions. Your task is to earn as many points as you can. Each point is worth l/15 cents. For example, if you earn 1500 points you will be paid $1. You may touch anything on this panel to earn points. The session will begin when one or more lights come on, and will end when all the lights turn off. To minimize interference with the equipment, please leave all metal objects (watches, jewelry, etc.) with the experimenter for the duration of the session. All other personal property (coats, books, writing utensils, pocketbooks, etc.) should also be left with the experimenter. These materials will be returned promptly at the session’s end.
Instructions were kept to a minimum because previous research has shown that, under certain conditions, with minimal instructions humans may show more sensitivity to the scheduled contingencies (e.g., Matthews, Shimoff, Catania, & Sagvolden, 1977; Shimoff, Catania, & Matthews, 1981). Subjects were instructed to leave their watches and jewelry in order to ensure that no subject had access to a timing device during the session. The use of timing devices in experiments can yield valuable data (Lowe, 1979); however, conditions in the present experiment were kept as similar as possible to those employed with pigeons in order to help identify the origins of any differences between the behavior of human and nonhuman subjects. The experimenter then left the room, closed the door, and turned off the overhead light. There was no further communication between the subject and the experimenter until the end of the session. At the beginning of a session, the left disc was green, the right disc
426
KING
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LOGUE
was red, and the white light on the top of the apparatus was lit. When a reinforcer was received for a rod push to the left, both discs and the white house light were darkened, and the left, green light on top of the apparatus was turned on. A reinforcer began with the programmed delay period (the delay to reinforcement), followed by the programmed period of access to reinforcement (the amount of reinforcement). During the reinforcer access period the green light remained on, the white light below the button was lit, and the button was enabled. Each press of the button added one point to the counter. Points exchangeable for money are used more frequently than any other reinforcer in operant research with humans (see Buskist & Miller, 1982, for references). After the reinforcer access period, both discs and the white light on top of the console were again lit. The sequence of events for reinforcement following a rod push to the right were similar to those for reinforcement following a rod push to the left except that the right, red light on top of the apparatus was lit instead of the left, green light. Rod pushes to the left or right were followed by a brief feedback click when the discs were lit; rod pushes when the discs were darkened had no effect and were not recorded. The amounts and delays used in the present experiment, grouped together in seconds for A,, A,, D,, D, (see Eq. (I)), were 5, 10, 0.1, 13; 6, 2, 6, 2; and 10, 5, 13, 0.1. At the end of each session each subject completed a questionnaire asking how she thought the button became available, and what she thought she did during the experiment. Subjects also received the money they had earned during the session. At the end of the entire experiment, subjects also received $1.25 for each session attended. Reinforcers were available according to a modified concurrent, independent VI 30-s VI 30-s schedule. The VI intervals for each schedule were constructed according to the method described by Fleshler and Hoffman (1962). The programming of the VI schedules was identical to the procedure used by Logue et al. (1984, Experiment 2) with pigeons, and also to the procedure used by Logue et al. (1986, Experiment 2-5) with humans, and was similar to the linear VI schedules used by Vaughan (1982), which generate response rates similar to traditional VI schedules (see discussion by Prelec, 1983). Each VI schedule timed continuously during a session. Each time an interval in one of the VI schedules timed out, the schedule continued, but a counter representing the number of available reinforcers was incremented. Each time a reinforcer was received, the appropriate counter was decremented. This type of concurrent VI VI programming tends to keep the overall reinforcer frequency for the two alternatives more similar than does the traditional concurrent VI VI programming (see Logue et al., 1984, Experiment 2), and also avoids the insensitive responding shown by human subjects on nonindependent concurrent VI VI schedules (see Logue, Chavarro, & King, 1987). A
CHANGEOVER
DELAY
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SELF-CONTROL
427
rod push toward a lit disc was followed by the reinforcer delay and reinforcer amount periods, if the counter for that VI schedule had a value of at least 1 and if the COD requirement had been fulfilled. The COD values used in the present experiment were 1 s, 15 s, and 30 s. For Group 1 (Subjects 1, 2, and 3) sessions ended after 30 min. For Group 2 (Subjects 4 and 5) sessions ended after 100, 50, or 25 reinforcers for the l-s, 15-s and 30-s COD conditions, respectively. These changes in the criterion number of reinforcers for ending sessions were made in order to keep session time for Group 2 roughly constant across COD conditions. In addition, these changes resulted in the number of reinforcers received by Group 2 in each COD condition being approximately the same as the number of reinforcers that subjects in Group 1 received in each COD condition. All subjects were exposed to all possible combinations of the three COD durations and the three values of A,, A,, D,, D,, for a total of nine conditions, close to the maximum number of conditions in which any subject would participate. Subjects were exposed to each of these conditions until their behavior satisfied a stability criterion. The stability criterion specified that a condition not be terminated for a given subject unless the values of the ratio of left rod pushes divided by right rod pushes in the last two half sessions were neither higher nor lower than the values of the same ratio for all previous half sessions of that condition (i.e., each session was divided in half, and the response ratios in each half session were neither higher nor lower than the value of the same ratio in all of the previous half-sessions, Logue et al., 1986). Table 1 shows the order of the conditions and the number of sessions for each condition for each subject. RESULTS General All subjects learned to use the panel efficiently during the first session. Table 1 presents the arithmetic means of the last two stable half sessions for the number of left and right responses and for the number of received reinforcers for each alternative, as well as the geometric means of the last two, stable, half sessions for the response ratios @r/B,, see Eq. (l)), for each condition. When, occasionally, no responses were made on one alternative, the standard transformation of log (x’ = X + 1) was used in order to calculate the geometric means of the response ratios (see Snedecor & Cochran, 1967, p. 329). Geometric means are a more appropriate measure for ratios than the arithmetic mean because the geometric mean is less sensitive to the extreme values easily generated by ratios (see, e.g., Logue & Chavarro, 1987, for similar analyses; and see below). Ratios of time spent responding on the two alternatives tended to produce
2
(5~13)/(10.0.1) (5~13)/(10~0.1) (5.13)/(10.0.1)
1
(10-0.1)/(5~13)
62)/P@ (6.2M2.6)
(10.0.1)/(5.13) (10.0.1)/(5.13)
(6~2)/(2.6)
(10.0.1)/(5.13) (5~13)/(10~0.1) (5.13)/(10.0.1) (5.13)/(10.0.1)
WV/(24 (6.2)/W)
(10~0.1)/(513) (10.0.1)/(5~13)
(6.2)/w9
M,W/(A;D,)
Subject
15 I 30 30 30 1 1 15 15 15 1 30 30 30 1 1 15 15
COD
Condition (in seconds)
5 3 4 2 2 2 3 2 2 2 7 3 2 2 4 6 3 3
Number of sessions 60 162 30 232 145 116 263 185 149 56 61 55 1623 1811 237 1313 2015 1395
Left B, 77 81 399 19 0 163 171 11 0 1570 395 1829 51 52 103 168 23 44
