Environmental data often include left-censored values reported to be less than some limit of detection (LOD). While simple imputation of a specific value such as LOD/2 is commonly implemented in practice, maximum likelihood methods accounting for censoring provide an alternate way of analyzing such data. Concentration levels of trace metal contaminants in water are typically modeled with normal or lognormal distributions. The corresponding maximum likelihood estimates (MLEs) of means and

more »

... es in univariate analyses can be obtained from standard software packages; however, a multivariate analysis may be more appropriate when multiple measurements are taken from the same entity. For example, the overall contamination level of freshwater streams may be represented by a linear combination of several dissolved trace metal amounts present within. Especially in less polluted areas, one or more of these levels may fall below the LOD. We propose a multivariate method that provides MLEs of mean and unstructured covariance parameters corresponding to a multivariate normal or lognormal distribution in the presence of left-censored and missing values. In conducting hypothesis tests and estimating functions of MLEs with appropriate standard errors, we apply this multivariate method to trace metal concentration data collected from freshwater streams across the Commonwealth of Virginia.