Does a probit regression should include the a dummy from the 'treatment' variable when choosing the right covariates for matching?

[Mirjana Grkovska]

Dear Statalist,

I have data from two years. I want to use matching to compare individuals from Wave 2 with the individuals from the Wave 1. Therefore my treatment variable is Wave. I am mainly following the steps described by Garrido et al (2014) ^‘Methods for Constructing and Assessing Propensity Scores’ to create propensity scores and then use kernel matching.

The first step is ‘Choice of Variables to Include in the Propensity Score’, where authors recommend running a probit regression with treatment as the outcome variable and the potential confounders as independent variables. However, the paper also says that when a variable is related to the outcome but not the treatment, is should be included as it should reduce bias. In contrary when the variable is related only to the treatment but not to the outcome are not beneficial for the calculation of the propensity scores.

From this, I understand that I should include the variables that are statistically significant when I run a probit regression with my original outcome variable.
My question is: Do I need to include Wave 2 (which is a dummy for wave) in this regression? Because some additional variables become significant when I control for Wave 2 in the probit regression. So I am not sure which one to use to calculate the propensity scores.


Best wishes,
Mirjana

[Marcos Almeida]

I'm not sure if I understood it right. Hazarding a guess, I gather you have 2 groups, one for each years, I mean, you don't have repeated measures, hence no panel data structure, hence no "waves", strictly speaking.

Being this so, "wave = 2" is, basically, a level of the binary variable ("treatment"). But "treatment" is already in the regression, both in the probit model (as DV) as well in the "final" model.

[Mirjana Grkovska]

Dear Marcos,

Thank you for your answer. I aplogise for not giving enough explanation.

I am using survey data, which are integrated cross-sectional data (not panel) from two waves (2007 and 2011). My outcome variable is Life Satisfaction and I look at socio-demographic factors that influence Life Satisfaction. I look at each year (wave) separately. There is a big improvment in Life Satisfaction in 2011 but as the people interviewed in both waves are different I wanted to check whether after matching people with similar propensity score, the improvment in Life Satisfaction will still exist.

I hope this is clear. Please let me know if you need further clarification.


Best wishes,
Mirjana

[Marcos Almeida]

Thank you for claryfing it, Mirjana. So, you have two binary ("dummy") variables (wave 1 and wave 2). As I remarked in #2, you just need a "wave" variable with 2 levels.Being this so, including the "treatment" variable - aka "wave" - in the PS model may do the trick. Otherwise, like when you did the estimations exclusively for wave 2, we'd have a subpop analysis, which, by the way, if I understood right, is not all your study question.

To end, you selected propensity score matching as a strategy to tackle the difference in sample characteristics. But there are some PS alternatives worth considering as well, such as inverse probability weights, for example. Hopefully that helps.

[Mirjana Grkovska]

Dear Marcos,

Sorry I am just seeing your asnwer now. Thank you for the answer again.

I have another question if you don't mind. Can you recommend the most suitable sensitivity check after matching when the treatment Wave is a binary varibale (1 and 0) and the dependat variable Life Satisfaction is measured on a scale 1-10. Because Stata help says that -mhbounds- suits when both treatment and the independent variables are binary. Also, is says that -rbound- works only at 1-1 matching and I have used Kernel matching.

Many thanks,
Mirjana

[Marcos Almeida]

Sorry, Mirjana, I have no experience with the user-written rbounds.

[Mirjana Grkovska]

That is okay Marcos. Thanks again for replying. All the best!