Right B,
Rod pushes
0.91 2.03 0.08 67.19 145.03 0.71 1.55 21.97 150.47 0.01 0.16 0.00 1204.25 1280.63 1.69 8.41 1450.59 32.46
B,l& 11 30 1 16 15 26 30 29 22 1 13 1 20 16 30 30 30 22
left
14 23 16 1 0 30 30 1 0 22 30 16 1 1 19 30 1 1
right
Reinforcers
and
3 21 0 1 0 13 23 1 0 0 15 4 0 0 4 23 1 1
Changeover responses
TABLE 1 Order of the Conditions. Number of Sessions per Condition, Mean Number of Rod Pushes. Response Ratios, Obtained Reinforcers, Changeover Responses for Each Subject
(10.0.1)/(5.13)
(6~2)/(2.6) (6.2)/(24
(10~0.1)/(5~13) (10.0.1)/(5.13)
(6.2)/W)
(10.0.1)/(5.13) (5.13)/(10.0.1) (5~13)/(10~0.1) (5~13)/(10~0.1)
62)AW (6.2)/W)
(10~0.1)/(5~13) (10.0.1)/(5.13)
62)/(2@
(10.0.1)/(5.13) (5.13)/(10*0.1) (5~13)/(10~0.1) (5.13)/(10.0.1)
(W/(2+4
(10.0.1)/(5.13) (10.0.1)/(5.13) 6.2)/(2.6)
WW(2.6)
(5.13)/(10~0.1) (5.13)/(10.0.1) (5~13)/(10~0.1)
15 15
30 30 30
15 15 15
30 30 30 1
15 15 15
30 30 30
15
4 2
2 4
5 4 2
56 128 40 354 249 81 359 561 322 2 57 3 87 50 58 111 88 109 49 131 0 1674 1923 249 1009 2060 2079
-
276 82 370 38 118 118 255 52 153 109 52 55 4 0 56 73 8 0 1078 125 1316 53 0 128 250 63 0
0.21 1.56 0.12 322.45 2.12 0.15 1.40 12.82 2.19 0.02 1.21 0.07 72.49 49.62 1.05 1.50 60.25 112.71 0.01 1.05 0.00 1261.52 1853.25 1.96 4.04 33.05 2079.84
4 30 2 19 12 26 30 30 18 0 23 1 14 15 22 23 24 25 1 21 0 14 15 25 23 24 25 0 20 22
0 24 24 15
20 25 15 2 6 29 30 2 9 25 22 14 1 0 23 22
5
4 202 0
:
F 7 0 0
40 0 0
i2 u
0 0
F
z
d
8 0 0 0 2 3 0
% 3 0
8
2 0 0
18 13 0 0 4 9 26
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KING
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LOCUE
results similar to the response ratios; therefore only the response ratio results are presented. The subjects did not appear to suspect why they were asked to remove their watches and jewelry, yet in postsession questionnaires they reported attempting to time the reinforcer amounts and delays. When the reinforcer amounts and delays were varied, subjects reported various strategies, but all were attempts to maximize the total number of points earned during the session. However, the subjects, as indicated by the postsession questionnaires, did not seem to realize that the changes in COD duration were time dependent. Subjects consistently reported that they had to make more responses in order to receive a reinforcer in the longer COD conditions. In other words, the subjects reported increases in the COD as an increasing ratio requirement. The significance level was set at p < .05, two tailed, for all statistical tests. Response
Ratios
A mixed-design analysis of variance was performed using the Base10 logarithmic transformations of the response ratios for each subject in each condition, with Group assignment (session termination criterion) as the between-subject variable, and COD duration and value ratio (the programmed amounts and delays inserted into the right side of Eq. (1) ((Afl,/A,.D,)) as the within-subject variables. The Base-10 logarithmic transformations of the response ratios were used as the dependent variable because of the large range of the untransformed response ratios (from 0.00 to 2079.84). Ranges of ratios are frequently problematic because ratios for which the numerator is larger than the denominator can vary between 1.0 and infinity, while ratios for which the numerator is less than the denominator can only vary between 0.0 and 1 .O. A logarithmic transformation helps to decrease this discrepancy. The results indicate that the COD (F(2, 6) = 13.88) and value ratio (F (2, 6) = 17.25) main effects are significant, as is the COD x value ratio interaction (F(4, 12) = 16.14). However, the group main effect is not significant (F(1, 3) = 0.01). Therefore, the data are collapsed across groups for all subsequent analyses. Overall, these results indicate that the subjects were sensitive to the experimental conditions, and that their behavior changed as a function of these conditions. These conclusions are supported by Fig. 2, which depicts the mean response ratios as a function of condition. Consistent with the dependent variable used in the analysis of variance, the response ratios are shown in logarithmic coordinates. Table 1 and Fig. 2 indicate that at the l-s COD subjects tended to distribute their responding approximately equally between the two response alternatives, but at the 15 and 30-s COD durations, the subjects tended to choose the larger, more delayed reinforcer virtually exclusively. An analysis of the subjects’ switching behavior
CHANGEOVER
DELAY
3\ gloo0F _
Ol-
431
f---..-. !! ?‘X’*,/T-Z !, 1: 6;
IOOO-
ilO8K
AND SELF-CONTROL
6 ,I’,i :I di
l -
COD
.----a A-----A
COD 15s COD 30s
Is
!
0.01’
’ ~5~13Mloal) VALUE
, (6~2Vl2.6) RATIO
I ~10~01,,~5431
((A,.DR)/(AR.DLi)
FIG. 2. Left divided by right responses (response ratios) as a function of the value ratio, separately for each COD duration. Note that the response ratios are plotted on logarithmic coordinates to attenuate the range problems associated with the use of ratios.
supports these conclusions (changing response alternatives after of a reinforcer was not counted as a changeover response). number of changeover responses per session is, for the l-s (SE = 2.2, N = 5); for the 15-s COD, 1.8 (SE = 1.2, N = the 30-s COD, 0.3 (SE = 0.4, N = 5).
the delivery The mean COD, 12.8 5); and for
Proportion of Obtained out of Programmed Reinforcers
Figures 3 and 4 present the proportion of reinforcers obtained out of total reinforcers programmed as a function of the value ratio, separately for each COD duration. Figure 3 presents the proportion of obtained out of programmed larger reinforcers as a function of the value ratio for each COD duration. Figure 4 presents the proportions of obtained out of programmed smaller reinforcers as a function of the value ratio for each COD duration. Figures 3 and 4 indicate that the proportions of both larger and smaller reinforcers obtained decrease as the COD duration increases; however, the decline is much larger for the smaller, less delayed reinforcers. Virtually none of the smaller, less delayed reinforcers were selected during the 15- and 30-s COD durations, consistent with the data presented in Table 1 and with the results of the mixed design analysis of variance. These conclusions are supported by two within-subjects analyses of
KING AND LOGUE
432
9 25
LO0.9-
8& 0.8av, k a 0.7 00” 5 g Ok 2 5 za gg
0.6 0.504-
OIX * Q 0.3 O-1 F :: 0.2$ a
-
CODlS
-
COD25s COD3oS
0.1 I
W3,1Kl.0.11 VALUE
1 (6.2!A2.6l RATIO
u0-0.11/(5~13)
((A,~D,MA,.D,))
FIG. 3. The proportion of obtained out of programmed larger reinforcers as a function of the value ratio, separately for each COD duration. The bars on each point indicate the standard error for that point.
VALUE
RATIO
((AL-D,MA,*D,))
FIG. 4. The proportion of obtained out of programmed smaller reinforcers as a function of the value ratio, separately for each COD duration. The bars on each point indicate the standard error for that point.
CHANGEOVER
DELAY
AND
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SELF-CONTROL
variance performed using the proportion of obtained out of programmed reinforcers for each subject in each condition with COD duration and value ratio as the within-subject variables. One analysis of variance was conducted for the proportion of obtained out of programmed larger reinforcers, and one for the proportion of obtained out of programmed smaller reinforcers. The analysis of variance for the larger reinforcers indicates that the COD main effect is significant (F(2, 6) = 552.99), as is the value ratio main effect (F(2, 6) = 38.59). The COD x value ratio interaction is also signiticant (F(4, 12) = 9.24). The analysis for the smaller reinforcers indicates that only the COD main effect is significant (F(2, 6) = 154.35). Sensitivity to Variation in Reinforcer Amount and Delay In order to assess the subjects’ sensitivity to variation in reinforcer amount and delay over the value ratios used in the present experiment, a multiple linear regression was employed using Eq. (3), the Base-10 logarithmic transform of Eq. (2): 1%
@h/f&)
=
SA 1%
(AdA,)
+
SD log
WD,).
