#### Abstract

Sometimes a nonlinear regression parameter for an individual is the outcome of interest. But due to variability among individuals, the individuals’ regression parameters cannot be estimated with the same amount of precision. This problem of heterogeneous variance complicates the ultimate goal of estimating population-level regression parameters with two usual methods: (i) the simple arithmetic mean of individually estimated regression parameters and (ii) random coefficients regression (RCR). Weights are proposed for each method to account for the heterogeneity problem. The methods are illustrated with chick weights collected over time. Monte Carlo simulation allows comparison of statistical properties of the four estimators for small, moderate and large sample sizes. The arithmetic means tended to outperform the RCR estimators with respect to mean square error and bias; and their associated confidence intervals held nominal levels. Actual coverage of confidence intervals produced from RCR methods fell below nominal levels in some cases; however this discrepancy may be an algorithm error. Overall, the simpler arithmetic mean estimators tend to have either better or comparable statistical properties to those estimators from RCR methods.

#### Creative Commons License

This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

#### Recommended Citation

Landes, Reid D.
(2010).
"NONLINEAR REGRESSION PARAMETERS AS OUTCOMES: SIMPLE VS. SOPHISTICATED ANALYSES,"
*Annual Conference on Applied Statistics in Agriculture*.
http://newprairiepress.org/agstatconference/2010/proceedings/13

NONLINEAR REGRESSION PARAMETERS AS OUTCOMES: SIMPLE VS. SOPHISTICATED ANALYSES

Sometimes a nonlinear regression parameter for an individual is the outcome of interest. But due to variability among individuals, the individuals’ regression parameters cannot be estimated with the same amount of precision. This problem of heterogeneous variance complicates the ultimate goal of estimating population-level regression parameters with two usual methods: (i) the simple arithmetic mean of individually estimated regression parameters and (ii) random coefficients regression (RCR). Weights are proposed for each method to account for the heterogeneity problem. The methods are illustrated with chick weights collected over time. Monte Carlo simulation allows comparison of statistical properties of the four estimators for small, moderate and large sample sizes. The arithmetic means tended to outperform the RCR estimators with respect to mean square error and bias; and their associated confidence intervals held nominal levels. Actual coverage of confidence intervals produced from RCR methods fell below nominal levels in some cases; however this discrepancy may be an algorithm error. Overall, the simpler arithmetic mean estimators tend to have either better or comparable statistical properties to those estimators from RCR methods.