Problem set 11

Complete this task in teams of up to three students.

Submission information: please submit on ZoneCours

• a PDF report
• your code

Task 1

Liu et al. (2022+) postulated in their Experiment 5b that the underestimation of the appreciation of initiators relative to recipients was mediated by the degree of surprise of the recipient. Their data can be obtained from LRMM22_S5b.

1. Fit the linear mediation model using the PROCESS macro or mediate function from the mediation package

• use the nonparametric bootstrap with the percentile method
• compare the coefficients with those of Figure 1 from the paper.

2. Identify the type of mediation (complementary, competitive or indirect only) based on coefficients.
3. The paper does not discuss any of the model assumptions. List the assumptions of the linear mediation model and explain how some may fail to be valid, thus casting doubt on the conclusions drawn by Liu et al. (2022+).

Task 2

Study 4 of Risen & Gilovich (2008) (pp. 297-299) perform a mediation analysis with a two-way ANOVA using the Baron & Kenny (1986) methodology.

1. Read the description and comment on the following aspects:
   1. use of the Baron and Kenny original testing procedure¹
   2. the plausibility of the causal model implied by the directed acyclic graph drawn in Figure 2.
2. Using the summary statistics and coefficients estimates reported, recompute Sobel’s statistic² and the p-value and compare them with the values reported. .³
3. List the assumptions of the linear causal mediation model. Are there any check of these and, if so, do they support the claims of the authors?
4. Can the authors successfully claim mediation considering the study uses an experimental design and randomly allocates condition? Why or why not?

References

Baron, R., & Kenny, D. (1986). The moderator-mediator variable distinction in social psychological research: Conceptual, strategic, and statistical considerations. Journal of Personality and Social Psychology, 51(6), 1173–1182. https://doi.org/10.1037/0022-3514.51.6.1173

Liu, P. J., Rim, S., Min, L., & Min, K. E. (2022+). The surprise of reaching out: Appreciated more than we think. Journal of Personality and Social Psychology. https://doi.org/10.1037/pspi0000402

Risen, J. L., & Gilovich, T. (2008). Why people are reluctant to tempt fate. Journal of Personality and Social Psychology, 95(2), 293–307. https://doi.org/10.1037/0022-3514.95.2.293

Footnotes

1. The latter is said to be suboptimal; explain why in your words.

2. Some authors may be excluding the \(\mathsf{Va}(\widehat{\gamma})\mathsf{Va}(\widehat{\alpha})\) term from the equation.

3. In R, the \(p\)-value for the two-sided test can be computed via 2*pnorm(abs(stat), lower.tail = FALSE), where stat is Sobel’s statistic.