(3)
A least squares multiple regression analysis was performed separately for each COD duration and each subject using the programmed amounts and delays (consistent with previous analyses, see Fantino & Davison, 1983; Logue et al., 1984, 1986). Table 2 presents the results of the regression analysis for each subject at each COD duration. An adjusted value of 3 (the percentage of variance accounted for by Eqs. (2) and (3)) is presented to compensate for the occasionally sometimes high values of r 2 generated by small samples (Pedhazur, 1982, pp. 147-149). Table 2 indicates that Eqs. (2) and (3) described the data reasonably well; only two of the adjusted values are below 0.60 (Subject 4 at the l-s COD and Subject 3 at the 30-s COD duration). The percentage of variance accounted for by Eqs. (2) and (3) did not vary significantly across COD durations: The values of ? are not significantly different between the l- and 15-s COD durations (t(4) - 1.14), between the l- and 30-s COD durations (t(4) = - .31), or between the 15- and 30-s COD durations (t(4) = 1.58). The values of sA/sD in Table 2 represent subjects’ sensitivity to variation in reinforcer amount relative to their sensitivity to variation in reinforcer delay. These values demonstrate that, in general, consistent with the results of Table 1 and Fig. 2 and the results of the analysis of variance on the response ratios, the subjects’ behavior appeared to be more sensitive to variation in reinforcer amount than to variation in reinforcer delay for the l-s and 15-s COD durations. Ignoring the signs of the values for sA/sn, this is also true for the 30-s COD duration. Figure 5 depicts changes in the amount and delay exponents as a function of COD duration. Figure 5 indicates that the absolute values of
KING AND LOGUE
434
TABLE 2 Results of the Regression Analysis for Each Subject and Each Changeover Delay Duration Subject
SD
s.4
SAISD
Adjusted i!
I 2 3 4 5 MC=)
0.49 2.44 -0.73 0.35 I .44 0.78cO.54)
l-s Changeover delay 0.17 2.35 0.07 34.86 8.11 -0.09 0.06 5.83 0.04 36.00 0.05(0.16) 17.43(7.39)
.91 .98 .85 .I3 .80 .73(0.15)
1 2 3 4 5 M(sE)
-0.02 4.32 2.27 1.94 0.66 1.83(0.75)
15-s Changeover delay 0.04 -0.55 -8.82 -0.49 0.04 56.75 -3.18 -0.61 -1.17 -0.56 8.85(12.06) -0.56(0.19)
.97 .8.5 .94 .93 .89 .92(0.02)
2.16 3.73 4.34 1.24 3.46 2.99(0.56)
30-s Changeover delay -0.60 -3.60 - 0.42 -8.88 0.30 14.47 -0.55 -2.25 - 1.01 - 3.43 -0.46(0.29) -0.74C3.97)
.83 .70 .57 .96 .93 .80(0.07)
1 2 3 4 5 M(W
+4
m----a
-I’
AMOUNT DELAY
I I CHANGEOVER
I I5 DELAY
T
30 (SECONDS)
FIG. 5. The amount and delay exponents (sA and so, respectively) as a function of the COD duration. The bars on each point indicate the standard error for that point.
CHANGEOVERDELAYANDSELF-CONTROL
435
the amount and delay exponents increased as the COD duration increased; subjects became more sensitive to both the amounts and delays of the reinforcers as the COD duration increased, consistent with the results of Table 1 and Fig. 2 and the results of the analysis of variance on the response ratios described above. However, the delay exponents became negative while the amount exponents became more positive as the COD duration increased. These results are partially supported by the results of two withinsubjects analyses of variance, one performed using the amount exponents as the dependent variable and one using the delay exponents, with COD duration as the within-subjects variable. The results of one analysis indicate that increasing the COD duration had no significant effect on the amount exponents (F(2, 6) = 3.23). The failure to find a significant COD effect for the amount exponent is due to the large variability in the individual estimates of sA. However, the analysis for the delay exponents indicates that the COD main effect is significant (F(2, 6) = 7.63); increasing the COD duration increased the absolute values of the delay exponents. DISCUSSION
The procedures employed in the present experiment were successful in obtaining consistent stable responding in adult human subjects in a relatively short period of time, perhaps because minimal instructions were used. Consistent with Logue et al. (1986), the results also indicate that the method for terminating a session had no significant effect on the response ratios. However, unlike Logue et al. (1986), the present results do not even suggest an effect of the termination criterion. The basis for such differences is not known. However, it is possible that the attempt here to equate session durations across groups is responsible for the present findings. The generalized matching law (Eq. (2)) seems to have described the present results reasonably well, with generally high values of the adjusted ?. However, in spite of the generally high percentage of variance accounted for (i.e., the good matching obtained), the matching law does not easily account for all of the findings. First, the matching law cannot readily explain the increase in the absolute value of both the amount and delay exponents as the COD duration increased (although the increase in the amount exponent was not significant). Second, the matching found at the 15 and 30-s COD durations is largely trivial, in that subjects generally exhibited virtually exclusive preference for the larger, more delayed reinforcer. The present results are incompatible with previous research that indicates that matching, and the fit of the generalized matching law, improves with increases in the COD duration (Catania & Cutts, 1963; de Villiers & Millenson, 1972; Hermstein, 1961; McSweeney, 1978; Shull & Pliskoff,
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1%7; Silberberg & Fantino, 1970). For example, McSweeney (1978) found that the fit of the matching law improved when the COD duration was increased from 0 to 5 or 0 to 20 s, although there was no improvement when the COD duration was increased from 5 to 20 s. In the present study, the fit of the generalized matching law did not improve when the COD duration was increased from 1 to 15 or 30 s. This is despite the fact that at the l-s COD duration, the subjects distributed their responding roughly equally between the two alternatives, which is similar to the responding found with no COD present (e.g., Hermstein, 1961). Several aspects of the data obtained here are consistent with the findings of Logue et al. (1986), in which subjects appeared to use a strategy that tended to maximize the total number of points earned. First, the human subjects in both studies consistently chose more of the larger, more delayed reinforcers than the smaller, less delayed reinforcers (i.e., consistently showed self-control). As stated above, given equal reinforcement rates for both alternatives, to maximize total received reinforcement, an organism should always choose the larger, more delayed reinforcer. Second, the values of $A, sn, and s*/s,, are generally within the same range in both studies, and indicate that subjects in both studies were relatively more sensitive to changes in reinforcer amount than to changes in reinforcer delay; in the present study, 13 of 15 of the values of this ratio show an absolute value greater than 1.0. Third, the results are consistent with optimal foraging theory, a theory based on maximization, in which travel time is analogous to COD duration (Baum, 1983; Kamil, Peters, & LindStrom, 1982). According to this theory, as travel time (COD duration) increases, subjects should stay longer on a given alternative. As predicted, at the l-s COD duration, the subjects distributed their responding roughly equally between the two alternatives, while at the 15- and 30-s COD durations the subjects tended to exhibit virtual exclusive preference for the larger, more delayed alternative, thereby maximizing overall obtained reinforcement. In summary, the present experiment indicates that adult human subjects consistently chose more of the larger, more delayed reinforcers at all COD durations, although this difference tended not to be large at the ls COD duration. The preference for the larger, more delayed reinforcers increased as the COD duration increased, such that, at the longest COD durations, the subjects tended to exhibit exclusive preference. In general, the matching law did not adequately describe the present results. The results of the present study are, however, qualitatively consistent with a strategy in which subjects attempted to maximize overall amount of reinforcement.
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REFERENCES Ainslie, G. W. (1974). Impulse control in pigeons. Journal of the Experimentnl of Behavior,
Analysis
21, 485-489.
