Pay Attention to the Ignorable Missing Data Mechanisms! An Exploration of Their Impact on the Efficiency of Regression Coefficients

The use of modern missing data techniques has become more prevalent with their increasing accessibility in statistical software. These techniques focus on handling data that are <i>missing at random</i> (MAR). Although all MAR mechanisms are routinely treated as the same, they are not equal. The impact of missing data on the efficiency of parameter estimates can differ for different MAR variations, even when the amount of missing data is held constant; yet, in current practice, only the rate of missing data is reported. The impact of MAR on the loss of efficiency can instead be more directly measured by the <i>fraction of missing information</i> (FMI). In this article, we explore this impact using FMIs in regression models with one and two predictors. With the help of a <i>Shiny</i> application, we demonstrate that efficiency loss due to missing data can be highly complex and is not always intuitive. We recommend substantive researchers who work with missing data report estimates of FMIs in addition to the rate of missingness. We also encourage methodologists to examine FMIs when designing simulation studies with missing data, and to explore the behavior of efficiency loss under MAR using FMIs in more complex models.