I have 2 variables (x and y) and an independent variable (z). I have the experimental data for x, y and z in the form of mean and SD. The equations that I am trying to fit my data in are a bit complex.
I have seen literature and people just put the mean values to fit the data into the equations and look at goodness-of-fit using R2, residuals, cAIC, etc.
I believe that this approach of substituting x's and y's in equation and comparing the experimental z's with theoretical z's is an oversimplification as we donot get to compare the experimental and predicted SD.
A typical equation can take the form of z=1/(ax+by) or z=(ax+bxy), etc... where a and b are constants. Is there a way to calculate SD of z and compare with the experimental SD? I have seen people applying Taylor's series but being a biologist I am not able to handle the complexities of Taylor's series. Can anyone suggest me an easier way or a software to do the task?
Thanks in advance!
Dear Raman,
Based on your description, it is difficult to tell what is exactly what you want do. For example, you say that z is your independent variable, but your example models suggest that z is the dependent variable. Anyway, to me your problem looks more or less like a standard nonlinear regression problem, and you’ll find the theory in any good textbook on this topic. In addition, you can carry out the fitting, and get for example the estimated standard deviation of the predicted values using any good statistics software.
If both dependent and independent variables are random variables with substantial standard deviation, standard regression software might not be sufficient, and the theory becomes more complicated. In that case, you may need e.g. bootstrap estimates in estimating the prediction error. However, in my experience, taking the random error of the independent variable into account has significant effect only if the standard deviations of these errors are large compared to the standard deviation of the response.
It would be a lot easier to give concrete advice if you could provide an example giving both the model and the data.
Cheers,
Veli-Matti
So long as you know the equation, this might be polynomial regression (z=ax+bxy). If the equation is z=1/(ax+by) I might take a log (log(z)=log(1)-log(ax+by). Non-linear is another option as already suggested by Veli-Matti.
If you are trying a number of equations of increasing complexity to see if anything works I would suggest stopping. z=ax^(by/(cx-dy))/(ey^(fx-gy)) is just not going to end well for anyone.
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