Association rules (market basket analysis) - rules involving the absence of items?

Question

I was wondering if associations rules can include the absence of an item, for example, in this simplified set of transactions:

milk, butter
milk, eggs
beer, eggs
beer, chips

I would be interested in rules stating:

if milk -> no chips
if beer -> no butter

If this is statistically plausible, can it be implemented in r, for example in arules?

Maybe I just need to select those rules that have a lift inferior to 1?

Answer 1

Yes, you can learn rules like that. Very simply, add "no chips" as an item. Obviously, for any one transaction or set of items, you cannot have both "chips" and "no chips" as these are mutually exclusive.