Ainslie, G. W., & Herrnstein, R. J. (1981). Preference reversal and delayed reinforcement. Animal
Learning
& Behavior,
9, 476-482.
Bangert, S., Green, L., Snyderman, M., & Turow, S. (1985). Undermatching in humans to amount of reinforcement. Behavioral Processes, 10, 273-283. Baum, W. M. (1974). On two types of deviation from the matching law: Bias and undermatching. Journnl of the Experimental Analysis of Behavior, 22, 231-242. Baum, W. M. (1983). Studying foraging in the psychological laboratory. In R. L. Mellgren (Ed.), Animal cognition and behavior (pp. 253-283). New York: North-Holland. Buskist, W. F., & Miller, H. L. (1982). The study of human operant behavior, 1958-1981: A topical bibliography. Psychological Record, 32, 249-268. Catania, A. C., & Cutts, D. (1963). Experimental control of superstitious responding in humans. Journal of the Experimental Analysis of Behavior, 6, 203-208. de Villiers, P. (1977). Choice in concurrent schedules and a quantitative formulation of the law of effect. In W. K. Honig & J. E. R. Staddon (Eds.), Handbook of operant behavior (pp. 233-287). Englewood Cliffs, NJ: Prentice-Hall. de Villiers, P., & Millenson, J. R. (1972). Concurrent performances: A baseline for the study of conditioned anxiety. Journal of the Experimental Analysis of Behavior, 18, 287-294. Eisenberger, R., Masterson, F. A., & Lowman, K. (1982). Effects of previous delay of reward, generalized effort, and deprivation on impulsiveness. Learning and Motivation, 13, 378-389.
Fantino, E., & Davison, M. (1983). Choice: Some quantitative relations. Journal of the Experimental Analysis of Behavior, 40, l-13. Fleshier, M., & Hoffman, H. S. (1962). A progression for generating variable-interval schedules. Journal of the Experimental Analysis of Behavior, 5, 529-530. Green, L., Fisher, E. B., Perlow, S., & Sherman, L. (1981). Preference reversal and selfcontrol: Choice as a function of reward amount and delay. Behavior Analysis Letters, 1, 43-51. Grosch, J., & Neuringer, A. (1981). Self-control in pigeons under the Mischel paradigm. Journal of the Experimental Analysis of Behavior, 35, 3-21. Herrnstein, R. J. (1961). Relative and absolute strength of response as a function of frequency of reinforcement. Journal of the Experimental Analysis of Behavior, 4,267272. Hermstein, R. J. (1970). On the law of effect. Journal of the Experimental Analysis of Behavior,
13, 243-266.
Kamil, A. C., Peters, J., & Lindstrom, F. J. (1982). An ecological perspective in the study of the allocation of behavior. In M. L. Commons, R. J. Herrnstein, & H. Rachlin (Eds.), Quantitative analyses of behavior (Vol. 2, pp. 189-203). Cambridge, MA: Ballinger. Logue. A. W. (1987). Models of self-control: Toward an integration. Manuscript submitted for publication. Logue, A. W., & Chavarro, A. (1987). The effect on choice of absolute and relative values of reinforcer delay, amount, and frequency. Journal of Experimental Psychology: Animal
Behavior
Processes,
13, 280-291.
Logue, A. W., Chavarro, A., & King, G. R. (1987). Impulsiveness in humans: The effect of the schedule of reinforcement. Manuscript submitted for publication. Logue, A. W., & Mazur, J. E. (1981). Maintenance of self-control acquired through a fading procedure: Follow-up on Mazur and Logue (1978). Behavior Analysis Letters, 1, 131-137.
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Logue, A. W., Rodriguez, M. L., Pena-Correal, T. E., & Mauro, B. C. (1984). Choice in a self-control paradigm: Quantification of experience-based differences. Journal of the Experimental
of Behavior,
Analysis
41, 53-67.
Logue, A. W., Pena-Correal, T. E., Rodriguez, M. L., & Kabela E. (1986). Self-control in adult humans: Variation in positive reinforcer amount and delay. Journal of the Experimental Analysis of Behavior, 46, 113-127. Lowe, C. F. (1979). Determinants of human operant behavior. In M. D. Zeiler & P. Harzem (Eds.), Reinforcement and the organization of behavior (pp. 159-192). New York: Wiiey. Matthews, B. A., Shimoff, E., Catania, A. C., & Sagvolden. T. (1977). Uninstructed human responding: Sensitivity to ratio and interval contingencies. Journal of the Experimental
Analysis
of Behavior,
27, 453-567.
Mazur, J. E., & Logue, A. W. (1978). Choice in a “self-control” paradigm: Effects of a fading procedure. Journal of the Experimental Analysis of Behavior, 30, 11-17. McSweeney, F. K. (1978). Prediction of concurrent keypeck treadle-press responding from simple schedule performance. Animal Learning and Behavior, 6, 444-450. Pedhazur, E. J. (1982). Multiple regression in behavioral research. New York: Holt, Rinehart & Winston. Prelec. D. (1983). The empirical claims of maximization theory: A reply to Rachlin and to Kagel, Battalio, and Green. Psychological Review, 90, 385-389. Rachlin, H., & Green, L. (1972). Commitment, choice and self-control. Journal of the Experimental Analysis of Behavior, 17, 15-22. Shimoff, E., Catania. A. C., & Matthews, B. A. (1981). Uninstructed human responding: Sensitivity to low-rate performance to schedule contingencies. Journal of the Experimenkd Analysis
of Behavior,
36, 207-220.
Shull, R. L., & Pliskoff, S. S. (1967). Changeover delay and concurrent schedules: Some effects of relative performance measures. Journal of the Experimental Analysis of Behavior,
10, 5 17-527.
Silberberg, A., & Fantino, E. (1970). Choice, rate of reinforcement, and the changeover delay. Journal of the Experimental Analysis qf Behavior, 13, 187-197. Snedecor, G. W., & Cochran. W. G. (1967). Statistical merhods. Ames: Iowa State Univ. Press. Vaughan, W. (1982). Choice and the Rescorla-Wagner model. In M. L. Commons, R. J. Hermstein, & H. Rachlin (Eds.), Quantitative analyses of behavior (Vol. 2, pp. 263279). Cambridge, MA: Ballinger. Wurster, R. M., & Griffiths, R. R. (1979). Human concurrent performances: Variation of reinforcer magnitude and rate of reinforcement. Psychological Record, 29, 341-354. Received October 13, 1986 Revised April 28. 1987
AND
MOTIVATION
18, 421-438 (1987)
Choice in a Self-Control Paradigm with Human Subjects: Effects of Changeover Delay Duration GEORGE R. KING AND A. W. LOGUE State University of New York at Stony Brook The present experiment examined the choices of human subjects as a function of changeover delay (COD) duration. A self-control paradigm was used; subjects chose between larger, more delayed and smaller, less delayed reinforcers. The COD durations were 1 s, I5 s, and 30 s. The results indicated that at the I-s COD, the subjects distributed their responses approximately equally between the two response alternatives. However, at the 15-s and 30-s COD durations, the subjects tended to demonstrate virtually exclusive preference for the larger, more delayed reinforcer. Furthermore, increasing the COD duration significantly increased the subjects’ sensitivity to variation in reinforcer delay. Increasing the COD duration also increased the subjects’ sensitivity to reinforcer amount, but this effect was not significant. The results are qualitatively consistent with an interpretation that the subjects followed a strategy which attempted to maximize overall amount of reinforcement. 0 1987 Academic Press, Inc.
