Dear allstat users,
I'm an Italian researcher, working at Centre for Alpine Ecology (Trento Province, Northern Italy). I have a statistical problem that I'm trying to work out, maybe you can give me some suggestions.
My problem is to calculate the limits for the sum of predictions in regression analysis. The problem can be quite easily solved for a simple linear model: y=a+bx. In this case I measured n values of x and y in my population and then once I estimated the parameters (a and b) of the model, I can predict the value of y (and related confidence limits, CI) for any given x; With a matrix approach I can calculate the CI for a sum of predicted y obtained from single x's (this is not the sum of the sigle CI: see O'Regan, 1964 - Limits for the sum of predictions in regression analysis. Forest Science 10:300-301). Now, what I'm trying to obtain are the confidence limits of a sum of predicted values for non-linear models, for example an exponential one: y=a*exp(b*x). I'm dealing with soil respiration measurements, so in my study, y= soil CO2 flux, and x= soil temperature.
During the year I measured y and x once a month, so I have n values of my variables. With this observed values I can estimate the a and b parameters of the model. At the same time during the year, I measured the soil temperature continuously at 10 min interval, so I have h values of the independent variable (these values are temporally autocorrelated!). With the single temperature values and the model, I can estimate an annual flux of CO2 for my study plot, this being the sum of the h values predicted by the model. What I'm trying to calculate are the confidence limits of this prediction; so as to have an annual CO2 flux ± something.
If you need some more explanations don't hesitate to contact me!
regards,
Mirco Rodeghiero.
See references:
*O'Regan, 1964 - Limits for the sum of predictions in regression analysis.
Forest Science 10:300-301.
*Schlaegel B.E., 1985 - Confidence bounds for the sum of volumes predicted
by weighted regressions. Forest Science 31:65-71.
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