cenmle: Regression by Maximum Likelihood Estimation for Left-censored...
In NADA: Nondetects and Data Analysis for Environmental Data

Description Usage Arguments Details Value Author(s) References See Also Examples

Regression by Maximum Likelihood (ML) Estimation for left-censored ("nondetect" or "less-than") data. This routine computes regression estimates of slope(s) and intercept by maximum likelihood when data are left-censored. It will compute ML estimates of descriptive statistics when explanatory variables following the ~ are left blank. It will compute ML tests similar in function and assumptions to two-sample t-tests and analysis of variance when groups are specified following the ~. It will compute regression equations, including multiple regression, when continuous explanatory variables are included following the ~. It will compute the ML equivalent of analysis of covariance when both group and continuous explanatory variables are specified following the ~. To avoid an appreciable loss of power with regression and group hypothesis tests, a probability plot of residuals should be checked to ensure that residuals from the regression model are approximately gaussian.

1	cenmle(obs, censored, groups, ...)

`obs`	Either a numeric vector of observations or a formula. See examples below.
`censored`	A logical vector indicating TRUE where an observation in ‘obs’ is censored (a less-than value) and FALSE otherwise.
`groups`	A factor vector used for grouping ‘obs’ into subsets.
`...`	Additional items that are common to this function and the `survreg` function from the ‘survival’ package. The most important of which is ‘dist’ and ‘conf.int’. See Details below.

This routine is a front end to the survreg routine in the survival package.

There are many additional options that are supported and documented in survfit. Only a few have relevance to the evironmental sciences.

A very important option is ‘dist’ which specifies the distributional model to use in the regression. The default is ‘lognormal’.

Another important option is ‘conf.int’. This is NOT an option to survreg but is an added feature (due to some arcane details of R it can't be documented above). The ‘conf.int’ option specifies the level for a two-sided confidence interval on the regression. The default is 0.95. This interval will be used in when the output object is passed to other generic functions such as mean and quantile. See Examples below.

Also supported is a ‘gaussian’ or a normal distribution. The use of a gaussian distribution requires an interval censoring context for left-censored data. Luckily, this routine automatically does this for you – simply specify ‘gaussian’ and the correct manipulations are done.

If any other distribution is specified besides lognormal or gaussian, the return object is a raw survreg object – it is up to the user to ‘do the right thing’ with the output (and input for that matter).

If you are using the formula interface: The censored and groups parameters are not specified – all information is provided via a formula as the obs parameter. The formula must have a Cen object as the response on the left of the ~ operator and, if desired, terms separated by + operators on the right. See Examples below.

a cenmle object. Methods defined for cenmle objects are provided for mean, median, sd.

R. Lopaka Lee <rclee@usgs.gov>

Dennis Helsel <dhelsel@practicalstats.com>

Helsel, Dennis R. (2005). Nondectects and Data Analysis; Statistics for censored environmental data. John Wiley and Sons, USA, NJ.

Cen, cenmle-methods, mean-methods, sd-methods, median-methods, quantile-methods, summary-methods

    # Create a MLE regression object 

    data(TCEReg)

    tcemle = with(TCEReg, cenmle(TCEConc, TCECen)) 

    summary(tcemle)
    median(tcemle)
    mean(tcemle)
    sd(tcemle)
    quantile(tcemle)

    # This time specifiy a different confidence interval
    tcemle = with(TCEReg, cenmle(TCEConc, TCECen, conf.int=0.80)) 

    # Use the model's confidence interval with the quantile function
    quantile(tcemle, conf.int=TRUE)

    # With groupings
    with(TCEReg, cenmle(TCEConc, TCECen, PopDensity))