Self-control can be defined as the choice of a larger, more delayed reinforcer over a smaller, less delayed reinforcer (Ainslie, 1974; Eisenberger, Masterson, & Lowman, 1982; Grosch & Neuringer, 1981; Rachlin & Green, 1972). Similarly, the opposite of self-control can be defined as impulsiveness, the choice of a smaller, less delayed reinforcer over a larger, more delayed reinforcer. Within a self-control paradigm, a subject should always choose the larger, more delayed reinforcer in order to maximize total received reinforcement, given equal rates of reinforcement for both alternatives. A version of the original matching law (Herrnstein, 1970) has provided The research reported here was supported by NSF Grant BNS-8416302, principal investigator A. W. Logue. Some of the data reported here were presented at the Annual Meeting of the Association for Behavior Analysis in Milwaukee, WI, June 1986. Comments by J. Higa, J. Hinson, and F. K. McSweeney on a previous version of this paper are greatly appreciated. Requests for reprints should be sent to A. W. Logue, Department of Psychology, State University of New York, Stony Brook, NY 11794. 421 0023-9690187 $3.00 Copyright 0 1987 by Academic Press, Inc. All rights of reproduction in any form reserved.
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an adequate description of pigeons’ choices between reinforcers of different amounts and delays in a self-control paradigm (Ainslie & Hermstein, 1981; Green, Fisher, Perlow, & Sherman, 1981). According to this law,
(2)=($?)
(1)
where B, and B, represent the number of choices for reinforcers obtained from the left and right response alternatives, respectively, and A,, A,, D,, D, represent the amounts (sizes) and delays of the left and right reinforcers, respectively. Logue, Rodriguez, Pena-Correal, and Mauro (1984) proposed the following equation (similar to Baum’s, 1974, generalized matching law) to model individual differences in sensitivity to reinforcer amount and delay, and describe subjects’ choices when reinforcer amount and delay are varied:
(2) = (~)““(g””
(2)
where B,, B,, A,, A,, D,, and D, are defined as in Eq. (l), and sA and SD represent sensitivity to reinforcer amount and reinforcer delay, respectively. The Logue et al. modification provided a better description of their and others’ results (Ainslie & Herrnstein, 1981; Green et al., 1981; Mazur & Logue, 1978) than did the original matching law in investigations of self-control with pigeons. Experimentally naive adult humans often show large discrepancies from matching when choosing between reinforcers of different amounts (Bangert, Green, Snyderman, & Turow, 1985; Logue, Pena-Cot-real, Rodriguez, & Kabela, 1986; Wurster & Griffiths, 1979). For example, in Logue et al. (1986, Experiments 2, 3, 4, and 5), subjects consistently chose more of the larger reinforcers than predicted by the original matching law. However, an inadequate changeover delay (COD) may have been used in the Logue et al. study. A COD specifies a minimum period that must elapse after a changeover response from making a response on one alternative to making it on the other atlternative, or after the first response following reinforcement, before a subsequent response can deliver a reinforcer. A COD is used to decrease the probability of reinforcement of response sequences involving responses on both alternatives (de Villiers, 1977; Herrnstein, 1961). Previous research indicates that matching on concurrent schedules of reinforcer frequency, with equal amounts and delays of reinforcement for both alternatives, improves with the introduction of a COD (Catania & Cutts, 1963; de Villiers & Millenson, 1972; Herrnstein, 1961; McSweeney, 1978; Shull & Pliskoff, 1967; Silberberg & Fantino, 1970). For example, McSweeney (1978) varied the COD duration from 0 to
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20 s with pigeons responding on simple concurrent keypeck treadle-press schedules. She found that matching and the fit of the generalized matching law for concurrent schedules (Baum, 1974) improved when the COD duration was increased from 0 to 5 or 20 s, but that there was no consistent difference between the fits of the equation when the COD was increased from 5 to 20 s. Human subjects’ responding on concurrent schedules also seems sensitive to the imposition of a COD. Catania and Cutts (1963) used a concurrent variable interval extinction (cone VI ext) schedule to examine the effects of a COD on human choice behavior during a button pressing task. These researchers found that, without a COD present, superstitious response sequences developed involving responses to both alternatives. However, with the introduction of a COD between 2 and 15 s, responding on the extinction schedule was substantially reduced, and in some cases eliminated, thereby improving matching. Thus, the findings of Catania and Cutts (1963) indicate that, when humans respond on simple concurrent schedules, a COD has a similar effect on humans’ choice as it does on other organisms’ choice behavior. de Villiers (1977) has argued that for the matching relation to hold, a minimum COD duration must be in effect. The minimum COD value that produces matching seems to be species dependent, and must be empirically determined. Therefore prior failures to find matching with humans in a self-control paradigm, such as Logue et al. (1986), may be the result of the COD durations used in those experiments being too short (e.g., Logue et al., 1986, Experiments 2-5, used a 3-s COD). Previous findings have suggested that the criterion for ending a session may also affect matching in human subjects. The Logue et al. (1986) data suggested that their adult human subjects chose a greater number of the larger, more delayed reinforcers when sessions ended after 90 reinforcers than when sessions ended after 30 min, although the effect was not significant. It is not clear to what extent the Logue et al. use of a perhaps inadequate COD affected these findings. The present experiment examined humans’ choice behavior during a self-control paradigm as a function of COD duration. This experiment attempted to discern what effect increasing the COD duration would have on human subjects’ self-control behavior. The effects of COD duration have not previously been examined within a self-control paradigm, either with human or nonhuman subjects. The present experiment also attempted to determine if the fit of the generalized matching law for self-control (Eq. (2)) would improve, similar to McSweeney (1978), as the COD duration was increased. Finally, in the experiment described here, the criterion for determining session termination (session time or number of received reinforcers) was manipulated to determine if this procedural
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KING AND LOGUE O@@ Lights
Counter 5
Left Disc
Button c3
0
Righ Disc cc
FIG. 1. Diagram of the aluminum panel used in the present experiment. The letters G, W, R indicate the colors green, white, and red, respectively.
variation would have any effect on subjects’ choice behavior when reinforcer amount and delay, as well as COD duration, were manipulated. METHOD Subjects The subjects were experimentally naive adult human females, numbered 1, 2, 3, 4, and 5. All of the subjects were enrolled at the State University of New York at Stony Brook. Subject 3 was a graduate student in astronomy; the other five subjects were undergraduates majoring in the humanities and social sciences. No subject was a psychology major. Apparatus The experiment was conducted in a small room, 3.1 x 3.4 m, that could be illuminated by a standard 60-W light bulb. One wall of the room contained a one-way mirror that allowed observation of the subject. The room contained a chair and a desk. The experimental apparatus was placed on the desk, which was located against one wall. The apparatus was a wooden box, 122 cm wide, 66 cm deep, and 81 cm high. The front of the apparatus was painted black. An aluminum panel (see Fig. l), 35 cm wide and 51 cm high, on the front of the apparatus, contained the experimental stimuli and the manipulandum, an aluminum rod. The rod, 1.6 cm in diameter, protruded 14 cm from the panel, and was mounted 4 cm from the bottom of the apparatus and equidistant from the sides. The rod could be pushed to
CHANGEOVER
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425
the left or the right and required a minimum force of 18.8 N to operate in either direction. One translucent Plexiglas disc, 3.8 cm in diameter, was located to each side of the rod. The left disc could be transilluminated green, and the right disc red. A hole, 2.5 cm in diameter, located 5 cm above the rod, allowed access to a black button, mounted 3.8 cm behind the surface of the panel. Button presses were effective only when a light, located below the button, was lit. A counter was located 11.8 cm above the hole. On the top front edge of the apparatus were three DBDSl 1 7.5-W light bulbs. The left light was green, the center light white, and the right light red. Located behind the three lights was a loudspeaker that emitted continuous white noise to mask extraneous noises. A PDP-8/A computer, located in another room, controlled the experimental stimuli and recorded responses using a SUPERSKED program. Procedure
During each session, subjects were escorted into the experimental chamber. They were given the following minimal instructions as to what they were to do during the experimental session: Please read carefully. Do not ask for additional instructions. Your task is to earn as many points as you can. Each point is worth l/15 cents. For example, if you earn 1500 points you will be paid $1. You may touch anything on this panel to earn points. The session will begin when one or more lights come on, and will end when all the lights turn off. To minimize interference with the equipment, please leave all metal objects (watches, jewelry, etc.) with the experimenter for the duration of the session. All other personal property (coats, books, writing utensils, pocketbooks, etc.) should also be left with the experimenter. These materials will be returned promptly at the session’s end.
