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I have data on monthly purchases of a certain type of product for different brands over the last several years. I also have estimates of consumers returning to the market to buy a new product. This data is also monthly and goes back four years, though the market has only stabilized in the last 1 1/2 to 2 years.

I would like to regress purchases (y) on market re-entry prediction (x) by brand to see if I can quantify the relationship. I know from graphical analysis that the two often but not always track together pretty well, but there are of course many other factors that go into purchases that aren't being modeled here. In addition, the extent to which they track well varies across brands and across time, though the relationship within each brand has been more consistent in the last 18-24 months.

Questions:
  1. Are there any special considerations for using two variables that have a time component but not including time in the model? (Such as auto-correlation)
  2. If I only have around 18 data points (the last year and a half) for each brand, does that create a small-sample problem? (I'm not sure because it isn't really a sample, just a shorter data history being included.)
  3. Does it matter that both variables are counts and are in a sense aggregates of underlying transaction data? (For example, the analysis is mostly focused on brand, but there are purchases of different models that are being rolled up into the brand figure.)
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  1. No special consideration other than introducing time as possible auxiliary predictor .

  2. I have had some success in introducing seasonal monthly dummies and then permitting necessity testing / stepdown modelling.

  3. I don't see any problem with count data / aggregate data

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  • $\begingroup$ Is stepdown modeling is the same as backward elimination? Is necessity testing the same? $\endgroup$ – Kevin M Jun 18 '15 at 14:29
  • $\begingroup$ preciseley while step-up modelling (sufficiency testing) deals with adding structure that is currently omitted $\endgroup$ – IrishStat Jun 18 '15 at 14:31
  • $\begingroup$ And how about the small sample size problem? Do I not need to worry about that when the small number of date points reflects the small number of periods? $\endgroup$ – Kevin M Jun 18 '15 at 14:32
  • $\begingroup$ Often with small sample size we bypass the formality/nicety of IDENTIFICATION and simply set up a straw-man model , estimate and step-down as needed. This is considered heretical in some quarters but I am a practical heretic. $\endgroup$ – IrishStat Jun 18 '15 at 14:35

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