From the previous example we can see that the effectiveness of any ad decays with time. The decay rate depends totally on business rules. The decay rate will be higher if frequency of ad is lesser and vice versa. So the decay rate depends on length of the ad, frequency and number of impressions. Frequency may be very high but customers are not watching that particular channel. So impressions will be lesser. There might be other factors as well. After discussion we can find the decay rate. Generally the effect of any ad becomes 0 after 2-3 weeks. So we will consider a window of 2 weeks only.

Let’s start the code.

From the understanding of the previous example, in my code I will consider effect rate which is vice versa of decay rate. If decay rate is 0.8 for the 2nd week then the effect rate of previous week’s ad on 2nd week will be 0.2.

Now there is inbuilt function “Filter” in R which can be used. Read more about the filter function here. In that case, only one week’s effect can be carried forward but we want to consider 2 weeks. According to our formula;

A(t) = X(t) + AdStock Rate_Week1 * A(t-1) + AdStock Rate_Week2 * A (t-2)

where,

A(t) = Cumulative effect

X(t) = Base effect

A(t-1) = Previous time period effect (last week)

A(t-2) = Last 2nd week’s effect

AdStock Rate_week1 = last 1st week’s effect

AdStock Rate_week2 = last 2nd week’s effect

So we can’t use filter function directly here. We will use our own function. Let’s create a data-set with number of impression in each week.

abc <- data.frame(1:6) abc$b <- 0 colnames(abc) <- c ("Weekly impression","Effect")

Now let’s apply our function to calculate ad impression on 2nd,3rd and so on weeks.

rate1 = 0.5 rate2 = 0.2 for (i in 1:nrow(abc)){ if (i ==1) abc[i,2] <- abc[i,1] else if (i == 2) #Effect = impression + last week effect * decay rate abc[i,2] <- abc[i,1] + (abc[i-1,2] * rate1) else #Effect = impression + last week effect * decay rate abc[i,2] <- abc[i,1] + (abc[i-1,2] * rate1) + (abc[i-2,2]*rate2) }

If we apply “Filter” function the code will be like:

abc$effect2 <- filter(abc$Data1, filter = 0.5, method = "recursive")

Now let’s compare our output.

As you can see “Filter” is considering only last week’s effect but we need to consider last 2 weeks’ effect as per our business requirement. Our job doesn’t end here. We need to make decay rate (effect rate) very carefully as different promotion activity would have different decay rate. For example TV ad will last longer than email ad.

Please comment below your thoughts and let me know if you can improve this article.