# Re: st: Calculation of total effects and the significance test of indirect effect

 From Richard Williams To statalist@hsphsun2.harvard.edu Subject Re: st: Calculation of total effects and the significance test of indirect effect Date Thu, 30 Sep 2004 07:15:57 -0500

```At 02:05 AM 9/30/2004 -0500, you wrote:
```
Dear listers,

I am writing to ask a few questions regarding the calculation of total effect = direct effect + indirect effect.

Suppose I am interested in the relationship between X and Y and Z. I also have demographic variables to consider such age and sex.

1) My first question is,
If I want to calculate the total effect of X on Y, do I have to control for Age and Sex or not?
In other words, is Rxy the total effect or Rxy.age,sex the total effect?
The correlation between X and Y can be due to several things: direct effects, indirect effects, common causes, correlated causes. Estimates of the total effect of X on Y will differ depending not only on the other vars in the model, but how you think they are interrelated. For example (hard to draw diagrams unfortunately!) if you thing A affects B, and A and B affect C, then B and C are correlated because B affects C and also because they share a common cause, A. But, if B affects A, and A and B both affect C, then B and C are correlated because B affects C directly and also indirectly (through A). Even though your estimates of the direct effects of A and B on C are the same in either model, your estimates of the total effect of B on C will differ.

Turning more specifically to your problem, you'll (a) have omitted variable bias if you leave out age and sex (b) part of the correlation between X and Y that is due to common or correlated causes (age and sex) will instead get attributed to the direct or indirect effects of X on Y.

In short -- if age and sex are theoretically relevant variables, then yes, they should be in there, and your estimates of the total effects will be affected by their presence or absence. Given your description, Rxy.age,sex may be the total effect of X on Y, but again the estimates of total effects are dependent not only on what vars are in the model but how you think they are interrelated (e.g. it wouldn't be the total effect if you thought that Z affects X rather than X affects Z).

2) My second question is,
As far as I know, the SEM package softwares (e.g. Lisrel or Amos) automatically calculate the direct and indirect effect of included components.
Unfortunately, I now do not use such softwares but just SPSS, and need to calculate the total, direct and indirect effect between X Z and Y.
For a simple model, it is not that hard to do by hand. But, there is a freebie student edition of Lisrel that might meet your needs:

http://www.ssicentral.com/other/entry.htm

I will appreciate it much more if you can suggest any reading materials to grasp these topics more clearly.
I've always liked Otis Dudley Duncan's book "Introduction to Structural Equation Models". My adaptation of his arguments can be found at

http://www.nd.edu/~rwilliam/stats2/l65.pdf

http://www.nd.edu/~rwilliam/stats2/l71.pdf

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Richard Williams, Notre Dame Dept of Sociology
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