Computes the ATS (Mann-Kendall trend test for censored data) after adjustment of censored data for a covariate.

```
centrend(
y.var,
y.cens,
x.var,
time.var,
link = "identity",
Smooth = "cs",
printstat = TRUE,
stackplots = FALSE
)
```

## Arguments

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

- y.cens
The column of indicators, where 1 (or `TRUE`

) indicates a detectionlimit in the `y.var`

column, and 0 (or `FALSE`

) indicates a detected value in `y.var`

.

- x.var
Column of a covariate (not time). `y.var`

will be smoothed versus `x.var`

and residuals taken to subtract out the relationship between `y`

and `x`

.

- time.var
Column of the time variable, either a sequence of days or decimal times, etc. Will be the scale used for time in ATS trend analysis.

- link
Default = `“identity”`

which means it uses data in the original units. See details.

- Smooth
Type of smoother used in the GAM. Default is `“cs”`

, shrinkage cubic regression splines. See details for other options.

- printstat
Logical `TRUE`

/`FALSE`

option of whether to print the resulting statistics in the console window, or not. Default is `TRUE.`

- stackplots
logical 'TRUE'/'FALSE' option to stack three plots that are output onto the same page instead of each on separate page. Default is 'FALSE', each separate.

## Value

Prints three plots: Y data vs time with GAM Smooth, Residuals from GAM Smooth vs time, and ATS trend line of residuals vs time.

Returns GAM residuals and ATS results on trend test of residuals (intercept, slope, Kendall's tau, p-value for trend)

## Details

Default `link`

= identity. The y variables are then used in their original units. Other options are available see `cenGAM::tobit1`

for more options.

Default `Smooth`

is `"cs"`

for shrinkage cubic regression splines. See `mgcv::smooth.terms`

for other types of smoothing algorithms. '"ts"' is a thin-plate regression spline and is also commonly used.

## References

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

## Examples

```
data(Brumbaugh)
Brumbaugh$time=1:nrow(Brumbaugh)
with(Brumbaugh,centrend(Hg,HgCen,SedTotHg,time.var=time))
#> Trend analysis of Hg adjusted for SedTotHg
#> Akritas-Theil-Sen line for censored data
#>
#> Hg residuals = -0.0493 -4e-04 * time
#> Kendall's tau = -0.036 p-value = 0.53998
#>
```