About the App

This web app allows users to take clustered multivariate data with a lower limit of detection and do the following: (1) estimate the mean vector, error covariance matrix, and clustering covariance matrix, and (2) draw new predictive values.

Models Used

The uncensored data is assumed to follow a $p$-dimensional multivariate normal distribution, where the variables are correlated within observation, and clustered observations are correlated. Unstructured covariances are used for both the within observation covariance matrix and the between covariance matrix. Please see the following paper for more details:

Insert citation(s) here.

If this web app is used, we request that the above work be cited.

How the App Works

1. Use the "Upload File" tab to upload your data in text format. Comma, tab, or semicolon delimited files accepted. Your uploaded data will be shown for you to confirm that it has been read in correctly. The first column must give the clustering identifiers; the remaining columns should contain the data. You should also upload as a text file the lower limit of detections for each of the variables in the same order as the columns (sans clustering ID). Additionally, if the data are more appropriately modeled as normally distributed on the log scale, you may select the box to do this automatically (both the data and the LODs will be transformed).

2. The "Model Fitting" tab allows users to download the posterior draws of the mean and covariance parameters, as well as the posterior draws of new predictive values if desired. First, determine the chain length and thinning. Then click the "Ready to run MV Tobit Gibbs sampler" button to run. This will probably take awhile. Once it is finished running, the posterior means for the model parameters will be shown, and further options are provided.

3. Download the data. This will be provided as an RDS file, which can be opened in R using readRDS(). This will provide you with a list object with the draws for mu, Sigma, and Omega.

4. (Optional) The next tab allows you to draw concentrations (or whatever your data represent) from the MCMC samples, thus giving posterior draws from the predictive distribution of concentrations. Select the number of replicates and whether or not the clustering ought to be accounted for. This will again be provided as an RDS file, providing you with a matrix object with the concentration draws.

4. Trace plots are provided in the remaining tabs. Determine at what point convergence is reached for all parameters, and then change the burn-in period to that number.

Questions

Any questions or problems should be sent to Daniel Sewell at daniel-sewell AT uiowa DOT edu