mismatch model based on a statistical artefact?

Behaa. Ref. The-r. Vol. 28.No. 3,pp. 249-253,1990

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CASE HISTORY

Copyright C 1990Pergamon Press plc

AND SHORTER

Is the match/mismatch ARNOUD ARNTZ,’ MARCEL A.

COMMUNICATION

model based on a statistical

VAN DEN HOUT,’

artefact?

RICHEL LOUSBERG’ and

ERIK SCHOUTEN’

‘Department of Medical Psychology and ‘Department of Mental Health Sciences, Limburg University. P.O. Box 616, 6200 MD Maastricht. The Netherlands (Receiwd 6 December

1989)

Summary-In the match/mismatch model, recently formulated by Rachman and coworkers. it is stated that incorrectly predicted aversive experiences are generally followed by an immediate adjustment of the predictions concerning aversiveness of the next experience. This model can be considered to reflect a psychological process of the formation of expectations. In the present article it is argued that a simple HO model, assuming that predictions are completely randomly generated by the subject, may account for the same effects. This HO model is used in a stringent test of empirical data to determine if there are any effects of the discrepancy between prediction and experience on next prediction that exceed the effects explained by the HO model. Although the HO model produces effects very similar to the empirically observed effects, there is clear support for the hypothesized influence of the discrepancy between prediction and experience. Therefore, the model appears to reflect ‘real’ psychological processes and not chance findings.

INTRODUCTION In 1985 and 1986 Rachman and coworkers published a series of articles on the processing of experiences of fear. emphasizing the part played by predictions of fear (Rachman & Levitt, 1985; Rachman & Lopatka. 1986a.b). Central to their ideas are the effects of experiences which are inaccurately predicted. In the laboratory they asked Ss to predict how much fear they would experience when confronted with a fear-provoking stimulus. Following exposure to the stimulus, Ss were asked to rate the amount of fear actually experienced and to make a prediction for the next trial. It was found that overpredictions of fear (defined by predicted fear that is larger than actually experienced) were generally followed by decreases in predictions: Ss decreased their fear predictions for the next trial. Following underpredictions (defined as predicted fear less than experienced fear), Ss generally increased their predictions. After a correct prediction (a match) Ss generally did not change their predictions. These findings form the core of the match/mismatch model. The model states that after mismatches (inaccurate predictions) the predictions are immediately corrected (overpredictions are followed by decreases in predictions, underpredictions are followed by increases), whereas matches (accurate predictions) do not lead to changes of prediction. The model is stated generally, and appears to describe the effects of inaccurate predictions on next expectations not only for fear-provoking stimuli, but for all kinds of stimuli. Further research has indeed shown that the model also holds for pain (Amtz & van den Hout, 1988; Rachman & Lopatka, 1988; Arntz, Heijmans & Van Eck. 1990) and for aversive sounds (Lavy. van den Hout & Arntz. 1990). Probably, it also holds for pleasant experiences. The central assumption of the model is that the inaccuracy of a prediction has an immediate influence on the next prediction. Appealing as the idea might be, it is not that easy to test it empirically. Spontaneous predictions and experiences of fear, pain, aversiveness etc. are outside the experimenters’ control and may be statistically interrelated in such a way that it is difficult to find the right statistical testing procedure. In an attempt to bypass this problem. Arntz & van den Hout (1988) tried to experimentally control the mismatch by unexpectedly increasing the level of painful electric shock. It was found that Ss increased their predictions for the next shock immediately, by which the model was supported. In further experiments using this manipulation this finding was replicated (Arntz & Lousberg, 1990; Arntz, Van Eck, de Jong & van den Hout. 1990). Although the experimentally controlled mismatches led to effects that are predicted by the model, the issue remains whether spontaneous mismatches do lead to ‘real’ corrections of predictions. Up to now. the attempts to test this hypothesis used statistical procedures (goodness of fit tests, crosstabulation with x” tests) that did not adequately control for possible chance effects (e.g. Rachman & Lopatka, 1986a; Arntz & van den Hout, 1988). To get more insight into the problem we proposed a simple statistical model, which represents the null hypothesis. The HO model Let us assume that predictions and reports of the experience are independent, that they have the same statistical distribution. and that predictions are randomly generated by the S (that is, they do not reflect any ‘real’ psychological process: predictions are not influenced by the experience).* Let us assume further-for the sake of simplicity-that l/3 of the predictions can be classified as ‘high’ (H), l/3 as ‘medium’ (M) and l/3 as ‘low’ (L): and that the same classification can be made for the experiences. The random combinations of predictions and experiences can be classified as overpredictions [(H, M), (H. L), (M, L)]. as matches [(H, H), (M, M), (L, L)], and as underpredictions [(M. H). (L, H),

*Whether BKTX,3--8

experiences

are randomly

generated

or have a ‘real’ basis is not important 249

for the model

under

HO.