Instructions were kept to a minimum because previous research has shown that, under certain conditions, with minimal instructions humans may show more sensitivity to the scheduled contingencies (e.g., Matthews, Shimoff, Catania, & Sagvolden, 1977; Shimoff, Catania, & Matthews, 1981). Subjects were instructed to leave their watches and jewelry in order to ensure that no subject had access to a timing device during the session. The use of timing devices in experiments can yield valuable data (Lowe, 1979); however, conditions in the present experiment were kept as similar as possible to those employed with pigeons in order to help identify the origins of any differences between the behavior of human and nonhuman subjects. The experimenter then left the room, closed the door, and turned off the overhead light. There was no further communication between the subject and the experimenter until the end of the session. At the beginning of a session, the left disc was green, the right disc
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was red, and the white light on the top of the apparatus was lit. When a reinforcer was received for a rod push to the left, both discs and the white house light were darkened, and the left, green light on top of the apparatus was turned on. A reinforcer began with the programmed delay period (the delay to reinforcement), followed by the programmed period of access to reinforcement (the amount of reinforcement). During the reinforcer access period the green light remained on, the white light below the button was lit, and the button was enabled. Each press of the button added one point to the counter. Points exchangeable for money are used more frequently than any other reinforcer in operant research with humans (see Buskist & Miller, 1982, for references). After the reinforcer access period, both discs and the white light on top of the console were again lit. The sequence of events for reinforcement following a rod push to the right were similar to those for reinforcement following a rod push to the left except that the right, red light on top of the apparatus was lit instead of the left, green light. Rod pushes to the left or right were followed by a brief feedback click when the discs were lit; rod pushes when the discs were darkened had no effect and were not recorded. The amounts and delays used in the present experiment, grouped together in seconds for A,, A,, D,, D, (see Eq. (I)), were 5, 10, 0.1, 13; 6, 2, 6, 2; and 10, 5, 13, 0.1. At the end of each session each subject completed a questionnaire asking how she thought the button became available, and what she thought she did during the experiment. Subjects also received the money they had earned during the session. At the end of the entire experiment, subjects also received $1.25 for each session attended. Reinforcers were available according to a modified concurrent, independent VI 30-s VI 30-s schedule. The VI intervals for each schedule were constructed according to the method described by Fleshler and Hoffman (1962). The programming of the VI schedules was identical to the procedure used by Logue et al. (1984, Experiment 2) with pigeons, and also to the procedure used by Logue et al. (1986, Experiment 2-5) with humans, and was similar to the linear VI schedules used by Vaughan (1982), which generate response rates similar to traditional VI schedules (see discussion by Prelec, 1983). Each VI schedule timed continuously during a session. Each time an interval in one of the VI schedules timed out, the schedule continued, but a counter representing the number of available reinforcers was incremented. Each time a reinforcer was received, the appropriate counter was decremented. This type of concurrent VI VI programming tends to keep the overall reinforcer frequency for the two alternatives more similar than does the traditional concurrent VI VI programming (see Logue et al., 1984, Experiment 2), and also avoids the insensitive responding shown by human subjects on nonindependent concurrent VI VI schedules (see Logue, Chavarro, & King, 1987). A
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rod push toward a lit disc was followed by the reinforcer delay and reinforcer amount periods, if the counter for that VI schedule had a value of at least 1 and if the COD requirement had been fulfilled. The COD values used in the present experiment were 1 s, 15 s, and 30 s. For Group 1 (Subjects 1, 2, and 3) sessions ended after 30 min. For Group 2 (Subjects 4 and 5) sessions ended after 100, 50, or 25 reinforcers for the l-s, 15-s and 30-s COD conditions, respectively. These changes in the criterion number of reinforcers for ending sessions were made in order to keep session time for Group 2 roughly constant across COD conditions. In addition, these changes resulted in the number of reinforcers received by Group 2 in each COD condition being approximately the same as the number of reinforcers that subjects in Group 1 received in each COD condition. All subjects were exposed to all possible combinations of the three COD durations and the three values of A,, A,, D,, D,, for a total of nine conditions, close to the maximum number of conditions in which any subject would participate. Subjects were exposed to each of these conditions until their behavior satisfied a stability criterion. The stability criterion specified that a condition not be terminated for a given subject unless the values of the ratio of left rod pushes divided by right rod pushes in the last two half sessions were neither higher nor lower than the values of the same ratio for all previous half sessions of that condition (i.e., each session was divided in half, and the response ratios in each half session were neither higher nor lower than the value of the same ratio in all of the previous half-sessions, Logue et al., 1986). Table 1 shows the order of the conditions and the number of sessions for each condition for each subject. RESULTS General All subjects learned to use the panel efficiently during the first session. Table 1 presents the arithmetic means of the last two stable half sessions for the number of left and right responses and for the number of received reinforcers for each alternative, as well as the geometric means of the last two, stable, half sessions for the response ratios @r/B,, see Eq. (l)), for each condition. When, occasionally, no responses were made on one alternative, the standard transformation of log (x’ = X + 1) was used in order to calculate the geometric means of the response ratios (see Snedecor & Cochran, 1967, p. 329). Geometric means are a more appropriate measure for ratios than the arithmetic mean because the geometric mean is less sensitive to the extreme values easily generated by ratios (see, e.g., Logue & Chavarro, 1987, for similar analyses; and see below). Ratios of time spent responding on the two alternatives tended to produce
2
(5~13)/(10.0.1) (5~13)/(10~0.1) (5.13)/(10.0.1)
1
(10-0.1)/(5~13)
62)/P@ (6.2M2.6)
(10.0.1)/(5.13) (10.0.1)/(5.13)
(6~2)/(2.6)
(10.0.1)/(5.13) (5~13)/(10~0.1) (5.13)/(10.0.1) (5.13)/(10.0.1)
WV/(24 (6.2)/W)
(10~0.1)/(513) (10.0.1)/(5~13)
(6.2)/w9
M,W/(A;D,)
Subject
15 I 30 30 30 1 1 15 15 15 1 30 30 30 1 1 15 15
COD
Condition (in seconds)
5 3 4 2 2 2 3 2 2 2 7 3 2 2 4 6 3 3
Number of sessions 60 162 30 232 145 116 263 185 149 56 61 55 1623 1811 237 1313 2015 1395
Left B, 77 81 399 19 0 163 171 11 0 1570 395 1829 51 52 103 168 23 44
Right B,
Rod pushes
0.91 2.03 0.08 67.19 145.03 0.71 1.55 21.97 150.47 0.01 0.16 0.00 1204.25 1280.63 1.69 8.41 1450.59 32.46
B,l& 11 30 1 16 15 26 30 29 22 1 13 1 20 16 30 30 30 22
left
14 23 16 1 0 30 30 1 0 22 30 16 1 1 19 30 1 1
right
Reinforcers
and
3 21 0 1 0 13 23 1 0 0 15 4 0 0 4 23 1 1
