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The NLIN Procedure |
A nonlinear regression model sometimes fails to be close to linear due to the properties of a single parameter. When this occurs, bias in the parameters can render inferences using the reported standard errors and confidence limits invalid. You can often fix the problem with reparameterization, replacing the offending parameter by one with better estimation properties.
You can use Hougaard's measure of skewness, g_{1i}, to assess whether a parameter is close to linear or whether it contains considerable nonlinearity. Specify the HOUGAARD option in the PROC NLIN statement to compute Hougaard's measure of skewness.
According to Ratkowsky (1990), if |g_{1i}| < 0.1, the estimator of parameter is very close-to-linear in behavior and, if 0.1 < |g_{1i}| < .25, the estimator is reasonably close-to-linear. If |g_{1i}| > .25, the skewness is very apparent. For |g_{1i}| > 1, the nonlinear behavior is considerable.
Hougaard's measure is computed as follows
where the sum is a triple sum over the number of parameters and
In the preceding equation, J_{m} is the Jacobian vector and H_{m} is the Hessian matrix evaluated at observation m. This third moment is normalized using the standard error as
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