arXiv subjects

John C. Galati

Publications and source records attributed to John C. Galati.

3 recordsLinked to original sources

arXiv2019

When is $Y_{obs}$ missing and $Y_{mis}$ observed?

In statistical modelling of incomplete data, missingness is encoded as a relation between datasets Y and response patterns R. The partitioning of Y into observed and missing components is often denoted Yobs and Ymis. We point out a mathematical defect in this notation which results from two different mathematical relationships between Y and R not being distinguished, (Yobs, Ymis, R) in which Yobs values are always observed, and Ymis values are always missing, and the overlaying of a missingness pattern onto the marginal distribution for Y, denoted (Yobs, Ymis). With the latter, Yobs and Ymis each denote mixtures of observable and unobservable data. This overlaying of the missingness pattern onto Y creates a link between the mathematics and the meta-mathematics which violates the stochastic relationship encoded in (Y, R). Additionally, in the theory there is a need to compare partitions of Y according to different missingness patterns simultaneously. A simple remedy for these problems is to use four symbols instead of two, and to make the dependence on the missingness pattern explicit. We explain these and related issues.

stat.ME↗

arXiv2019

Three issues impeding communication of statistical methodology for incomplete data

We identify three issues permeating the literature on statistical methodology for incomplete data written for non-specialist statisticians and other investigators. The first is a mathematical defect in the notation Yobs, Ymis used to partition the data into observed and missing components. The second are issues concerning the notation `P(R|Yobs, Ymis)=P(R|Yobs)' used for communicating the definition of missing at random (MAR). And the third is the framing of ignorability by emulating complete-data methods exactly, rather than treating the question of ignorability on its own merits. These issues have been present in the literature for a long time, and have simple remedies. The purpose of this paper is to raise awareness of these issues, and to explain how they can be remedied.

stat.OT↗

arXiv2019

What is meant by 'P(R|Yobs)'?

Missing at Random (MAR) is a central concept in incomplete data methods, and often it is stated as $P(R\mspace{3mu}|\,Y_{obs}, Y_{mis}) = P(R\mspace{3mu}|\,Y_{obs})$. This notation has been used in the literature for more than three decades and has become the de facto standard. In some cases, the notation has been misinterpreted to be a statement about conditional independence. While previous work has sought to clarify the required definitions, a clear explanation of how to interpret the standard notation is lacking, and a definition of the function $P(R\mspace{3mu}|\,Y_{obs})$ for non-MAR mechanisms is difficult to locate in the literature. The aim of this paper is to fill these gaps.

stat.ME↗