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

Read Rohrer et al. (2022) and write a summary.

Task 2

Liu et al. (2023) 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 LRMM23_S5b in the R package hecedsm. You can also download the SPSS database via this link.

1. Fit the linear mediation model using the PROCESS macro or the mediate function from the mediation R package
   • use the nonparametric bootstrap with the percentile method to get confidence intervals
   • compare the coefficients with those of Figure 1 from the paper.
2. Zhao et al. (2010) review the typology of mediation. Identify the type of mediation (complementary, competitive or indirect only) based on coefficients.
   • complementary mediation when both direct and indirect effects are of the same sign and non-zero.
   • competitive mediation when direct and indirect effects are of opposite signs.
   • indirect-only mediation when the direct effect of \(X \to Y\) is null, but the effect \(X \to M \to Y\) isn’t.
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. (2023).

Task 3

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 experimental 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. (2023). The surprise of reaching out: Appreciated more than we think. Journal of Personality and Social Psychology, 124(4), 754–771. 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

Rohrer, J. M., Hünermund, P., Arslan, R. C., & Elson, M. (2022). That’s a lot to process! Pitfalls of popular path models. Advances in Methods and Practices in Psychological Science, 5(2). https://doi.org/10.1177/25152459221095827

Zhao, X., Lynch, Jr., John G., & Chen, Q. (2010). Reconsidering Baron and Kenny: Myths and truths about mediation analysis. Journal of Consumer Research, 37(2), 197–206. https://doi.org/10.1086/651257

Footnotes

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

2. The square of the std. error of \(\widehat{\gamma}\widehat{\alpha}\) is \(\widehat{\gamma}^2\mathsf{Va}(\widehat{\alpha}) + \widehat{\alpha}^2\mathsf{Va}(\widehat{\gamma}) + \mathsf{Va}(\widehat{\gamma})\mathsf{Va}(\widehat{\alpha})\), where \(\mathsf{Va}(\widehat{\alpha})\) is the square of the standard error for \(\widehat{\alpha}\) in the summary table of the linear regression. Some authors may be excluding the \(\mathsf{Va}(\widehat{\gamma})\mathsf{Va}(\widehat{\alpha})\) term from the equation.

3. Spoiler alert: you may not manage to reproduce this result. 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. You can use an online calculator to compute the test statistic and it’s variants.