Explaining individual differences in cognitive processes underlying hindsight bias

Abstract

After learning an event’s outcome, people’s recollection of their former prediction of that event typically shifts toward the actual outcome. Erdfelder and Buchner (Journal of Experimental Psychology: Learning, Memory, and Cognition, 24, 387–414, 1998) developed a multinomial processing tree (MPT) model to identify the underlying processes contributing to this hindsight bias (HB) phenomenon. More recent applications of this model have revealed that, in comparison to younger adults, older adults are more susceptible to two underlying HB processes: recollection bias and reconstruction bias. However, the impact of cognitive functioning on these processes remains unclear. In this article, we extend the MPT model for HB by incorporating individual variation in cognitive functioning into the estimation of the model’s core parameters in older and younger adults. In older adults, our findings revealed that (1) better episodic memory was associated with higher recollection ability in the absence of outcome knowledge, (2) better episodic memory and inhibitory control and higher working memory capacity were associated with higher recollection ability in the presence of outcome knowledge, and (3) better inhibitory control was associated with less reconstruction bias. Although the pattern of effects was similar in younger adults, the cognitive covariates did not significantly predict the underlying HB processes in this age group. In sum, we present a novel approach to modeling individual variability in MPT models. We applied this approach to the HB paradigm to identify the cognitive mechanisms contributing to the underlying HB processes. Our results show that working memory capacity and inhibitory control, respectively, drive individual differences in recollection bias and reconstruction bias, particularly in older adults.

Appendices

Appendix 1: Additional analyses using a normally distributed error term

To test whether our results would hold when we assumed that the error terms of the underlying latent variables (e.g., b ^* _km ) were normally rather than logistically distributed, we reconducted our primary analyses with older adults and younger adults using an ogive link function. We modeled the core parameters (b _k , r _Ck , r _Ek ) as the following ogive functions of the cognitive covariates:

$$ \begin{array}{c}\hfill {b}_k=\Phi \left({\alpha}_{\mathrm{b}}+{\beta}_{\mathrm{b}1} X{1}_k+{\beta}_{\mathrm{b}2} X{2}_k+\dots +{\beta}_{\mathrm{b}\mathrm{C}} X{C}_k\right)\hfill \\ {}\hfill {r}_{\mathrm{C} k}=\Phi \left({\alpha}_{\mathrm{con}}+{\beta}_{\mathrm{con}1} X{1}_k+{\beta}_{\mathrm{con}2} X{2}_k+\dots +{\beta}_{\mathrm{con}\mathrm{C}} X{C}_k\right)\hfill \\ {}\hfill {r}_{\mathrm{E} k} = \Phi \left({\alpha}_{\exp }+{\beta}_{\exp 1} X{1}_k+{\beta}_{\exp 2} X{2}_k+\dots +{\beta}_{\mathrm{expC}} X{C}_k\right)\hfill \end{array}, $$

(A1)

where α and β _c , c = 1, . . . , C, are the parameters to be estimated, Xc _k , c = 1, . . . , C, denotes the value of participant k on the variable Xc, and Φ(.) represents the cumulative distribution function of the standard normal distribution. We thus refer to this model as the ogive HB13 model with core parameters b _k , r _Ck , r _Ek .

Model evaluation

Our model evaluation comparing the AIC values and Akaike weights for the ogive HB13 model against the remaining three candidate models (cf. Table 4 above) revealed that the ogive HB13 model was the preferable model in both age groups. In older adults, the rounded AIC value for the ogive HB13 model was only slightly worse than the AIC value for the logistic HB13 model (AIC logistic HB13 = 12,027; AIC ogive HB13 = 12,029). In younger adults, the rounded AIC values for the ogive HB13 model and the logistic HB13 model were the same (AIC = 12,412). For both age groups, the probability estimate that the ogive HB13 model was the best of our four candidate models was very close to 1. Thus, the ogive model and the logistic model provide equally good approximations to our data, and both outperform the other three candidate models.

