Maximum Likelihood Estimation of Multivariate Normal Parameters in the Presence of Left-Censored and Missing Data: A Pseudo-Likelihood Approach

• Activity Number: 195
• Type: Contributed
• Date/Time: Monday, August 5, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Heather Hoffman*+ and Robert E. Johnson
• Companies: George Washington University and Vanderbilt University Department of Biostatistics
• Keywords: limit of detection ; multivariate normal distribution ; maximum likelihood estimation ; trace metal concentrations

Abstract

Environmental data often include left-censored values less than some limit of detection (LOD). While simple imputation of LOD/2 is common, maximum likelihood methods accounting for censoring are preferred. Concentration levels of trace metal contaminants in water are typically modeled with (log)normal distributions. Maximum likelihood estimates (MLEs) of means and variances in univariate analyses are obtainable from standard software packages; however, multivariate analyses are more appropriate when multiple measurements come from the same entity. For example, the contamination level of freshwater streams is represented by a linear combination of dissolved trace metal amounts present within. In less polluted areas, these levels may fall below the LOD. We propose a pseudo-likelihood method utilizing pairs of variables that provides MLEs of mean and unstructured covariance parameters corresponding to a multivariate (log)normal distribution in the presence of left-censored and missing values. In conducting hypothesis tests and estimating functions of MLEs with standard errors, we apply this method to trace metal concentration data collected from freshwater streams across Virginia.