I want to look into the causal effects of an education program on a binary employment outcome (positive vs negative). I have two groups of students- one that took the education program (the treatment group) and one that did not (the control group).
The groups are highly unbalanced proportionally on background demographics. I have implemented 1:1 nearest neighbour propensity score matching using the background demographics such as sex, ethnicity, socioeconomic class etc in the
MatchIt package in R. After assessing my balance statistics, I am now confident that the sample is well matched on these background demographics.
I have spent a long time looking through papers such as Stuart (2010) and Austin (2007) with regards to advice on how to proceed with post-matching analysis and this is where my confusion begins.
I am trying to follow Stuart's paper. and it suggests that it is not necessary to take into account the matched pairs after k:1 matching but rather 'conditioning on the variables that were used in the matching process (such as through a regression model) is sufficient.' Should I interpret this as to include the background demographics, alongside the educational program indicator as independent variables in the logistic regression model with employment outcome being my dependent variable (e.g., using
glm in R)? Or is it suggesting that I should be using conditional logistic regression? From my understanding, conditional logistic regression does take into account the matched aspect of the data, is that right?
I am also not sure if it is appropriate to incorporate the background demographics in the modelling of the post-propensity score matching analysis? I have seen some studies do this as they say although there is no difference between the treatment/control groups on these variables they may have an impact on the outcome of interest, e.g., although the socioeconomic classes of those students in / not in the educational program are balanced, this variable may have an impact on employment outcome. I have also seen some studies completely ignore them.
I don't have access to many books but am happy to be directed to available papers on the web.