Older-adult ogive HB13 model tests

To test whether any of the cognitive variables independently predicted recollection ability or reconstruction bias in older adults, we bootstrapped the 95 % confidence intervals for the beta coefficients on each cognitive covariate for each of the core parameters (r _Ck , r _Ek , and b _k ) in the ogive HB13 model. As is shown in Table 6, the findings from our logistic HB13 model held: Episodic memory was the only significant predictor of r _Ck , β = 0.03, 95 % CI = [0.01, 0.06], p _b < .001; both episodic memory, β = 0.04, 95 % CI = [0.02, 0.06], p _b < .001, and inhibition, β = –0.01, 95 % CI = [–0.02, –0.01], p _b < .001, were significant predictors of r _Ek ; working memory capacity was a marginally significant predictor of r _Ek , β = 0.04, 95 % CI = [–0.001, 0.07], p _b = .10; and inhibition was the only significant predictor of b _k , β = 0.03, 95 % CI = [0.01, 0.04], p _b < .001.

Table 6 Model tests for the ogive HB13 model by age group

Younger-adult ogive HB13 model tests

To test whether any of the cognitive variables independently predicted recollection ability or reconstruction bias in younger adults, we bootstrapped the 95 % confidence intervals for the beta coefficients on each cognitive covariate for each of the core parameters (r _Ck , r _Ek , and b _k ) in the ogive HB13 model. As is shown in Table 6, we once again replicated the findings from our logistic HB13 model: On the basis of 500 bootstrapped samples, the 95 % confidence intervals for the beta coefficients revealed that none of the cognitive covariates significantly predicted b _k , r _Ck , or r _Ek . Taken together, these results suggest that replacing logistically distributed errors with normally distributed errors does not change the substantive conclusions.

Appendix 2: Aggregate analysis using the HB13 model

We analyzed the data using the HB13 multinomial model developed by Erdfelder and Buchner (1998). To assess model fit, we compared the aggregate HB13 model against the general multinomial model for 2 · 10 data categories using parametric bootstrapping. In accordance with prior work (e.g., Bayen et al., 2006), we set an alpha level of .01 for the model fit test because we did not want to reject a model that only slightly differed from the comparison model. The model evaluation was based on 6,040 data points (122 participants · 50 items – 60 missing responses). Power analysis indicated that we had high power (.99) to detect even small deviations (w = .1; Cohen, 1988) from the general multinomial model. On the basis of 500 bootstrapped samples, we found an acceptable model fit, G ²(10) = 31.27, p _b = .01.

Table 7 presents the results of the parameter tests across age groups, and Table 8 reports the parameter estimates and their standard errors by age groups. We used the conventional alpha level of .05 to test for statistical differences in the parameters. As expected, on the basis of 500 bootstrapped samples, our analysis revealed significant age differences in overall recollection ability—that is, parameters r _C and r _E. In comparison to younger adults, older adults had poorer recollection of the OJs for both control and experimental items. Furthermore, older but not younger adults demonstrated a significant recollection bias, defined as poorer recollection of the OJ for experimental as compared to control items. Descriptively, the recollection bias was slightly larger in older adults (.04) than in younger adults (.03). Bayen et al. (2006) also observed recollection biases for both younger and older adults, but the bias was not statistically significant for younger adults and fell short of statistical significance for older adults. Perhaps our significant recollection bias finding in older adults was due to our relatively large sample of 62 younger and 60 older adults, which was more than double the sample of Bayen et al. (2006; 26 younger and 26 older adults).

Table 7 Parameter tests using the aggregate HB13 model

Table 8 HB13 model parameter estimates (and standard errors) by age group

Older adults demonstrated a larger reconstruction bias than did younger adults; however, this difference did not reach statistical significance (p _b = .23). Although Bayen et al. (2006) found a significant age difference in reconstruction bias, this difference did not reach statistical significance in Bernstein et al. (2011, p = .18). Nevertheless, in all three studies, there was at least a descriptive trend toward older adults demonstrating larger reconstruction bias than did younger adults. Finally, we observed a significant age difference in parameter c, with older adults demonstrating significantly more CJ adoptions than younger adults. This is consistent with Bayen et al.’s (2006, Exp. 2) finding of increased CJ adoptions when the CJ is accessible during ROJ. Overall, our findings of age differences in the core HB parameters are generally consistent with those of prior work.

