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I have performed the path analysis using the sem function in R. The model which I fitted consists of both direct and indirect paths. I have some trouble in interpreting the estimates of the SEM coefficients.

  • Does R gives the value of total effect = (direct effect + indirect effect) directly or do I have to multiply the coefficients which are on the indirect path and then add them to the coefficients which is on the direct path? This is the usual way of doing path analysis with the raw/absolute correlation coefficients.

For example consider X (independent variable), Y (dependent variable) and M (Mediating variable).

The raw/absolute correlation/ standardized regression coefficients between them are X and Y -0.06; X and M 0.22 and M and Y 0.28 whereas on the path analysis/sem in R, the above coefficients are X and Y -0.13; X and M 0.22 and M and Y 0.31.

  • Thus is the total effect of X and Y equal to -0.13?
  • Alternatively how should I interpret this coefficient considering the effect of variable M into the account?
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sem gives direct effects only. To get total as well as indirect effects use the functions given by John Fox.

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  • $\begingroup$ Thank you very much for this reply. I used the function which you were referring. Now I am able to extract indirect and total effects from the sem model. However I still have some concern. As mentioned above, the direct effect of X and Y are almost double for sem model as compare to correlation coefficient (-0.13 Vs -0.06), whereas the coefficients for other variables are quite similar. What could be the source of this discrepancy? Do you think that the interpretation of absolute correlation coefficient and sem model coefficient (direct) will be similar for the relation between X and Y? $\endgroup$ – Amol Pande Sep 5 '11 at 12:16
  • $\begingroup$ @Amol Pande: It'd be nice if you provide a reproducible example. I guess what you are talking about is the difference between standardized and unstandardized coefficients. The only way I know to get standardized coefficients is to use 'path.diagram' with 'standardize=TRUE'. $\endgroup$ – MYaseen208 Sep 5 '11 at 16:33
  • $\begingroup$ Thank you again. I am comparing the standardized coefficients only. This can be obtained from sem function after specifying the correlation matrix. The unstandardized coefficient can be obtain after specifying the covariance matrix, which can be converted to standardized coefficient using “standardized.coefficients” in R (please correct me if I am wrong). The example which I have mentioned is from the birth cohort data. Here X is birth weight, Y is current adiposity (at 21 yr age) and M is current weight. I am trying to study the direct and indirect effect of birth weight on the adiposity. $\endgroup$ – Amol Pande Sep 6 '11 at 5:30

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