Still getting comments from Dean1230 about this post. He insists that the cubic fit is insignificantly better than the linear model (for the tide gauge data from Sewell’s Point), and that the cubic model shouldn’t be extrapolated (which I said in the first place).
I suspect he thinks he now has ironclad proof of his point. It’s based on extrapolating curve fits based on limited data, ending before the present.
There’s this one:
In another post, i suggested doing curve-fits up to 2000, and then projecting them from that point forward. What happens with AIC if you only use the data to 2000? Does it still exhibit the much higher predictive power?
There’s also this:
No, if you limited your information to ending in 1960, then by definition the end of that line in a cubic would be up-turned. It would not be a predictor of the future. But it still has a better AIC than the linear model.
If I did this right (using annual data for Sewell Point and the linear and cubic fit models in R), the AIC for the linear model for the data up to 1960 is 316.7091, the AIC for the cubic fit is 311.7673, hence the cubic fit is “better”. And yet, it still had no predictive ability. If we extrapolated the cubic fit from 1960 to 2010, the predicted rise would be almost 2 meters! The actual rise is about 200 mm.
Dean, you don’t know what you’re doing.
First of all, you’re mistaken that “by definition the end of that line in a cubic would be up-turned.” It depends on when the inflection point occurs. In this case a cubic does end up-turned, but not “by definition.” That’s a minor point.
It’s true that a cubic model has lower AIC than a linear one for this time span. We could even call the difference “significant.” Here’s the data, up to and including 1960, together with a linear fit (in blue) and cubic fit (in red):
But it’s not true that AIC suggests the cubic model is best. In fact it specifically suggests it isn’t.
I didn’t pick “cubic” out of a hat. I picked it because it had the best AIC of all polynomial models from 1st to 10th degree. Let’s see what happens when we do that using data only up to the year 1960:
It turns out that it’s not the cubic model which gives the lowest AIC, it’s the quadratic model. Adding a cubic term isn’t justified by this analysis. But Dean, you didn’t think about that. Because you really don’t know what you’re doing.
If we extrapolate the quadratic model up to 2010, we would not conclude that “the predicted rise would be almost 2 meters!” We’d get this:
This further illustrates my point: that extrapolating statistical models to make predictions is fraught with danger at best, and a fool’s errand at worst. Yes, that was the point.
Now let’s consider what it was that I actually said about the cubic model in the original post:
Of course it’s only a model and maybe (almost certainly in fact) not the best one, but it does prove (in the statistical sense) one thing: that the trend is not a straight line. It’s not. Claiming that it is, is foolish.
Note that I said the cubic model was almost certainly not the best one. I certainly didn’t flatter it. The only useful result I ascribed to it was to prove (in the statistical sense) that the trend is not a straight line.
I went on to extrapolate the cubic model, not to suggest that such was a good idea but to show how different it was from a linear extrapolation.
Then, I stated explicitly that it’s not valid to extrapolate this to the end of the century. Same goes for the linear model. That was the point.
Dean, you have two choices. First: you can repeat this exercise using data up to and including 2000. That will enable you to come back here and continue to argue with those of us who know what we’re talking about. You don’t. Second: you might admit to yourself that you don’t know what you’re talking about and actually learn something.
It seems to me that those two choices are mutually exclusive.