# Determining the effect of number of likes

Let's say I have marketing data and I need to determine how effective the marketing is. The marketing strategy is to publish facebook posts at inconsistent intervals.

The goal is to see how the number of likes translates into revenue.

The data that I have is:

• Daily revenues (revenue vs time since a facebook post)
• Number of likes (with date)
• The weather (sunshine, cloudy, rainy/snowy, and daytime temperature)
• (derived) Season and day of the week

Most likely the relationship between number of likes and revenue will be non-linear and greatly depend on weather and the day of the week. Also, the weather is not independent of season. Finally, the effect of facebook posts is lagged, and potentially the lag varies significantly.

Questions

• Do I need to correct for growth of revenues over the years? If yes, how? (by finding a regression model, and then adjusting the values around it?)
• How would I find the average lag period between a post and a change in revenue "due" to that post?
• What models can I use to determine the effect of likes?

Personal thoughts

• ARIMA (not quite sure how it works)
• Regression trees. For example, if I wanted to see how the power (to increase revenue) of the number of likes is affected by the weather, I could make a plot of likes vs weather by:
1. To find one point on that plot, keep number of likes and weather static.
2. Iterate over all possible values of all other variables.
3. Merge the predictions into one (the average or the median).
• Fourier analysis to determine the lag
• Would a Markov model work here? Or potentially conditional random fields?
• Seems like you're interested in a causal effect of likes on revenue, yes? Rather than a strictly predictive model? If so, you need to consider whether likes is endogenous to revenue. For example, likes presumably cause revenue to increase, but higher revenue could imply that the product is getting out into the population, which could affect the number of likes. Strategies for addressing this probably exist with your data. – generic_user May 27 '15 at 18:23
• Do you know of any strategies for this purpose? – Anton May 27 '15 at 18:27
• They fall under the broad heading of instrumental variables. Some combination of lags could probably serve as instruments in your case, but I'd need to think about it further. What temporal resolution does your data have? – generic_user May 27 '15 at 18:36
• It would definitely have daily, if not down to the minute (raw data that is) – Anton May 28 '15 at 1:52