Estimation of parameters where dependent observations are related by equality constraints

Pirt's model for microbial growth and product formation are reparameterized to obtain multiresponse models with common parameters. The dependent variables in the models are related through the available electron and carbon balance constraints. Covariance adjustment is used to reduce the growth model to a unit variate linear model with covariates. Therefore, standard multiple regression programs can be used to obtain combined point and interval estimates of true biomass energetic yield, true product yield and maintenance coefficient. This approach may yield “better” estimates than the maximum likelihood approach when an appropriately selected subset of covariates is used. Nonlinear estimation procedures are also considered; these procedures are efficient with few responses; however, as the number of responses per observation increase, they may require a lot of computing time. For illustration several data from the biochemical engineering literature are analyzed by the proposed methods.