Three Variable Mediation Model

Permanent Note Created: 01-07-2022 10:13 #statistics

The three variable model consists of testing three linear regression models. First, is the simple one where only the effect of the independent variable is regressed onto the dependent (outcome) variable. The parameter estimate \(c\) is also called the total effect.

graph LR;
A-->|c| C;

\(C = \beta_0 +c\cdot A\)

Next the following two regression equations are fit. There is the model to assess the size of the effect of the indepdent variable on the mediator, A –> B, and then the effect of independent variable on the dependent variable, after accounting for the effect of the mediator variable.

graph LR;
A-->|a| B;
B-->|b| C;
A-->|c'| C;

Direct Effects Matrix

ABC
A000
B100
C110

\(B=\beta_0+a\cdot A\) \(C = \beta_0+c'\cdot A+b\cdot B\)

output = regstats(B, [A]) output = regstats(C, [A B])

Once these regression models are fit to the data the following effects are reported:

  1. a
  2. b
  3. c’ : this is called the direct effect
  4. c: this is called the total effect
  5. \(a\cdot b\): this is called the indirect effect

Effects 1 through 4 can be evaluated with standard statistics (t-tests). The indirect effect needs to be evaluated with Bootstrap Resampling and Bias-corrected Confidence Intervals.

Caution

Caution for Mediation Analyses when there is moderation

References

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