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Thread: combining error terms for two dissimilar regressions

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    combining error terms for two dissimilar regressions




    I have a linear regression for Y on X, and a power regression for Z on Y, each having associated error. (the Y values are different (independent) in each case). I have combined the equations to model Z as a function of X.

    What I want is a confidence envelope around the model estimates of Z.

    Thanks,

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    Re: combining error terms for two dissimilar regressions

    Can you write out your model equations, so that we can better understand what you are doing.


    Thanks.
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    Re: combining error terms for two dissimilar regressions

    N = aM +b, where N = number of eggs, M = mass of a small quantity of eggs
    T = cS^f, where T = total mass of eggs, S = size of crab

    so substituting produces the model estimating number of eggs N from size (S): N = a(cS^f)+b

    what I'd like to be able to show are confidence envelope around the model predictions

    thanks
    Last edited by George Kraemer; 09-22-2017 at 11:12 AM.

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    Re: combining error terms for two dissimilar regressions

    Do you have the data which you use to estimate a, b, c and f?

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    Re: combining error terms for two dissimilar regressions

    yes. So the estimates have error terms associated.

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    Re: combining error terms for two dissimilar regressions

    You have problems because the model isn't linear and can't be made so. Things are also complicated because a and b (and c and f) are correlated.
    This should (possibly could?) work -
    Re-sample the first set of data, do the regression and get an a,b pair.
    Re-sample the second set of data (log-logged), and do the regression to get a c,f pair.
    For a particular size S, use a,b,c, and f to calculate N.
    Repeat the three steps a few 1000 times to get a distribution for N. Find the 2.5% and 97.5%tiles.

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    Re: combining error terms for two dissimilar regressions

    thanks; that sounds do-able.

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    Re: combining error terms for two dissimilar regressions

    Are you looking for a confidence interval or are you actually interested in a prediction interval?
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    Re: combining error terms for two dissimilar regressions

    one more question; what's the rule - assuming there is one - on the resample n (i.e., how many observations from the full data set used to estimate the constants each time?)?. The power curve data set has 258 observations. The linear data set has 102 observations

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    Re: combining error terms for two dissimilar regressions

    not sure; a measure of confidence around the predictions from the model

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    Re: combining error terms for two dissimilar regressions

    Quote Originally Posted by Dason View Post
    Are you looking for a confidence interval or are you actually interested in a prediction interval?
    A good point, Dason. This will give a confidence interval for the mean value of the N for some given value of S. For a prediction interval you would also need to find the spread around the mean. But how to do that?

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    Re: combining error terms for two dissimilar regressions

    Quote Originally Posted by George Kraemer View Post
    one more question; what's the rule - assuming there is one - on the resample n (i.e., how many observations from the full data set used to estimate the constants each time?)?. The power curve data set has 258 observations. The linear data set has 102 observations
    Use the full data set for each, and re-sample with replacement. The accuracy of the constants depends on the sample size, so use all you have.

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    Re: combining error terms for two dissimilar regressions

    sorry, but still unsure. E.g., for the 102 mass-count observations, how many should be resampled each time for the estimates of the constants?

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    Re: combining error terms for two dissimilar regressions


    Make a new list of 102 pairs, choosing each pair at random from your original 102 pairs. Get a and b for that re-sampled list. This will give you a plausible a and b, correlated appropriately.
    Do the same with the 258 pairs for the other set (after log-logging) to get a plausible c, f pair.
    Find N.
    Repeat.

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