cenreg: Compute regression equations and likelihood correlation...
In NADA: Nondetects and Data Analysis for Environmental Data

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

Computes regression equations for singly censored data using maximum likelihood estimation. Estimates of slopes and intercept, tests for significance of parameters,and predicted quantiles (Median = points on the line) with confidence intervals can be computed.

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

`obs`	Either a numeric vector of observations or a formula. See examples below.
`censored`	If a formula is not specified, this should be a logical vector indicating TRUE where an observation in obs is censored (a less-than value) and FALSE otherwise.
`groups`	If a formula is not specified, this should be a numeric or factor vector that represents the explanatory variable.
`...`	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.

The reported likelihood r correlation coefficient measures the linear association between y (groups) and x (obs), based on the difference in log likelihoods between the fitted model and the null model. Slopes and intercepts are fit by maximum likelihood. A lognormal distribution is fit by default, with a normal distribution being an option. Estimates of predicted values on the line can be obtained by specifying the values for all x variables at which y is to be predicted. Requesting the median (p=0.5) will provide estimates on the line for a lognormal distribution. Estimates of the mean are also possible, as are estimates of other percentiles. Equations for confidence intervals follow those of Meeker and Escobar (1098).

Returns a summary.cenreg object.

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.

Meeker, W.Q. and L. A. Escobar (1998). Statistical Methods for Reliability Data. John Wiley and Sons, USA, NJ.

Cen, cenmle, predict-methods

    # (examples in Chap 12 of the NADA book)
    data(TCEReg)

    # Using the formula interface
    with(TCEReg, cenreg(Cen(TCEConc, TCECen)~PopDensity))

    # Two or more explanatory variables requires the formula interface
    tcemle2 = with(TCEReg, cenreg(Cen(TCEConc, TCECen)~PopDensity+Depth))

    # Prediction of quantiles at PopDensity=5 and Depth=110
    predict(tcemle2, c(5, 110))