Nonlinear Regression: Residual Analysis

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able_archer 2016-12-1

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评论： able_archer 2016-12-1

Hi,

when performing a residual analysis of a classic linear regression model, the residuals typically have to fulfill three requirements:

1) Normal distribution

2) Constant Variance (Homoscedasticity)

3) Freedom of Autocorrelation

However, few sources can be found about residual analysis in nonlinear regression (especially if robust methods such as bisquare or LAR are applied). Does anyone know if the requirements to the residuals remain the same?

Thanks

Vince

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Answer 1

Krispy Scripts 2016-12-1

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My understanding is that non-linear regression is needed when such things as normal distribution, homoscedasticity, and autocorrelation are not met, that is that there is some correlation among dimensions that is not linear. I do not know as to any stated residuals that are required or necessary for non-linear regression. However, those performing non-linear regression normally plot the residual plot, which in non-linear regression tends to show hyperbolic or other abnormal like distributions instead of the normal spread around the horizontal of a residual plot.

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able_archer 2016-12-1

Hi,

thank you for answering. Indeed, my residuals plot indicates there is some sort of periodic fluctuation in the residuals. The QQ-Plot of residuals over a normal distribution shows a good (though not perfect) match. I'm ok with the observed deviations as I don't need a model that explains every little temporary change as long as the overall trend is met. The question is if this is ok or if such an approach is violating basic assumptions, thus rendering the regression invalid (the plots will be part of a thesis, so I want to be waterproof :).

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