I have observed binary variable [Ex. Low birth weight: Yes/No]. I would like to add this variable into path analysis. How can I interpret the regression coefficient of this variable?
Sorry, I just realized that you wanted to include a binary variable in a path analysis. In this case, binary variables could be predictor, mediator, or dependent variables.
There is a nice article by Dawn Iacobucci which may be helpful for you:
Iacobucci, D. (2012). Mediation analysis and categorical variables: The final frontier. Journal of Consumer Psychology, 22, 582–594.
Just search for this article in the internet, there may be a ressource where you can download this paper.
HTH
Karin
Karthikeyan,
there are two possibilities to include binary variables: as a predictor (independent) variable or as the criterion (dependent variable). I guess that you would like to use the binary variable as a predictor variable?
First, you have to code your variable as No = 0 and Yes = 1. Then, the interpretation of b0 (intercept) is the mean of Y of the group coded as 0, and b1, the regression coefficient, is the difference in means between both groups.
There are some good textbooks in which this is explained in more detail, e.g., Cohen, Cohen, West & Aiken (2003). Applied multiple regression/correlation.
Regards,
Karin
Sorry, I just realized that you wanted to include a binary variable in a path analysis. In this case, binary variables could be predictor, mediator, or dependent variables.
There is a nice article by Dawn Iacobucci which may be helpful for you:
Iacobucci, D. (2012). Mediation analysis and categorical variables: The final frontier. Journal of Consumer Psychology, 22, 582–594.
Just search for this article in the internet, there may be a ressource where you can download this paper.
HTH
Karin
In addition to Karin's excellent advice, if low birth weight is exogenous, you may want to consider mean-centering it after coding it as (for example) 0/1. In a main-effects model, this only affects intercepts and does not affect any inferences about paths, but it can be convenient. If you want to interpret model-implied values of the levels of your outcomes at different levels of other predictors, it is easiest if you pick a scaling where '0' is most interpretable, whether that's normal birth-weight, low birth-weight, the sample balance point (i.e., mean), or something else.
If you have interactions with an exogenous birth-weight variable, the proper choice of 0 becomes extremely important for interpreting main effects.
Pat
David,
I tried to explain in my post. Do you have a more specific question?
David,
Gotcha. It's not at all necessary, it's simply sometimes convenient for the same reasons centering continuous variables can be.
Pat
Karin,
I tried the solution mentioned in "Mediation analysis and categorical variables: The final frontier". Then the indirect effect in my analysis isn't significant. However, when I use Mplus code, there exists indirect effect. what does it mean?
Gangmin, could you please be more precise? Did you use Mplus with binary variables or with continuous variables? Which was your comparison method, SPSS or some other program?
Regards, Karin
Sorry, here is my Mplus code:
DATA:file is user1.dat;
VARI:names are x m y;
usevari is x m y;
categorical is m;
MODE:m ON x;
y ON m x;
MODEL INDIRECT: y VIA m x;
ANAL: bootstrap = 5000;
OUTPUT: cinterval(bcbootstrap);
And I use SPSS and excel to compute "Zmediation" mentioned in the article.
Thank you for your reply!
Gangmin, I think the difference is the use of the Sobel test (SPSS) compared to bootstrapping (Mplus). Bootstrapping should be preferred, as the standard error of the indirect effect, which is the product of the parameters a*b, is not normally distributed. In SPSS, the Z value of the product is tested for significance by comparing it with tabled values of the normal distribution, while it would be more appropriate to compare it to an nonnormal distribution. This is explained in the following article:
MacKinnon & Cox (2012). Commentary on “Mediation analysis and categorical variables: The final frontier” by Dawn Iacobucci. Journal of Consumer Psychology, 22, 600–602.
Bootstrapping is one of the best methods to use here.
Regards, Karin
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