Keywords: censored, indicator variable, maximum-likelihood estimation, multiple regression, parameter, Newton-Raphson iteration, underspecification
The National Descriptive Model of Mercury in Fish (NDMMF) is a multiple linear regression model that uses fish length as a covariate to control for biomagnification. This model provides a pragmatic way to make use of available but heterogeneous data on mercury concentration in fish tissue, including censored observations. These data are derived from fish samples independently collected by various agencies over a period of several decades from a large number of different lakes and streams. To be able to predict fish-tissue mercury concentrations by time, species, fish length, and location throughout large geographic regions, this model may include tens of thousands of parameters and indicator variables. Computation of maximum-likelihood parameter estimates for the model requires typically lengthy Newton-Raphson iteration over all of the numerous parameters, and the set of observations used for parameter estimation must exclude isolated values that would leave the model underspecified. The amount of computation required is, however, greatly reduced when the set of parameters is relatively small or when Newton-Raphson iteration begins with near-optimal parameter estimates. Custom software implements incremental estimation by partitioning the observations into small groups that may be appended sequentially to the growing set of observations for each successive round of estimation without including any isolated species or water bodies that would leave the model underspecified in that round.