Appendix 3: List of questions (and correct answers in metric units) used in the memory judgment task

• 1. At what temperature does copper melt? (2,415 Celsius)

• 2. How high is the Statue of Liberty including its base? (93 meters)

• 3. What year did the mutiny on the Bounty occur? (1790)

• 4. What is the distance between New York and Los Angeles (by road)? (4,546 kilometers)

• 5. In what year was the monkey wrench invented? (1841)

• 6. In what year was the harmonica invented? (1821)

• 7. How long is the Rhine River? (1,320 kilometers)

• 8. What year did the Hundred Years’ War begin? (1339)

• 9. What year was the lightning rod invented? (1752)

• 10. How long is the Great Wall of China? (3,460 kilometers)

• 11. What year were X-rays discovered? (1895)

• 12. At what speed must wind blow to be classified as a Moderate Gale Force? (51 kilometers per hour)

• 13. What is the average depth of the Pacific Ocean? (3,940 meters)

• *14. At what temperature does tin melt? (2,930 Celsius)

• 15. On average, how many days is a female elephant pregnancy? (631 days)

• 16. How long is the Amazon River? (6,556 kilometers)

• 17. How long is the Mississippi River? (3,779 kilometers)

• 18. What year did William Herschel discover the planet Uranus? (1781)

• 19. In what year was Jane Austin’s Pride and Prejudice first published? (1813)

• 20. What is the average temperature of the Antarctic winter? (-68 Celsius)

• 21. What is the highest temperature ever measured on Earth? (57 Celsius)

• 22. What percentage of the world’s population was under the age of five in 1995? (7.7 %)

• 23. What year was Leonardo da Vinci born? (1452)

• 24. How long is the world’s longest bridge? (38.42 kilometers)

• 25. What year did Sir James Dewar, an English chemist, invent the thermos flask? (1873)

• 26. When was the first reflecting telescope developed? (1671)

• 27. How many carats is the world’s largest reported diamond? (3,106 carats)

• *28. What is the official land speed record for a land vehicle? (1,019 kilometers per hour)

• 29. How many days does the planet Mercury take to make one trip around the sun? (88 days)

• 30. How long is an international nautical mile? (1,852 meters)

• 31. What percentage of the world’s population lived in Africa in 1994? (12.4 %)

• 32. How many plays did William Shakespeare write? (37 plays)

• 33. When travelling 97 kilometers per hour in a car, how much room should you allow yourself to brake? (83 meters)

• 34. What is the distance between Tokyo and Chicago (by air)? (10,137 kilometers)

• 35. What year was the parking meter invented? (1935)

• 36. What year was radiotelegraphy invented? (1899)

• 37. What year did Leonardo da Vinci create Mona Lisa? (1503)

• *38. In what year was Harvard University founded? (1686)

• 39. What year did Franz Joseph I, the emperor of Austria, die? (1916)

• 40. What year did Albert Einstein formulate the theory of relativity? (1903)

• 41. What is the diameter of the planet Mars? (6,787 kilometers)

• 42. How high is the highest point on Mount Kilimanjaro? (5,895 meters)

• 43. What year were the first modern-day Olympic games celebrated? (1896)

• 44. What percentage of the world’s population lived in Europe in 1994? (9 %)

• 45. How many muscles does the human body have? (639 muscles)

• 46. What percentage of the human body is composed of nitrogen? (8.5 %)

• 47. What year was the first mailbox invented? (1653)

• 48. When was slavery officially abolished in the United States? (1865)

• 49. How many films did Alfred Hitchcock direct? (56 films)

• 50. In what year was William Shakespeare’s The Tragedy of King Lear first published? (1608)

• 51. In what year was Socrates born? (470 BC)

• 52. In what year was Daniel Defoe’s “Robinson Crusoe” first published? (1719)

• 53. What year was the mechanical loom invented? (1785)

• 54. How many detective books did Agatha Christie write? (67 books)

^* Note: The items marked by an asterisk were excluded from the analyses because they violated the model’s symmetry assumption.