Analysis of Mediating Effects - Method and Model Development 【Detailed Explanation of the Paper】

Mediation Effect Analysis - Method and Model Development – ​​Intensive reading of Pan Deng’s thesis

Considering the influence of independent variable X on dependent variable Y, if X influences Y through influencing variable M, then M is called an intermediary variable.

$$\begin{gathered} Y=cX+e_1(1) \\ M=aX+e_2(2) \\ Y=c^{\prime }X+bM+e_3(3) \end{gathered}$$

Test mediation process

1. Check the coefficient c of equation (1). If it is significant, it is considered as a mediating effect, otherwise it is considered as a masking effect. But regardless of whether it is significant or not, follow-up tests are carried out.
2. Check the coefficient a of equation (2) and the coefficient b of equation (3) in turn, if both are significant, then the indirect effect is significant, go to the fourth step; if at least one is not significant, go to the third step.
3. Use the Bootstrap method to directly test $H_0:ab=0$ . If significant, then the indirect effect is significant, proceed to the fourth step; otherwise, the indirect effect is not significant, stop the analysis.
4. Check the coefficient c ′ c' of equation (3)$c^{\prime }$ , if not significant, that is, the direct effect is not significant, indicating that there is only a mediating effect. If it is significant, that is, the direct effect is significant, go to the fifth step.
5. Compare ab and $c^{\prime }$ , if they have the same sign, it is a partial mediation effect, and the proportion of the mediation effect to the total effect is reported$\frac{ab}{c}$. If the opposite sign is a masking effect, report the absolute value of the ratio of the indirect effect to the direct effect $|\frac{ab}{c^{\prime }}|$。

direct effect, indirect effect and total effect

1. Direct Effects: Coefficient $c^{\prime }$ is the direct effect of the independent variable X on the dependent variable Y after controlling the influence of the intermediary variable M;
2. Indirect effect: The mediation effect is equal to the indirect effect (indirect effect), which is equal to the coefficient product ab;
3. Total Effect = Direct Effect + Indirect Effect
   $$c=c^{\prime }+ab$$

Two questions:

1. Do you want to check the coefficient c?

Of course, because the researcher will certainly care whether X significantly affects Y. For two specific variables X and Y, if there is no relationship between X and Y based on theory, experience, or the third variable M that is closely related to them, will you still study how X affects Y? How will the article stand? Therefore, the researcher must be concerned about the relationship between X and Y.

2. Should the mediation effect be premised on the significance of the coefficient c?

According to the definition of Baron and Kenny (1986), the mediation effect is based on the premise that the coefficient c is significant, that is, the premise that X significantly affects Y. Under this definition, the analysis of the mediation effect can explain "how X affects Y", and the mediation process provides "the mechanism of X's action on Y". If the coefficient c is not significant, it means that the impact of X on Y is not significant. If you also ask " How X affects Y" or "What is the mechanism by which X acts on Y" is not common sense.

If the coefficient c derived from question 2 is not significant, it may be that the signs of the indirect effect and the direct effect are opposite, and the total effect is covered, which is called the masking effect

In this way, we do not need to argue whether the mediation effect should be based on the premise that the coefficient c is significant, but we should make arguments based on the actual situation, reasonably raise corresponding questions, establish models for analysis, and give corresponding explanations. Although the coefficient c is not significant, the analysis can still be continued, but it should be understood that whether the coefficient c is significant or not is a different matter, and it is wise to use different names to distinguish it.

Fully Mediated vs Partially Mediated

By checking the coefficient $c^{’}$ to distinguish between complete mediation and partial mediation. If the coefficient$c^{\prime }$ is not significant, and belongs to complete mediation (James & Brett, 1984). Baron and Kenny (1986) believed that complete mediation is the strongest proof of the existence of mediation effect.

Stata code

The code comes from the article of Lian Yujun's team

sgmediation2Command to install:

net install sgmediation2, from("https://tdmize.github.io/data/sgmediation2")

sgmediation2Command syntax:

sgmediation2 depvar [if exp] [in range] , iv(focal_iv) mv(mediator_var) [options]

Among them, depvaris the dependent variable, iv(focus_iv)is the independent variable, and mv(mediator_var)is the mediator variable.

Example:

• Assuming that highly educated people (edyrs) will have better health status (health), there is a possible intermediary explanation: high education is often accompanied by high income, and people with higher income tend to care more about their bodies health, and thus better health. The theoretical causes and effects of the three are as follows:
  

In this example, we control variables such as age, gender, and race of the respondents, and use the Sobel-Goodman mediation test to test the above explanations.

use "https://tdmize.github.io/data/data/cda_ah4", clear
drop if missing(health, edyrs, income, race, woman, age)
sgmediation2 health, iv(edyrs) mv(income) cv(i.race i.woman age)

Three regression tables are output as a result, along with a test table and a table describing the effects

Next, we will further introduce how to use the bootstrap method (Bootstrap) to obtain the indirect effect ( $a\ast b$ ) Standard errors and confidence intervals. In general, the default Sobel-Goodman test above has low statistical power. A common solution is to use bootstrapping to obtain standard errors and/or confidence intervals (Preacher and Hayes, 2004; Zhao et al., 2010) with 1000 or more replicates (Preacher and Hayes, 2008).

return list
bootstrap r(ind_eff) r(dir_eff) r(tot_eff), reps(1000): sgmediation2 health, ///
         iv(edyrs) mv(income) cv(i.race i.woman age)
estat bootstrap, bc percentile  // 用百分位数表示和偏差修正的置信区间

Confidence intervals expressed in percentiles and bias-corrected: