Confidence regions, reactivity ratios

The error-in-variables method was used to estimate the reactivity ratios. This method was developed by Reilly et al. (57, 58), and it was first applied for the determination of reactivity ratios by O Driscoll, Reilly, and co-workers (59, 60). In this work, a modified version by MacGregor and Sutton (61) adapted by Gloor (62) for a continuous stirred tank reactor was used. The error-in-variables method shows two important advantages compared to the other common methods for the determination of copolymer reactivity ratios, which are statistically incorrect, as for example, Fineman-Ross (63) or Kelen-Tiidos (64). First, it accounts for the errors in both dependent and independent variables the other estimation methods assume the measured values of monomer concentration and copolymer composition have no variance. Second, it computes the joint confidence region for the reactivity ratios, the area of which is proportional to the total estimation error. 

Figure 3. Joint confidence regions for the reactivity ratios in AAM-DMAEM at 60 °C. Key —, KPS initiator ---------------, ACV initiator.

Figure 4. Joint confidence region for the reactivity ratios in AAM-DMAEA at 60 °C with ACV as the initiator.

Einally, we are concerned with the precision of the reactivity ratios or, in other words, the joint confidence regions of the parameter estimates. We have stated at the beginning of this section that our objective is to estimate reactivity ratios of maximum precision. This is equivalent to minimizing the joint confidence region of the parameters. The joint confidence regions can be generated using methods such as shown by Polic et al. [117]. 

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