FCM lags suspicious results

[priamai]

Hi there,
I wanted to see the effects of lagged variables on the car dataset so I did a quick sanity check:

from causallearn.search.FCMBased import lingam

for lags in range(1,4):
  print("\n\nLags %d" % lags)
  print("Total columns %d " % data.shape[1])
  model = lingam.VARLiNGAM(lags=lags,random_state=1,prune=False)
  model.fit(data)

  print("Causal Order features %d " % len(model.causal_order_))
  print(model.causal_order_)
  print("Matrix lags %d " % model.adjacency_matrices_.shape[0])
  #print(model.adjacency_matrices_[0])
  #print(model.adjacency_matrices_[1])
  #print(model.residuals_)

The output doesn't show any influence of the lag factor, see below:

Lags 1
Total columns 10 
Causal Order features 10 
[4, 8, 1, 6, 3, 0, 2, 7, 5, 9]
Matrix lags 2 


Lags 2
Total columns 10 
Causal Order features 10 
[4, 8, 1, 6, 3, 0, 2, 7, 5, 9]
Matrix lags 2 


Lags 3
Total columns 10 
Causal Order features 10 
[4, 8, 1, 6, 3, 0, 2, 7, 5, 9]
Matrix lags 2 

I would expect that the matrix lag and the causal order features increases as the lag increases?
For example when Lag is equal to 2, I should see double the columns and features?

[Yujia Zheng]

Thanks for the question. The optimal order (lag) for the vector regression model is determined automatically using bayesian information criterion. As a result, even if we set lags as 100, the optimal one might still be selected as 2. To avoid that optimization process, you may consider setting criterion as None, e.g.,

model = lingam.VARLiNGAM(lags=3, criterion=None)

[priamai]

What's the expected result when lags=3, is it going to permutate all the possible columns 3 times?

[Yujia Zheng]

Sorry, I'm not sure if I fully understand the question. The lags here mean those for lagged causal relations (in contrast to contemporaneous causal relations).

[priamai]

Okay so this is my understanding so far (we should really put some basic example in the test folder):
let's say I have a classical fork DAG: X <- A -> Y.
The generation process implies that: A- lag (5) -> X and A -> lag (7) -> Y.
What's the output going to look like?
Will each edge have a different lag value?
Can we build a simple toy example to verify the desired behaviour?

[priamai]

Also would be interesting to see how to import the output into a DAG for DoWhy.