I've found simple explanation how to use monte carlo simulations to evaluate parameter uncertainties for non-linear regression in following publications:
Lambert, Ronald J. W., Ioannis Mytilinaios, Luke Maitland, and Angus M. Brown. ‘Monte Carlo Simulation of Parameter Confidence Intervals for Non-Linear Regression Analysis of Biological Data Using Microsoft Excel’. Computer Methods and Programs in Biomedicine 107, no. 2 (August 2012): 155–63. doi:10.1016/j.cmpb.2011.05.009.
Hu, Wei, Jing Xie, Henry Wai Chau, and Bing Cheng Si. ‘Evaluation of Parameter Uncertainties in Nonlinear Regression Using Microsoft Excel Spreadsheet’. Environmental Systems Research 4, no. 1 (January 2015). doi:10.1186/s40068-015-0031-4.
Could anyone point me a method to get prediction and confidence intervals (bands) of the non-linear model that can be included in the plot of best-fit curve? I've found a description of the Delta Method, but it requires sophisticated partial derivative calculations. I would be more interested in simpler methods (like Monte Carlo, described in above publications).
Best regards,
Marcin Stec
You seem to be talking of using bootstraping to get standard errors. If your model is linear in the regression coefficients there are simple formulae to use to use to get the bands. See Kutner et al, Applied linear Statistical Models, 5th ed. McGraw Hill, This book also discusses the case if models nonlinear in the coeff's but that is more complicated. Best, david
Marcin -
This is not a primary area for me, but I want to comment on something here: You seem to be interested in the accuracy of your predictions, but are asking about confidence intervals about regression coefficients, rather than prediction intervals about predicted y-values (which are random variables). Even if you obtain your confidence intervals, those regressors (independent variables) may have substantial interactions, including collinearity, and/or there could be an omitted variable(s) with substantial impact, such that confidence intervals about their coefficients (parameters) may not be very helpful in determining accuracy of predictions. Then there is the appropriateness of the error structure to consider.
But if you can estimate the variances of the prediction errors, you could obtain prediction intervals for given predicted y-values. (Your software may even do that for you.) If you can estimate or make a reasonable assumption about the degree of heteroscedasticity, applying the nonlinear model, then perhaps you could simulate sigma in some manner, since you appear comfortable with simulation. Perhaps you could try this for different models to compare.
You might, instead, just want to research 'model validation' techniques using part of your data as test data. You could check into performance for each of several models.
Anyway, you may just want to stop for a moment and think about what are your actual goals.
Cheers - Jim
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