Creating a counterfactual for the reference group in an mlogit, interrupted time series analysis.

[Joost Wammes]

I have an issue with creating a counterfactual for the reference group in an mlogit, interrupted time series analysis.

The outcome variable y is location: hospital (reference group), home, nursing home, elsewhere.

Explanatory variables in the model are:
- time variable, which is monthly intervals
- interruption point (coded as 0 pre-interruption and 1 post-interruption), which is commonly referred to as step change in time series literature
- interaction term between the time variable and interruption point, which is also known as the slope change

Model specification:
mlogit y interruption interaction time

mlogit, rrr

Then we predict per outcome the relative risk ratios

predict y1 y2 y3 y4

_____________________________________

Now we create the counterfactuals per outcome by:

generate cf1 = y1/exp(_b[ interruption] + _b[ interaction] * interaction) if interruption==1
generate cf2 = y2/exp(_b[ interruption] + _b[ interaction] * interaction) if interruption==1
generate cf3 = y3/exp(_b[ interruption] + _b[ interaction] * interaction) if interruption==1
generate cf4 = y4/exp(_b[ interruption] + _b[ interaction] * interaction) if interruption==1


If we plot the graph (see below) you see that for nursing home, home and elsewhere the counterfactual extends from the pre-reform trend line, however for the reference group hospital it does not.

This certainly has to do with the fact that all RRR combined is always 1 in total

We changed the reference group in our model specification and generated a new counterfactual the same way as presented above, however that also did not created a counterfactual for hospital that extends from the pre-reform trend.


Does anyone have a suggestion to create a counterfactual for the reference group?