Interpreting significant intereactions in

[Christa Hansen]

Hello,

I post below a results table for a diff in diff model. For simplicities sake, please look only at model M2. Here we see my policy variable is insignificant, implying the policy did not have a significant effect on the dependent variable "weight." Also, We see the covariate wealth is insignificant. However, the interaction of wealth and policy variables (variable "wealthxpolicy") is significant. How do I interpret this? Does this suggest that while the policy did not have an average effect on "weight," it does have an effect for wealthier (given the positive coefficient) individuals?

Many thanks for reading.

[Fei Wang]

Christa, the "-0.005" indicates policy effect for people with zero-wealth (may not be a useful result). The "0.001" means policy effect significantly increases by 0.001 as wealth increases by one unit.

[Christa Hansen]

Ah. Apologies for the slow response. That is extremely helpful. And the -0.001 coefficient on the "wealth" variable?

[Christa Hansen]

Keeping in mind "weight" is the dependent variable. I would assume the wealth coefficient carries the standard interpretation. And as you say, "the "0.001" means policy effect significantly increases weight by 0.001 as wealth increases by one unit"?

[Andrew Musau]

Christa, you should rescale your dependent variable so that your coefficients are readable. So, e.g., if weight is your dependent variable, instead of recording weight in kilograms, record it in grams (i.e. multiply by 1000). It is not difficult to interpret coefficients of continuous by continuous interactions and their main effects. You can do a lot with the margins command. But I will recommend that you have a look at the following notes by Richard Williams to have a general understanding: https://www3.nd.edu/~rwilliam/stats2/l55.pdf

[Christa Hansen]

Its not actually a weight (agreed the table is rough) - its weighted health-related quality of life scores? So we are constrained to a min slightly less than zero and a max slightly less than one.

[Andrew Musau]

It is common to adjust scales without loss of information. On the other hand, you can rescale the independent variables, e.g., reporting wealth in thousands of dollars instead of raw dollar amounts. Bottom line is that such transformations do not have an effect on your results, but they do on how the results are presented which is an important goal when communicating the results.

[Christa Hansen]

Agreed. Thank you.

[Fei Wang]

Back to the question in #3: The -0.001 of "wealth" means one unit increase in wealth is on average associated with 0.001 unit decrease in weight for those not exposed to the policy.