Initial Parameter Estimate for Baker and Lonsdale Equation
It can be difficult to determine equations for automatic initial parameter estimation that are robust across many data sets. For this reason the method used for the Baker and Lonsdale equation is briefly discussed here.
Part of the equation for automatic initial parameter estimation is shown in the Variables edit box of the Edit Code dialog. This equation is:
The first two arguments of the “ape” function (automatic parameter estimation) are the x and y variables for a rational polynomial regression. The last three arguments specify the rational polynomial to have a numerator of order 1, a denominator of order 0 and a 0 indicating the lack of an intercept parameter in the numerator; i.e., a rational polynomial of the form kx.
Thus the “ape” function fits the left hand side of the Baker and Lonsdale equation to the right hand side (kt) and obtains the parameter k that we use as an initial estimate for k in the nonlinear regression.
The statement k = G(0) in the Initial Parameters section simply says to use the first parameter of the linear regression as an estimate for the parameter k (q is a dummy variable and can take any value).