Approximate confidence levels and regions for non-linear models

3 Approximate confidence levels and regions for non-linear models 

An important method for calculating approximate confidence intervals is through linearization with a first-order Taylor series expansion around the estimated parameter, which results in 

Practically, an approximation of the Jacobian can be detemtined by the following procedure. First, find the parameters (9) that give a minimum SSE(0). Change one parameter at a time by a certain amoimt, for example 1% of the parameter value, with this parameter denoted 6p,i%. Note that in 9p i%, only one parameter,p, changes, while all others remain at the minima. Thereafter, change this parameter back, change the next one, and so on. The approximated Jacobian can then be retrieved 

The 1 — a approximate confidence interval for the parameter p in the model can be determined by 

Note the similarities between this equation and the case of the linear equation. The only difference is that X is replaced /. The standard deviation, s, can be retrieved from the variance, s  

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