Computes three parametric correlation coefficients for one X variable and the corresponding R squared for multiple X variables, and a regression equation for censored data.

cencorreg(y.var, cen.var, x.vars, LOG = TRUE, verbose = 2)



The column of y (response variable) values plus detection limits.


The column of indicators, where 1 (or TRUE) indicates a detection limit in the y.var column, and 0 (or FALSE) indicates a detected value is in y.var.


One or more uncensored explanatory variable(s). For multiple variables it must be a data frame of numeric, character and factor variables. See Details


Indicator of whether to compute the regression in the original y units, or on their logarithms. The default is to use the logarithms (LOG = TRUE). To compute in original units, specify the option LOG = FALSE (or LOG = 0).


default verbose=2, see details.


When x.vars is one variable, likelihood, rescaled likelihood and McFaddens correlation coefficient (R) are printed. When x.vars is a data.frame of more than one variable, likelihood, rescaled likelihood and McFaddens coefficent of determination (R2) are printed.

Model coefficients (intercept and slopes), Chi-Squared statistic and p-value for the test that all slope coefficients equal zero (overall test), and model AIC and BIC are provided.

A Q-Q plot of model residuals with corresponding Shapiro-Francia W and p-value are plotted for evaluation of model distributional assumptions when verbose=2 (the default).


x.vars: If one x variable only, enter its name. If multiple x variables, enter the name of a data frame of columns of the x variables. Only columns used as X variables in the regression are allowed. Create this by x.frame <- data.frame (Temp, Flow, Time) for 3 variables (temperature, flow and time) used as the X variables in the regression.

AIC and BIC are printed to help evaluate the ‘best’ regression model.

The default is that the Y variable will be log transformed.

verbose option. Default is 2 which provides full output in the console and qqplots in a graphics window. A value of 1 only provides partial results in the console and no qqplots. A value of 0 provides no output; the returning computations will be stored in the specified object.


Helsel, D.R., 2011. Statistics for censored environmental data using Minitab and R, 2nd ed. John Wiley & Sons, USA, N.J.

Helsel, D.R., 2005. Nondetects and Data Analysis: Statistics for Censored Environmental Data, 1st ed. John Wiley and Sons, USA, N.J.

See also


data(Brumbaugh) # One variable cencorreg(Brumbaugh$Hg,Brumbaugh$HgCen,Brumbaugh$SedMeHg)
#> Likelihood R = 0.2765 AIC = 366.2191 #> Rescaled Likelihood R = 0.2855 BIC = 373.9126 #> McFaddens R = 0.1691 #>
#> Call: #> survreg(formula = "log(Brumbaugh$Hg)", data = "Brumbaugh$SedMeHg", #> dist = "gaussian") #> #> Coefficients: #> (Intercept) `Brumbaugh$SedMeHg` #> -1.7594846 0.1238447 #> #> Scale= 0.960393 #> #> Loglik(model)= -179.6 Loglik(intercept only)= -184.9 #> Chisq= 10.58 on 1 degrees of freedom, p= 0.00114 #> n= 133
# More than one variable for demonstration purposes cencorreg(Brumbaugh$Hg,Brumbaugh$HgCen,Brumbaugh[,c("SedMeHg","PctWetland")])
#> Likelihood R2 = 0.1371 AIC = 359.1937 #> Rescaled Likelihood R2 = 0.1461 BIC = 369.7851 #> McFaddens R2 = 0.05301555 #>
#> Call: #> survreg(formula = "log(Brumbaugh$Hg)", data = "SedMeHg+PctWetland", #> dist = "gaussian") #> #> Coefficients: #> (Intercept) SedMeHg PctWetland #> -1.79140776 0.06634913 0.01402344 #> #> Scale= 0.9264126 #> #> Loglik(model)= -175.1 Loglik(intercept only)= -184.9 #> Chisq= 19.61 on 2 degrees of freedom, p= 5.53e-05 #> n= 133