Possible Interaction?


I've fit the following logistic regression model:

Y = waking up with a soar throat (y=1 if yes, y=0 if no)
T = type of device (t=1 if type 1, t=0 if type 2)
D = duration in minutes.

Y ~ T + D.

It's a multi-step problem and I'm on the last part! I think the following question is asking something about a possible interaction?

Here it is verbatim

"Carry out a likelihood ratio test to assess whether these data provide evidence that the effect of a minute increase in duration time on the log odds that a patient will wake up with a soar throat is different for the two types of devices. Give the value of the likelihood ratio statistic, p-value and interpret"

Please advise!

I've read the problem over several times and it seems like its asking whether or not an interaction exists. So I fit the interaction model and noted its Log-Likelihood Value. I took the Log-Likelihood value from the model with no interaction term. Using these I computed the LRT. -2 (L0 - L1).

Does this sound right?