250

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(L, M)]. It will be clear that the expected probabilities of these classihcations are I;3 for each (l/3 is overprediction, etc).* Since we assumed that predictions are randomly generated. after each type of (mis)match l/3 of the predictions will be ‘H’, 1!3 ‘M’ and lj3 ‘L’. Computation shows that after an overprediction, the chance that the next prediction will be lower than the previous prediction is S/9: that is. considerably higher than the chance that an overprediction is followed by no change in prediction (l/3) or by an increase (l/9).? By the same logic, the chance that after an underprediction the next prediction will be higher is 519, etc. These expected frequencies are depicted in Fig. I and are remarkably similar to the patterns that are empirically observed. The expected pattern derived from HO resembles the observed patterns. This pattern of course reflects the ‘regression to the mean effect’ that occurs when a measurement is repeated after an extreme outcome as far as there is a random error in measurement: after a high prediction, it is most probable that the experience will be relatively lower (thus, that the prediction will be an overprediction). This holds also for the next prediction. which will also with (the same) high probability be lower. Although the predictions are assumed to be statistically independent,$ overpredictions and decrease in predictions are related by the nature of the random process generating the predictions. and the same holds of course for underpredictions and increases in predictions. Therefore. the question arises whether the observed effects of spontaneous mismatches reflect a psychological process or are bdSed on regression to the mean. If there is any psychologically meaningful process underlying changes after mismatches, it must be demonstrated that changes in predictions after mismatches are more strongly influenced by the discrepancy between prediction and experience than can be predicted by a regression of the main effect alone. In the following, two studies will be described that tried to test the hypothesis that there is such a process. The studies use real data obtained in a study with agoraphobic patients (van den Hout et al., 1990) and in a laboratory study on repeated painful experiences (Arntz & Lousberg. 1990). STUDY

1

The data in this study were gathered from agoraphobic patients treated by means of exposure in ciao at the local mental health centre. Immediately after each exposure exercise, each patient rated anxiety experienced (on a 100 mm VAS) during

*It is interesting to note that these frequencies approximate the empirically observed frequencies very well (see Rachman & Lopatka, 1986a; Arntz & van den Hout, 1988). There are. however, exceptions, in that the number of overpredictions is much higher in clinical problems (e.g. Arntz, Heijmans & Van Eck, 1990). toverpredictions are combinations of (H. M), (I-I. L) or (M, L), all with a chance of l/3. After (H. M). 113 of the predictions will be H. l/3 M and I/3 L. The last two predictions are lower than the previous predictions, each with a chance of 113 x Ii3 = 119. The (prediction-experience-next prediction) sequences (H, M. M) and (H, M, L), as well as (H. L, M), (H. L, L) and (M, L, L) are overpredictions that are followed by decreased prediction. Each has a chance of I/3 x l/3 = 119. Thus, the chance of decreased prediction after overprediction is the sum of the chances of these five sequences, 519. $Generally, the regression of the mean effect occurs proportionally to the independent random error of the observations. Here it is assumed that each observation is a completely random ‘error’.

319

3/9

Match

~,m,u

Increased

Predrctions Fig. 1. Probabilities of increase, ove~rediction in random data

3/9

No

change

Decreased Predrctrans

no change, and decrease in prediction after underprediction, match and (HO model). The distribution closely resembles the empirically found distributions.

