Comparing models in R to detect significant change I am doing some data analysis in R and have reached a roadblock due to limited statistical knowledge. Basically I am trying to find a significant difference between two models. These models were made basically by splitting a data set in half. In the middle of the study, we implemented an environmental change and are trying to prove that this environmental change significantly increased the output of Variable B. My idea on how to prove this was to somehow compare the two models but I am not sure how. 
Thank you for your help. 
 A: I would analyze the composite data set including a dummy 0/1 indicator variable when the intervention took place. The model would include any suggested predictor series . The anlysis would suggest contemporaneous and lag effects that these series may have on the Y series and any level shifts , local time trends , seasonal pulses and pulses that may be found while also including any arima component reflecting omitted stochastic series. This is referred to as an ARMAX model. Testing the significance of the dummy can yield a determination of it's importance. AUTOBOX a piece of software that I have helped to develop is available in R to enable all that I have mentioned here. 
The problem with this approach is that the response given the de jure (known) date may be different from the de facto date when the response actually initialized perhaps due to a delay. This delay can also be a negative or anticipatory effect as when people change their behavior BEFORE a law goes into effect
Another common issue is that may be a dynamic response to the intervention as compared to an immediate effect... this is not referred to as a delay which is the amount of time the new regime comes into effect. .
This problem is sometimes referred to in the social science literature as "The Interrupted Experiment" and some very dated material can be found here 
https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=0ahUKEwjU9-T25pPVAhVFdT4KHXMBCOUQFgglMAA&url=http%3A%2F%2Fmethods.sagepub.com%2Fbook%2Finterrupted-time-series-analysis&usg=AFQjCNHFyZ3PHCzzyQjxGoZ8OGxoFqwToQ and https://www.google.com/?gws_rd=ssl#q=interrupted+time+series+design
