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cleaning up equations
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steffejr committed Jan 20, 2022
1 parent 5949fc9 commit 6a1a927
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5 changes: 5 additions & 0 deletions Serial Mediation.md
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Expand Up @@ -12,11 +12,16 @@ A--> |c'| C;
```

$B1 = \beta_0 + a_1 \cdot A + e_i$

$B2 = \beta_0 + a_2 \cdot A + b_1 \cdot B1 + e_i$

$C=\beta_0 + c' \cdot A + b_3 \cdot B1 + b_2 \cdot B2 + e_i$

## Pathways
$a_1 \cdot b_1 \cdot b_2$

$a_2 \cdot b_2$

$a_1 \cdot b_3$

---
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3 changes: 3 additions & 0 deletions Simple Moderation.md
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Expand Up @@ -12,8 +12,11 @@ W --> D{ };
W --> |m| C;
```
$C = \beta_0 + c\cdot A + m\cdot W + b\cdot A\cdot W$

This is the regression equation for this model. Which can be rewriteen as:

$C = \beta_0 + m\cdot W + (c + b\cdot W)\cdot A$

When written like this you can see how the A variable is now a linear function of the moderating variable.

To interpret this model first determine if parameter $b$ is significant. Then the model can be [[Probing an Interaction|probed]] to identify the range of values of W for which the A effect is significant.
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5 changes: 3 additions & 2 deletions The direct effects matrix.md
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Expand Up @@ -21,10 +21,11 @@ A-->|c'| C;
|C|1|1|0|

This matrix is read row by row with the variable in each row being the outcome variable. Each column with a value in it is a predictor in the model. In the above figure, there are two equations. The two equations are:

$B = \beta_0 + \beta_1 \cdot A + e_i$

$C = \beta_0 + \beta_1 \cdot A + \beta_2 \cdot B + e_i$




It is also possible that an analysis requires the same outcome variable in multiple equations. Even in the simplest model this is the case. Therefore, there needs to be a second layer (third dimension) to the above matrix. It will be like this:

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