Path Analysis Using sem – Dummy Coding for Categorical Independent Variables

[Sarah Won]

Hello everyone,

Thank you so much in advance for your time and support.

I am conducting a path analysis using the sem command in Stata. All of my mediators and outcome variables are continuous. The independent variables include continuous, dichotomous, and categorical variables.

As I understand it, the sem command does not support factor variable notation (e.g., i.varname), so I created dummy variables manually for the categorical variables with three or more categories. I would appreciate it if you could review my approach and let me know if it is correct.


Example: Race/Ethnicity Variable

tab racehisp_2015

                          racehisp_2015 |      Freq.     Percent        Cum.
----------------------------------------+-----------------------------------
                   0 Non-Hispanic White |        894       61.53       61.53
                   1 Non-Hispanic Black |        405       27.87       89.40
2 Others (AI/AN/Asian/NHPI/Other/Hispan |        154       10.60      100.00
----------------------------------------+-----------------------------------
                                  Total |      1,453      100.00

To set Non-Hispanic White (0) as the reference group, I created the following dummy variables:

gen black_dummy_2015 = (racehisp_2015 == 1)
gen others_dummy_2015 = (racehisp_2015 == 2)

These dummy variables are coded as 1 if the participant belongs to the specified group, and 0 otherwise.

 tab black_dummy_2015

black_dummy |
      _2015 |      Freq.     Percent        Cum.
------------+-----------------------------------
          0 |      1,048       72.13       72.13
          1 |        405       27.87      100.00
------------+-----------------------------------
      Total |      1,453      100.00

 tab others_dummy_2015

others_dumm |
     y_2015 |      Freq.     Percent        Cum.
------------+-----------------------------------
          0 |      1,299       89.40       89.40
          1 |        154       10.60      100.00
------------+-----------------------------------
      Total |      1,453      100.00

Questions:

1. Does this approach correctly treat Non-Hispanic White as the reference group?
   I understand that each dummy variable includes Non-Hispanic White and the remaining group(s) in the 0 category. Is this appropriate for creating dummy variables?
2. Should all dichotomous variables in the model be coded as 0 and 1?
   For example, should “1” consistently indicate the presence of a characteristic or condition, and “0” indicate absence?

Thank you again for your time and support. I would greatly appreciate your feedback.

[Felix Bittmann]

1. Your coding is fine. Simply include black_dummy_2015 and others_dummy_2015 in your model and the non-hispanic white will be the reference group. You can also save time by using tab for creating dummies for you:

tab racehisp_2015, gen(race_dummies)

2. Stata does not care whether 1 means "presence" or "absence" of a group or characteristic. Of course, a consistent pattern makes the interpretation of the results easier for you and helps you avoid mistakes.

[Sarah Won]

Felix Bittmann Thank you so much for your review and suggestions. It is really helpful.

[Clyde Schechter]

Another way to automate the creation of indicator ("dummy") variables is with the -xi- command or -xi:- prefix. Although this is largely obsolete, its remaining role is for use in those commands that, like -sem- don't support factor variable notation. It looks a great deal like factor-variable notation. In your situation you could write your -sem- command as:

xi: sem (dv <- iv1 iv2 i.racehisp_2015)

replacing the italicized parts with the actual corresponding variables in your model. Note that all though this approach resembles factor-variable notation typographically, it does not enable you to subsequently use -margins- correctly. See -help xi- for a full explanation of the -xi- command.

[Sarah Won]

Clyde Schechter Thank you very much for suggesting an alternative approach. This is very helpful!

[Bruce Weaver]

Note too that -gsem- allows factor variables. See the Intro 3 section here for more info.


PS- You mentioned "mediators" in #1. IMO, it is better to call them putative or presumed mediators. The article by Fiedler et al. (2018) explains why I say that. I think this article should be required reading for doing mediation analysis. YMMV.

Fiedler, K., Harris, C., & Schott, M. (2018). Unwarranted inferences from statistical mediation tests–An analysis of articles published in 2015. Journal of Experimental Social Psychology, 75, 95-102.

[Sarah Won]

Bruce Weaver Thank you so much for your invaluable information and suggestions regarding the terminology. This has been truly helpful!