I have replied offlist to Mr. Jarvis with my reasons for not
proceeding further with advice about implementing this request. Others
should feel free to step in if they are so inclined.
--
David.
On Jun 19, 2010, at 12:44 AM, David Jarvis wrote:
Hi, David.
Let me start at the beginning. Between the years (y) 1900 to 2009 I
have some observed temperature readings (o). For example:
y <- seq(1900, 2009)
o <- runif(110, 9, 15)
So the ordering is fixed: y and o are a time series (shown in the
linked image below). I then calculate a naïve, non-parameterised
model (m) of the data using GAM, as follows:
m <- data.frame( x, fitted( gam( y ~ s(x) ) ) )
The values from m are then actually plotted as the trend line
depicted at:
http://i.imgur.com/X0gxV.png
What I am trying to do now is to calculate how accurately GAM fits
the data. The suggestion I was given was to use RMSE on the observed
data versus the model data. It was also suggested that I use mean
bins, with each bin containing 5 values, to reduce the amount of
error in the calculation. Algorithmically, I pictured it as:
• Let index = 1
• Let size = 5
• Let o = vector of observed data
• Let ob = empty vector
• Append mean( o[index:index+size-1] ) into ob
• Let index = index + size
• Repeat from Step 5 until no more elements in o
At this point, ob would contain the average of: the first five
values, the second five values, and so on. Thus length( ob ) =
round(length( o ) / 5).
I would then repeat the same calculation on m to get mb, the model's
bins.
With those averages, I could use ob and mb to calculate the normal
root mean square deviation:
nrmse <- sqrt( mean( ob - mb ) ^ 2 ) / (max( ob ) - min( ob ))
Then turn that into a percentage:
100 - nmse
At that point I was hoping I could say that, in general, the result
indicates how closely the model fits the data. The closer to 100%,
the more accurate the trend line.
As you can tell, I have very little experience in statistics and R
so any feedback, suggestions, or general guidance would be greatly
appreciated.
Dave
P.S.
The years, the type of weather data, and the locations that the
measurements were taken can all be selected by users when they
generate the report. So sometimes the data will have 110 years,
inclusive, other times it could be 37 years (thus 37 data points).
So choosing to average 5 elements per bin is a bit arbitrary... I am
looking to get something working first before tweaking the possible
parameters for the calculation.
Thanks again!
David Winsemius, MD
West Hartford, CT
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