Changeover responses
TABLE 1 Order of the Conditions. Number of Sessions per Condition, Mean Number of Rod Pushes. Response Ratios, Obtained Reinforcers, Changeover Responses for Each Subject
(10.0.1)/(5.13)
(6~2)/(2.6) (6.2)/(24
(10~0.1)/(5~13) (10.0.1)/(5.13)
(6.2)/W)
(10.0.1)/(5.13) (5.13)/(10.0.1) (5~13)/(10~0.1) (5~13)/(10~0.1)
62)AW (6.2)/W)
(10~0.1)/(5~13) (10.0.1)/(5.13)
62)/(2@
(10.0.1)/(5.13) (5.13)/(10*0.1) (5~13)/(10~0.1) (5.13)/(10.0.1)
(W/(2+4
(10.0.1)/(5.13) (10.0.1)/(5.13) 6.2)/(2.6)
WW(2.6)
(5.13)/(10~0.1) (5.13)/(10.0.1) (5~13)/(10~0.1)
15 15
30 30 30
15 15 15
30 30 30 1
15 15 15
30 30 30
15
4 2
2 4
5 4 2
56 128 40 354 249 81 359 561 322 2 57 3 87 50 58 111 88 109 49 131 0 1674 1923 249 1009 2060 2079
-
276 82 370 38 118 118 255 52 153 109 52 55 4 0 56 73 8 0 1078 125 1316 53 0 128 250 63 0
0.21 1.56 0.12 322.45 2.12 0.15 1.40 12.82 2.19 0.02 1.21 0.07 72.49 49.62 1.05 1.50 60.25 112.71 0.01 1.05 0.00 1261.52 1853.25 1.96 4.04 33.05 2079.84
4 30 2 19 12 26 30 30 18 0 23 1 14 15 22 23 24 25 1 21 0 14 15 25 23 24 25 0 20 22
0 24 24 15
20 25 15 2 6 29 30 2 9 25 22 14 1 0 23 22
5
4 202 0
:
F 7 0 0
40 0 0
i2 u
0 0
F
z
d
8 0 0 0 2 3 0
% 3 0
8
2 0 0
18 13 0 0 4 9 26
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KING
AND
LOCUE
results similar to the response ratios; therefore only the response ratio results are presented. The subjects did not appear to suspect why they were asked to remove their watches and jewelry, yet in postsession questionnaires they reported attempting to time the reinforcer amounts and delays. When the reinforcer amounts and delays were varied, subjects reported various strategies, but all were attempts to maximize the total number of points earned during the session. However, the subjects, as indicated by the postsession questionnaires, did not seem to realize that the changes in COD duration were time dependent. Subjects consistently reported that they had to make more responses in order to receive a reinforcer in the longer COD conditions. In other words, the subjects reported increases in the COD as an increasing ratio requirement. The significance level was set at p < .05, two tailed, for all statistical tests. Response
Ratios
A mixed-design analysis of variance was performed using the Base10 logarithmic transformations of the response ratios for each subject in each condition, with Group assignment (session termination criterion) as the between-subject variable, and COD duration and value ratio (the programmed amounts and delays inserted into the right side of Eq. (1) ((Afl,/A,.D,)) as the within-subject variables. The Base-10 logarithmic transformations of the response ratios were used as the dependent variable because of the large range of the untransformed response ratios (from 0.00 to 2079.84). Ranges of ratios are frequently problematic because ratios for which the numerator is larger than the denominator can vary between 1.0 and infinity, while ratios for which the numerator is less than the denominator can only vary between 0.0 and 1 .O. A logarithmic transformation helps to decrease this discrepancy. The results indicate that the COD (F(2, 6) = 13.88) and value ratio (F (2, 6) = 17.25) main effects are significant, as is the COD x value ratio interaction (F(4, 12) = 16.14). However, the group main effect is not significant (F(1, 3) = 0.01). Therefore, the data are collapsed across groups for all subsequent analyses. Overall, these results indicate that the subjects were sensitive to the experimental conditions, and that their behavior changed as a function of these conditions. These conclusions are supported by Fig. 2, which depicts the mean response ratios as a function of condition. Consistent with the dependent variable used in the analysis of variance, the response ratios are shown in logarithmic coordinates. Table 1 and Fig. 2 indicate that at the l-s COD subjects tended to distribute their responding approximately equally between the two response alternatives, but at the 15 and 30-s COD durations, the subjects tended to choose the larger, more delayed reinforcer virtually exclusively. An analysis of the subjects’ switching behavior
CHANGEOVER
DELAY
3\ gloo0F _
Ol-
431
f---..-. !! ?‘X’*,/T-Z !, 1: 6;
IOOO-
ilO8K
AND SELF-CONTROL
6 ,I’,i :I di
l -
COD
.----a A-----A
COD 15s COD 30s
Is
!
0.01’
’ ~5~13Mloal) VALUE
, (6~2Vl2.6) RATIO
I ~10~01,,~5431
((A,.DR)/(AR.DLi)
FIG. 2. Left divided by right responses (response ratios) as a function of the value ratio, separately for each COD duration. Note that the response ratios are plotted on logarithmic coordinates to attenuate the range problems associated with the use of ratios.
supports these conclusions (changing response alternatives after of a reinforcer was not counted as a changeover response). number of changeover responses per session is, for the l-s (SE = 2.2, N = 5); for the 15-s COD, 1.8 (SE = 1.2, N = the 30-s COD, 0.3 (SE = 0.4, N = 5).
the delivery The mean COD, 12.8 5); and for
Proportion of Obtained out of Programmed Reinforcers
Figures 3 and 4 present the proportion of reinforcers obtained out of total reinforcers programmed as a function of the value ratio, separately for each COD duration. Figure 3 presents the proportion of obtained out of programmed larger reinforcers as a function of the value ratio for each COD duration. Figure 4 presents the proportions of obtained out of programmed smaller reinforcers as a function of the value ratio for each COD duration. Figures 3 and 4 indicate that the proportions of both larger and smaller reinforcers obtained decrease as the COD duration increases; however, the decline is much larger for the smaller, less delayed reinforcers. Virtually none of the smaller, less delayed reinforcers were selected during the 15- and 30-s COD durations, consistent with the data presented in Table 1 and with the results of the mixed design analysis of variance. These conclusions are supported by two within-subjects analyses of
KING AND LOGUE
432
9 25
LO0.9-
8& 0.8av, k a 0.7 00” 5 g Ok 2 5 za gg
0.6 0.504-
OIX * Q 0.3 O-1 F :: 0.2$ a
-
CODlS
-
COD25s COD3oS
0.1 I
W3,1Kl.0.11 VALUE
1 (6.2!A2.6l RATIO
u0-0.11/(5~13)
((A,~D,MA,.D,))
FIG. 3. The proportion of obtained out of programmed larger reinforcers as a function of the value ratio, separately for each COD duration. The bars on each point indicate the standard error for that point.
VALUE
RATIO
((AL-D,MA,*D,))
FIG. 4. The proportion of obtained out of programmed smaller reinforcers as a function of the value ratio, separately for each COD duration. The bars on each point indicate the standard error for that point.
CHANGEOVER
DELAY
AND
433
SELF-CONTROL
variance performed using the proportion of obtained out of programmed reinforcers for each subject in each condition with COD duration and value ratio as the within-subject variables. One analysis of variance was conducted for the proportion of obtained out of programmed larger reinforcers, and one for the proportion of obtained out of programmed smaller reinforcers. The analysis of variance for the larger reinforcers indicates that the COD main effect is significant (F(2, 6) = 552.99), as is the value ratio main effect (F(2, 6) = 38.59). The COD x value ratio interaction is also signiticant (F(4, 12) = 9.24). The analysis for the smaller reinforcers indicates that only the COD main effect is significant (F(2, 6) = 154.35). Sensitivity to Variation in Reinforcer Amount and Delay In order to assess the subjects’ sensitivity to variation in reinforcer amount and delay over the value ratios used in the present experiment, a multiple linear regression was employed using Eq. (3), the Base-10 logarithmic transform of Eq. (2): 1%
@h/f&)
=
SA 1%
(AdA,)
+
SD log
WD,).
