Matthew Mata

Postmodeling Sensitivity Analysis to Detect the Effect of Missing Data Mechanisms

Incomplete or missing data is a common problem in almost all areas of empirical research. It is well known that simple and ad hoc methods such as complete case analysis or mean imputation can lead to biased and/or inefficient estimates. The method of maximum likelihood works well; however, when the missing data mechanism is not one of missing completely at random (MCAR) or missing at random (MAR), it too can result in incorrect inference. Statistical tests for MCAR have been proposed, but these are restricted to a certain class of problems. The idea of sensitivity analysis as a means to detect the missing data mechanism has been proposed in the statistics literature in conjunction with selection models where conjointly the data and missing data mechanism are modeled. Our approach is different here in that we do not model the missing data mechanism but use the data at hand to examine the sensitivity of a given model to the missing data mechanism. Our methodology is meant to raise a flag for researchers when the assumptions of MCAR (or MAR) do not hold. To our knowledge, no specific proposal for sensitivity analysis has been set forth in the area of structural equation models (SEM). This article gives a specific method for performing postmodeling sensitivity analysis using a statistical test and graphs. A simulation study is performed to assess the methodology in the context of structural equation models. This study shows success of the method, especially when the sample size is 300 or more and the percentage of missing data is 20% or more. The method is also used to study a set of real data measuring physical and social self-concepts in 463 Nigerian adolescents using a factor analysis model.

A numerical scheme for particle-laden thin film flow in two dimensions

The physics of particle-laden thin film flow is not fully understood, and recent experiments have raised questions with current theory. There is a need for fully two-dimensional simulations to compare with experimental data. To this end, a numerical scheme is presented for a lubrication model derived for particle-laden thin film flow in two dimensions with surface tension. The scheme relies on an ADI process to handle the higher-order terms, and an iterative procedure to improve the solution at each timestep. This is the first paper to simulate the two-dimensional particle-laden thin film lubrication model. Several aspects of the scheme are examined for a test problem, such as the timestep, runtime, and number of iterations. The results from the simulation are compared to experimental data. The simulation shows good qualitative agreement. It also suggests further lines of inquiry for the physical model.

Advances in Analysis of Mean and Covariance Structure when Data are Incomplete

Abstract Missing data arise in many areas of empirical research. One such area is in the context of structural equation models (SEM). A review is presented of the methodological advances in fitting data to SEM and, more generally, to mean and covariance structure models when there is missing data. This encompasses common missing data mechanisms and some widely used methods for handling missing data. The methods fall under the classifications of ad-hoc, likelihood-based, and simulation-based. Also included are the results of some of the published simulation studies. In order to encourage further research, a method is proposed for performing sensitivity analysis, which up to now has been seemingly lacking. A simulation study was done to demonstrate the method using a three-factor factor analysis model, focusing on MCAR and MNAR data. Parameter estimates from samples of all available data, in the form of box plots, are compared with parameter estimates from only the complete data. The results indicate a possible distinction for determining missing data mechanisms.