Modeling number of phone calls with OLS

Question

Have anyone tried modeling number of phone calls using OLS? The dataset is number of calls per months for each customer's account. The dependent variable is number of calls or average number of calls, and the explanatory variables are customer specific variables including number of purchases, total spend and so on....

How do you deal with zero callers? Only small proportion of customers actually call, 5%. I am attempting to build a predictive model, so I want to keep zero callers in the model.

I do not believe that number of call is bounded or censored random variable? I thought zero number of calls is a true zero and there is to account for it? Do I need to use Tobit for the estimation here?

M

Answer 1

Just from knowing that there are many zeros in the data, this would suggest to me that you use a zero-inflated poisson model - a generalised linear model.

Answer 2

• Since this is time series data you would be well advised to include some form of "time variable" in the model. This could be accomplished by including seasonal dummies and/or seasonal autoregressive structure. You might also have one or more Level Shifts and/or one or more trends in the data. You might have changes in parameters or error variance over time that might need to be incorporated. Incorporating predictor variables would be important making sure that correct contemporaneous and lag effects were treated. Additionally you might want to detect anomalies/pulses so that your model parameters were robust to them via Intervention Detection. In general this is referred to as a Box-Jenkins Model with Causal Variables (ARMAX or Transfer Functions).You might want to Google "regression vs box-jenkins" to find out more about the whys and wherefores of incorporating time series structure into your model. Be careful about some web content that incorrectly positions Box-Jenkins as being non-causative. The univariate (single series approach) is called ARIMA Modelling. This approach is only suggested when you don't want to include predictor variables. Lots of incorrect textbooks and web sites don't make this clear as they assert things like “Box-Jenkins ignores information that might be contained in a structural regression model”

For example google "difference between box-jenkins and regression" and you will get some other hits on this topic. The first hit leads to a typical misrepresentation of what Box-Jenkins models are. For example "Box-Jenkins ignores information that might be contained in a structural regression model" is a half-truth as what is more correct is to say “Box-Jenkins without Causal Variables etc.”