#### Abstract

In random coefficients regression, we are often interested in the mean of a certain para-meter particular to the experimental unit (EU). When the mean depends on some treatment regimen, we are then interested in comparing the means among the different treatments. When the EUs are repeatedly measured on a variable containing information about the EU parameter, a standard procedure is to estimate each EU parameter and treat the estimates as the response variables. This is especially true when the regression model for an EU is non-linear. Often, for designed experiments with a factorial treatment structure, the estimated EU parameters are then modeled with an appropriate linear (mixed) model. Here, we consider a split-plot experiment conducted to detect differences in the half-life of a compound between different treatment regimens of the compound, namely compound preparation and temperature (whole-plot factors) and initial compound amount (split-plot factor). Initially, we provide a standard (classical) analysis plan, and then present a Bayes random coefficients regression model to address the researcher’s questions of interest. We finally compare the results from the standard and Bayes analyses.

#### Keywords

hierarchical model, MCMC

#### Creative Commons License

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

#### Recommended Citation

Landes, Reid D.; Spencer, Trey; and Zelaya, Ian A.
(2005).
"A BAYESIAN RANDOM COEFFICIENT NONLINEAR REGRESSION MODEL FOR A SPLIT-PLOT EXPERIMENT,"
*Conference on Applied Statistics in Agriculture*.
http://newprairiepress.org/agstatconference/2005/proceedings/10

A BAYESIAN RANDOM COEFFICIENT NONLINEAR REGRESSION MODEL FOR A SPLIT-PLOT EXPERIMENT

In random coefficients regression, we are often interested in the mean of a certain para-meter particular to the experimental unit (EU). When the mean depends on some treatment regimen, we are then interested in comparing the means among the different treatments. When the EUs are repeatedly measured on a variable containing information about the EU parameter, a standard procedure is to estimate each EU parameter and treat the estimates as the response variables. This is especially true when the regression model for an EU is non-linear. Often, for designed experiments with a factorial treatment structure, the estimated EU parameters are then modeled with an appropriate linear (mixed) model. Here, we consider a split-plot experiment conducted to detect differences in the half-life of a compound between different treatment regimens of the compound, namely compound preparation and temperature (whole-plot factors) and initial compound amount (split-plot factor). Initially, we provide a standard (classical) analysis plan, and then present a Bayes random coefficients regression model to address the researcher’s questions of interest. We finally compare the results from the standard and Bayes analyses.