y

]]>.. and no line connecting Sunday with Monday — the biggest difference out of all adjacent days?

]]>Aki:

But wouldn’t the log scale help when considering the long term trend (which moves about 20% from min to max)? Put it this way: suppose there is a fixed multiplicative effect of day of year or day of week or whatever. In the additive model, this will show up as a larger effect in 1976 (when the total #births is lowest). And, indeed, if you look at the day-of-week effects, the curve for 1976 is pretty high. It’s not the highest—1988 is the highest, presumably because there were real changes during this period with more scheduled births—but it’s up there, perhaps an artifact of the additive model for what fundamentally is a multiplicative process.

Regarding the Gaussian approximation, I wonder if there would be a way to do a multiplicative model by fitting an additive model on the log of the raw data and just adjusting the data variance accordingly. So the computation would be just as easy, it’s just that instead of approximating the binomial density with a Gaussian, we’d be applying the Gaussian approx to the density of the log of a binomially-distributed random variable.

]]>Rahul: Scale is not arbitrary. I first used absolute scale, but since I was interested in comparing the sizes of the different effects, it required extra mental effort to calculate whether the relative changes are big or not. I used % scale, because it looks prettier than having decimals (0.8 0.9 1.0 1.1). This scale has also benefit that when I made similar figure for Finland, I could immediately see that the size of the relative effects were similar. During these years on a average Friday there were about 10,000 births. We could have the absolute scale on the right.

Andrew: the data is count data, but with so high mean counts it can approximated very well with a Gaussian model. Log scale is not needed to ensure positivity and would transform the distribution away from Gaussian.

]]>Or exploit the unused right hand y-axis. You could relabel that in #births?

]]>Rahul:

Good point. I think it would make sense to put the top graph (trends) on an absolute scale (perhaps #births per day, as you suggest) and the others on relative scales. Also, looking at the description in the book, it appears that we fit an additive model directly on the data, but now I’m thinking it would make more sense to work on the log scale.

]]>D.O.:

Yes, as we discuss in the book, the model could be improved by replacing the daily spikes by little functions with “ringing” so that a dip on a particular day corresponds to smaller increases on the days right before and after. In the above graphs, I think that some of the daily effects have been inappropriately absorbed into the seasonal effect.

]]>e.g. How many actual births do happen on a average Friday?

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