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the exposure exercise. and then predicted anxiety of the next exercise. There are 15 patients, who 211 rated the first 10 exposure exercises of their treatment hierarchy. Because of missing data. there were 144 valid observations of predicted anxiety, reported anxiety. and predictions of anxiety for the next exercise. For further details the reader is referred to van den Hout, Arntz. Hoekstra and Schouten (1990). In this study it was assumed that each S generated his/her predictions randomly from his/her own distribution. The effects of mismatches on next predictions under this null hypothesis were tested by taking within each S all possible combinations of two predictions and one experience (complete randomization). A criterion of a 7 mm* difference between prediction (P) and experience (E) was used for classifying combinations as underpredictions (P - E c -7 mm). overpredictions (P - E > 7 mm) or matches (- 7 mm < P - E Q 7 mm). The same criterion was used for classifying increases in predictions and no change (-7mm7mm) The randomization was used to estimate the HO distribution of 144 (mis)matches. The randomization did not produce exactly the same frequencies of underpredictions. overpredictions and matches as the empirical distribution. The randomized distribution resembled the empirically distribution. If it is submitted to a xz test. as was done in the Arntz and van den Hout study (1988). the result is significant [x’(4) = 17.81. P < 0.011, despite the fact that it was based entirely on chance. The distribution produced by the randomization procedure was used as a reference to test the empirically observed distribution in a I’ test (the frequencies produced by the randomization were used as estimates of the expected frequencies under HO). The empirical relationship was stronger than the relationship produced by the randomization [x’(4) = 16.33, P < O.Ol]. One could argue that the numbers of underpredictions, overpredictions and matches should be equal in both distributions. Therefore, the randomization was used to estimate the HO distribution assuming the same numbers of underpredictions. overpredictions and matches as in the empirical findings. The resulting distribution is depicted in Fig. 2. 2s is the empirical distribution. As can be seen in the figure, the empirical distribution is still stronger than the HO distribution [x:(4) = 12.60, P = 0.013]: after an underprediction. there were more increases in prediction and fewer decreases in prediction than expected under HO; whereas after overprediction, there were more decreases in prediction and fewer increases in predictions. However, the differences are small. Thus. there is some evidence that the patients were more influenced in forming new predictions by their experiences than can be explained by random processes only. STUDY

2

The data in this study are from 46 normal 5s who participated in a laboratory study on pain (Arntz & Lousberg. 1990). Each S received 20 painful electric shocks and rated experienced and predicted pain on 100 mm VASs. As in Study 1, it was assumed that each S generated predictions randomly from his/her own private distribution. It was decided to use a different statistical procedure to control for the regression effect that can be expected under HO. By means of a stepwise multiple regression analysis we tested if the experience of the S added any significant information to the regression equation, when the previous prediction level was controlled for (that is, controlling for the regression to the mean ellect). The variable expressing the regression effect was the individual difference between prediction P, and the mean (individual) prediction level M. The change in prediction was expressed as P, _ , - P,. Thus, first the regression model, P ,+,-P,=&,+p,x(P,-M)

(1)

was tested. It was expected that /J, would be negative (a high P, would be generally followed by a smaller P,, ,: a small P, by a larger P,+ ,). And indeed, this was found, as is shown in Table 1. Again, the regression effect seems to explain the match/mismatch model. However. entering the discrepancy between prediction P, and experience E, into the equation dramatically changed the equation. as is shown in Table 1. Thus. in the regression mode! P I+, the most important states.

information

is yielded

- P,= Br,+ B, x P, - Ml + P: x P - E,) by the discrepancy

between

prediction

and experience,

(2) precisely

2s

the model

DISCUSSION Although the HO model, assuming no ‘real’ infuence of discrepancy between prediction and experience on next prediction, produced effects that are hypothesized by the match/mismatch model, there is clear evidence that the discrepancy is important in the adjustment of predictions as empirically found. That is. Ss generally adjust their predictions if there is such a discrepancy; even if they made an extreme prediction, they did not adjust their predictions if the experience had been correctly predicted. Furthermore. the regression analysis clearly indicates that the size of adjustment of prediction is not so much related to the extremeness of the prediction, as to its inaccuracy. Therefore, there is convincing evidence that the match/mismatch model reflects a ‘real’ psychological process and not some chance process. Given the important part that is attributed to predictions in modern learning theory (e.g. Gray, 1985). and in cognitive theories. this is an important finding. It supports the notion that predictions are more than epiphenomena. With respect to fear. anxiety. pain and aversive experiences in general, it is supposed that predictions play an essential part in such areas as dishabituation. anticipatory anxiety. excessive emotional suffering, escape and avoidance behaviour. The match/mismatch model offers insight in the way predictions are changed. Of considerable importance are the conditions that do not lead to the adjustment of inaccurate predictions, 2s can be observed in clinical problems (Rachman & Bichard, 1988: Arntz, Van Eck & Heymans, 1990). It is interesting to note that both the match/mismatch model and the HO (random) model would predict that very high inaccurate predictions should decrease quickly. In many climcal cases, however, this is not the case. which gives further evidence that the HO model cannot be adequate and that there are psychological influences on expectation,

*This criterion is higher than the 2 mm criterion proposed by Rachman. It was determined empirically in order to obtain approximately equal frequencies in each cell of the cross tabulation. With the 2 mm criterion the number of matches was very small. A reason for this deviation from laboratory studies may be the larger interval between ratings of prediction and experience in this study (up to several days).

