Missing data mechanisms and their implications on the analysis of categorical data

We review some issues related to the implications of different missing data mechanisms on statistical inference for contingency tables and consider simulation studies to compare the results obtained under such models to those where the units with missing data are disregarded. We confirm that although, in general, analyses under the correct missing at random and missing completely at random models are more efficient even for small sample sizes, there are exceptions where they may not improve the results obtained by ignoring the partially classified data. We show that under the missing not at random (MNAR) model, estimates on the boundary of the parameter space as well as lack of identifiability of the parameters of saturated models may be associated with undesirable asymptotic properties of maximum likelihood estimators and likelihood ratio tests; even in standard cases the bias of the estimators may be low only for very large samples. We also show that the probability of a boundary solution obtained under the correct MNAR model may be large even for large samples and that, consequently, we may not always conclude that a MNAR model is misspecified because the estimate is on the boundary of the parameter space.

Atmospheric pressure photoionization mass spectrometry as a tool for the investigation of the hydrolysis reaction mechanisms of phosphite antioxidants

The hydrolysis reaction mechanism of phosphite antioxidants is investigated by liquid chromatography-mass spectrometry (LC/MS). The phosphites were chosen because they differed in chemical structure and phosphorus content. Dopant assisted-atmospheric pressure photoionization (DA-APPI) is chosen as the ion source for (lie ionization of the compounds. [it our previous work, DA-APPI was shown to offer an attractive alternative to atmospheric pressure chemical ionization (APCI) since it provided background-ion free mass spectra and higher sensitivity [M. Papanastasiou, et al., Polymer Degradation and Stability 91 (11) (2006) 2675-2682]. In positive ion mode, the molecules are generally detected in their protonated form. In negative ion mode, the phosphites are unstable and only fragment ions are observed: these however, are characteristic of each phosphite and may be used for the identification of the analytes in complex mixtures. The analytes under investigation are exposed to accelerated humid ageing conditions and their hydrolytic pathway and stability is investigated. Different substituents around the phosphorus atom are shown to have a significant effect on the stability of the phosphites, with phenol substituents producing very hydrolytically stable structures. Alkanox P24 and PEP-36 follow a similar hydrolytic pathway via the scission of the first and then the second P-O-phenol bonds, eventually leading to the formation of phenol, Phosphorous acid and pentaerythritol as end products. HP-10 exhibits a rather different Structure and the products detected suggest scission of either the P-O-hydrocarbon or one of the P-O-phenol bonds. A phenomenon similar to that of autocatalysis is observed for all phosphites and is attributed to the formation of dialkyl phosphites as intermediate products. (C) 2008 Elsevier B.V. All rights reserved.