Parameter Estimation in Nonlinear Regression: Exploring Confidence Intervals for Estimated Coefficients
Date of Award
Bachelor of Science
Department Chair or Program Director
Major or Concentration
Previously, we explored generating data using four different curved source functions with normally distributed errors and then fitting various curved models to this generated data. This research aimed to study the reliability of the goodness-of-fit measures, such as R2 and AIC, when the data originates from a curved source model. Ultimately, we found that, for logarithmic source models, AIC picks the correct source model most often, while R2 selects either the logarithmic or quadratic source models. For quadratic source models, AIC picks the power source model most often, whereas R2 selects the correct source model. Lastly, we expanded our project to investigate how AIC and R2 perform when violating the assumptions for regression analysis and concluded that the presence of an influential point impacts goodness-of-fit measures more for logarithmic than quadratic source models.
This semester, we have explored producing bootstrap confidence intervals for the coefficients of nonlinear regression models to fit generated data for a variety of different curved models. More specifically, using R, I use a command for nonlinear modeling to find the best-fit curved model given data from a known curved association and then apply bootstrap methods to produce the confidence interval estimates. The datasets will be generated for models with different levels of curvature, amounts of variation in the points around the best-fit model for normal and non-normal error distributions, and with varying numbers of data points. The observed proportion of intervals containing the true parameter values are observed.
Williams, Brandon, "Parameter Estimation in Nonlinear Regression: Exploring Confidence Intervals for Estimated Coefficients" (2021). Student Research Submissions. 390.