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Under-prediction

Match

Over-predictcon

Increased predictrons

No change

Decreased predictrons

Fig. 2. Distributions of changes in prediction of fear after (mis)-matches (1) as found after individually randomizing the predictions of agoraphobic patients (solid bars) and (2) as empirically found in the sample (dotted bars). The numbers of underpredictions, overpredictions and matches in the randomized data were held equal to the empirical numbers. Although the randomization produced a distribution much alike the empirical distribution, the empiricai findings differ significantly from the random distribution, supporting the match~mismatch model h’(4) = 12.60. P = 0.013].

The results of Study 1 gave less evidence for the model than those of Study 2. A number of reasons may be offered. In Study 1, the patients had to make predictions of 10 different exercises, which may have produced excessive error variance, whereas in Study 2, Ss had to make predictions about the same pain stimulus. fiowever, the most important reason is probably that in Study 1 patients had to make predictions several days before the exercise. whereas in Study 2 the time interval between prediction and experience was < 1 min. Since predictions probably are state dependent. asking Ss to predict how anxious they will be several days before the event is an imprecise procedure. Therefore, stronger support may have been found if the patients had been asked to rate predictions just before the exercise. Finally, our research indicates that more stringent tests for analyzing the effects of spontaneous mismatches should be used than has been done in the past. It should be kept in mind that under HO the effects seem to support the model, whereas

Table

I. Regression

analysis of changes in prediction repression to the mean

controlling

a

i

d.f.

P

step 1 (R?=O.ZI) P, - M

-0.36

~ 15.72

918

<:10--j

Step 2 (AZ= P,- M P,-E,

-0.14 0.54

-7.49 27.40

917 91-I

<1o-6 I: 10-j

Variable

for

0.57)

P, - M denotes the difference between prediction of trial i and the mean prediction of the S. This factor controls for regression to the mean. P, - E, denotes the discrepancy between prediction and experience of trial i. This factor represents the hypothesized mismatch effect. The dependent variable was P,, , -P,. the change in next prediction.

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the model (if it does more than describe chance findings) is not implied. More stringent tests can be done in a number of ways. Probably the most simple way is to employ the regression analysis as described above, where the regression to the mean effect is controlled. If an analysis of a cross-tabulation is needed, the probabilities under HO should be estimated (for instance by randomization) and used as a reference to test the empirical distribution. REFERENCES

Arntz, A. & Hout van den, M. (1988). Generahzability of the match/mismatch model of fear. Behauiour Research and Therapy, 26, 207-223. Arntz, A. & Lousberg, R. (1990). The effects of underestimated pain and their relationship to habituation. Behauiour Research and Therapy. 28, 15-28. Arntz, A., Heijmans, M. & Eck Van, M. (1990). Predictions of dental pain: The fear of any expected evil is worse than the evil itself. Behaoiour Research and Therapy, 28, 2941. Arntz, A., Eck Van, M., Jong de, P. & Hout van den, M. (1990). The relationship between underpredicted pain and escape. Behaviour Research and Therapy, 28. 87-90. Gray, J. A. (1975). Elements of a two-process theory of learning. London: Academic Press. Hout van den. M. A., Arntz, A., Hoekstra. R. & Schouten, E. (1990). In preparation. Lavy, E., Hout van den, M. A. & Arntz, A. (1990). Prediction of aversive events. Effects of matches and mismatches in agoraphobic and neutral situations. Behariour Research and Therapy, 28, 43-50. Rachman. S. & Bichard. S. (1988). The overurediction of fear, Clinical Psychology Review. 8. 303-313. Rachman, S. & Levitt, K. (1‘985).‘Panics and their consequences. Behavioir Research & Therapy, 23, 58540. Rachman, S. & Lopatka, K. (1986a). Match and mismatch in the prediction of fear--I. Behauiour Research & Therapy, 24, 387-393. Rachman. S. & Lopatka, K. (1986b). Match and mismatch of fear in Gray’s theory--II. Behauiour Research & Therapy, 24, 395401. Rachman. S. & Lopatka, K. (1988). Accurate and inaccurate predictions of pain. Behauiour Research & Therapy, 26, 291-296.