(3)
A least squares multiple regression analysis was performed separately for each COD duration and each subject using the programmed amounts and delays (consistent with previous analyses, see Fantino & Davison, 1983; Logue et al., 1984, 1986). Table 2 presents the results of the regression analysis for each subject at each COD duration. An adjusted value of 3 (the percentage of variance accounted for by Eqs. (2) and (3)) is presented to compensate for the occasionally sometimes high values of r 2 generated by small samples (Pedhazur, 1982, pp. 147-149). Table 2 indicates that Eqs. (2) and (3) described the data reasonably well; only two of the adjusted values are below 0.60 (Subject 4 at the l-s COD and Subject 3 at the 30-s COD duration). The percentage of variance accounted for by Eqs. (2) and (3) did not vary significantly across COD durations: The values of ? are not significantly different between the l- and 15-s COD durations (t(4) - 1.14), between the l- and 30-s COD durations (t(4) = - .31), or between the 15- and 30-s COD durations (t(4) = 1.58). The values of sA/sD in Table 2 represent subjects’ sensitivity to variation in reinforcer amount relative to their sensitivity to variation in reinforcer delay. These values demonstrate that, in general, consistent with the results of Table 1 and Fig. 2 and the results of the analysis of variance on the response ratios, the subjects’ behavior appeared to be more sensitive to variation in reinforcer amount than to variation in reinforcer delay for the l-s and 15-s COD durations. Ignoring the signs of the values for sA/sn, this is also true for the 30-s COD duration. Figure 5 depicts changes in the amount and delay exponents as a function of COD duration. Figure 5 indicates that the absolute values of
KING AND LOGUE
434
TABLE 2 Results of the Regression Analysis for Each Subject and Each Changeover Delay Duration Subject
SD
s.4
SAISD
Adjusted i!
I 2 3 4 5 MC=)
0.49 2.44 -0.73 0.35 I .44 0.78cO.54)
l-s Changeover delay 0.17 2.35 0.07 34.86 8.11 -0.09 0.06 5.83 0.04 36.00 0.05(0.16) 17.43(7.39)
.91 .98 .85 .I3 .80 .73(0.15)
1 2 3 4 5 M(sE)
-0.02 4.32 2.27 1.94 0.66 1.83(0.75)
15-s Changeover delay 0.04 -0.55 -8.82 -0.49 0.04 56.75 -3.18 -0.61 -1.17 -0.56 8.85(12.06) -0.56(0.19)
.97 .8.5 .94 .93 .89 .92(0.02)
2.16 3.73 4.34 1.24 3.46 2.99(0.56)
30-s Changeover delay -0.60 -3.60 - 0.42 -8.88 0.30 14.47 -0.55 -2.25 - 1.01 - 3.43 -0.46(0.29) -0.74C3.97)
.83 .70 .57 .96 .93 .80(0.07)
1 2 3 4 5 M(W
+4
m----a
-I’
AMOUNT DELAY
I I CHANGEOVER
I I5 DELAY
T
30 (SECONDS)
FIG. 5. The amount and delay exponents (sA and so, respectively) as a function of the COD duration. The bars on each point indicate the standard error for that point.
CHANGEOVERDELAYANDSELF-CONTROL
435
the amount and delay exponents increased as the COD duration increased; subjects became more sensitive to both the amounts and delays of the reinforcers as the COD duration increased, consistent with the results of Table 1 and Fig. 2 and the results of the analysis of variance on the response ratios described above. However, the delay exponents became negative while the amount exponents became more positive as the COD duration increased. These results are partially supported by the results of two withinsubjects analyses of variance, one performed using the amount exponents as the dependent variable and one using the delay exponents, with COD duration as the within-subjects variable. The results of one analysis indicate that increasing the COD duration had no significant effect on the amount exponents (F(2, 6) = 3.23). The failure to find a significant COD effect for the amount exponent is due to the large variability in the individual estimates of sA. However, the analysis for the delay exponents indicates that the COD main effect is significant (F(2, 6) = 7.63); increasing the COD duration increased the absolute values of the delay exponents. DISCUSSION
The procedures employed in the present experiment were successful in obtaining consistent stable responding in adult human subjects in a relatively short period of time, perhaps because minimal instructions were used. Consistent with Logue et al. (1986), the results also indicate that the method for terminating a session had no significant effect on the response ratios. However, unlike Logue et al. (1986), the present results do not even suggest an effect of the termination criterion. The basis for such differences is not known. However, it is possible that the attempt here to equate session durations across groups is responsible for the present findings. The generalized matching law (Eq. (2)) seems to have described the present results reasonably well, with generally high values of the adjusted ?. However, in spite of the generally high percentage of variance accounted for (i.e., the good matching obtained), the matching law does not easily account for all of the findings. First, the matching law cannot readily explain the increase in the absolute value of both the amount and delay exponents as the COD duration increased (although the increase in the amount exponent was not significant). Second, the matching found at the 15 and 30-s COD durations is largely trivial, in that subjects generally exhibited virtually exclusive preference for the larger, more delayed reinforcer. The present results are incompatible with previous research that indicates that matching, and the fit of the generalized matching law, improves with increases in the COD duration (Catania & Cutts, 1963; de Villiers & Millenson, 1972; Hermstein, 1961; McSweeney, 1978; Shull & Pliskoff,
436
KINGANDLOGUE
1%7; Silberberg & Fantino, 1970). For example, McSweeney (1978) found that the fit of the matching law improved when the COD duration was increased from 0 to 5 or 0 to 20 s, although there was no improvement when the COD duration was increased from 5 to 20 s. In the present study, the fit of the generalized matching law did not improve when the COD duration was increased from 1 to 15 or 30 s. This is despite the fact that at the l-s COD duration, the subjects distributed their responding roughly equally between the two alternatives, which is similar to the responding found with no COD present (e.g., Hermstein, 1961). Several aspects of the data obtained here are consistent with the findings of Logue et al. (1986), in which subjects appeared to use a strategy that tended to maximize the total number of points earned. First, the human subjects in both studies consistently chose more of the larger, more delayed reinforcers than the smaller, less delayed reinforcers (i.e., consistently showed self-control). As stated above, given equal reinforcement rates for both alternatives, to maximize total received reinforcement, an organism should always choose the larger, more delayed reinforcer. Second, the values of $A, sn, and s*/s,, are generally within the same range in both studies, and indicate that subjects in both studies were relatively more sensitive to changes in reinforcer amount than to changes in reinforcer delay; in the present study, 13 of 15 of the values of this ratio show an absolute value greater than 1.0. Third, the results are consistent with optimal foraging theory, a theory based on maximization, in which travel time is analogous to COD duration (Baum, 1983; Kamil, Peters, & LindStrom, 1982). According to this theory, as travel time (COD duration) increases, subjects should stay longer on a given alternative. As predicted, at the l-s COD duration, the subjects distributed their responding roughly equally between the two alternatives, while at the 15- and 30-s COD durations the subjects tended to exhibit virtual exclusive preference for the larger, more delayed alternative, thereby maximizing overall obtained reinforcement. In summary, the present experiment indicates that adult human subjects consistently chose more of the larger, more delayed reinforcers at all COD durations, although this difference tended not to be large at the ls COD duration. The preference for the larger, more delayed reinforcers increased as the COD duration increased, such that, at the longest COD durations, the subjects tended to exhibit exclusive preference. In general, the matching law did not adequately describe the present results. The results of the present study are, however, qualitatively consistent with a strategy in which subjects attempted to maximize overall amount of reinforcement.
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DELAY
AND SELF-CONTROL
437
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