DiD: allow for multiple pre and post intervention observations

[drbenvincent]

At the moment the code works but it assumes there are observations at one pre and one post intervention time.

So we need to relax this assumption and generalise the code.

Probably best to do this while working through the 'bank failure' dataset, see #44.

This will also impact plotting

And it will impact reporting of the summery stats.

Bank failure dataset/example + robustifying

• add data
• data processing + visualisation
• need to add treated and units columns
• check if I need to either specify the grouping column (e.g. district) as categorical OR enter that as C(district) in the model formula

Classic 2x2 DID

• Analysis 1 with just pre and post (Bayesian)
  • model fit working
  • plotting working
• Implement example for the frequentist approach

'Extended' DID with more than 2 observed time points

• Analysis 2 with all data
  • Consider if we need to have separate classes for classic 2x2 DID and another for more time points, or try to make the one DifferenceInDifferences class deal with all situations.
  • model fit working
  • plotting working
• Make it work for the frequentist model
• Update tests
• Update README + index.rst

[drbenvincent]

Model formula will be bib ~ 1 + district + year + district:treated

[drbenvincent]

At this point it seems that model fitting does work, although we'll have to wait for the visualisation to see if the results make sense.

Plotting is going to get more complex. The initial plot that I had only makes sense when we have two time points (pre/post) AND we have multiple observed units per group.

So we've potentially got a 2*2 grid of different plot types to produce

	pre/post only	multiple time points
one unit observed per group
multiple units per group	existing plot

[drbenvincent]

• fix green arrow for causal impact
• fix plotting of data

[drbenvincent]

The magnitude of the causal impact is wrong. I think this might be fixed by enforcing an order on the levels of the groups.

[drbenvincent]

Plotting now works for the original dataset (multiple units in the treatment and control conditions) and the new banking example (one unit in the treatment and one in the control condition).

Although the aesthetics could do with some work, the priority is to focus on getting it working in the case where we have more observations over time, not just the pre/post times.

And the inferences are particularly bad. But this is because we are just using whatever default priors at the moment and because we only have one observation per condition. This is not an ideal scenario as a lot rides on the sigma parameter. But this can be worked on when we use Bambi (see #22).

Original dataset

Banking dataset

[drbenvincent]

Currently sampling from the posterior works with

result = DifferenceInDifferences(
    df_long,
    formula="bib ~ 1 + district + year + district:treated",
    time_variable_name="year",
    group_variable_name="district",
    treated="Sixth District",
    untreated="Eighth District",
    prediction_model=LinearRegression()
    )

But breaks when we get to doing the other stuff and expected. This is the next step.

[drbenvincent]

Currently working in the did_multiple_observations branch.

[drbenvincent]

At this point we have DiD working for:

1. Single pre and post treatment observation (although we have some shape issues, calculating posterior predictions and counterfactuals for each item)

But there are clearly some issues to be resolved for the banks dataset.

2. Multiple pre and post treatment observations.

Looks like this for the full banks dataset

[drbenvincent]

In the banks dataset, we are getting 1 surplus degree of freedom. I think it is because the group is coded as a string (therefore treated as a category) rather than as a numerical 0/1.

[drbenvincent]

I've made meaningful improvements to DiD at this point. There were a number of things about the code before which were muddled and a bit wrong. I've fixed those up, made the code cleaner, got DiD working for multiple pre and post treatment observations, and improved the plotting.