Estimation of ED values using model-averaging

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Description

Estimates and confidence intervals for ED values are estimated using model-averaging.

Usage

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maED(object, fctList = NULL, respLev, interval = c("none", "buckland", "kang"), 
linreg = FALSE, clevel = NULL, level = 0.95, type = c("relative", "absolute"), 
display = TRUE, na.rm = FALSE, extended = FALSE)

Arguments

object

an object of class 'drc'.

fctList

a list of non-linear functions to be compared.

respLev

a numeric vector containing the response levels.

interval

character string specifying the type of confidence intervals to be supplied. The default is "none". The choices "buckland" and "kang" are explained in the Details section.

linreg

logical indicating whether or not additionally a simple linear regression model should be fitted.

clevel

character string specifying the curve id in case on estimates for a specific curve or compound is requested. By default estimates are shown for all curves.

level

numeric. The level for the confidence intervals. The default is 0.95.

type

character string. Whether the specified response levels are absolute or relative (default).

display

logical. If TRUE results are displayed. Otherwise they are not (useful in simulations).

na.rm

logical indicating whether or not NA occurring during model fitting should be left out of subsequent calculations.

extended

logical specifying whether or not an extended output (including fit summaries) should be returned.

Details

Model-averaging of individual estimates is carried out as described by Buckland et al. (1997) and Kang et al. (2000) using AIC-based weights. The two approaches differ w.r.t. the calculation of confidence intervals: Buckland et al. (1997) provide an approximate variance formula under the assumption of perfectly correlated estimates (so, confidence intervals will tend to be too wide). Kang et al. (2000) use the model weights to calculate confidence limits as weighted means of the confidence limits for the individual fits; this procedure corresponds to using the standard error in Equation (3) given by Buckland et al. (1997) (assuming symmetric confidence intervals based on the same percentile).

Value

A matrix with two or more columns, containing the estimates and the corresponding estimated standard errors and possibly lower and upper confidence limits.

Author(s)

Christian Ritz

References

Buckland, S. T. and Burnham, K. P. and Augustin, N. H. (1997) Model Selection: An Integral Part of Inference, Biometrics 53, 603–618.

Kang, Seung-Ho and Kodell, Ralph L. and Chen, James J. (2000) Incorporating Model Uncertainties along with Data Uncertainties in Microbial Risk Assessment, Regulatory Toxicology and Pharmacology 32, 68–72.

See Also

The function mselect provides a summary of fit statistics for several models fitted to the same data.

Examples

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## Fitting an example dose-response model
ryegrass.m1 <- drm(rootl~conc, data = ryegrass, fct = LL.4())
  
## Comparing models (showing the AIC values)  
mselect(ryegrass.m1, 
list(LL.5(), LN.4(), W1.4(), W2.4(), FPL.4(-1,1), FPL.4(-2,3), FPL.4(-0.5,0.5)))
  
## Doing the actual model-averaging  
maED(ryegrass.m1, 
list(LL.5(), LN.4(), W1.4(), W2.4(), FPL.4(-1,1), FPL.4(-2,3), FPL.4(-0.5,0.5)), 
c(10, 50, 90))  
  
## With confidence intervals according to Buckland et al. (1997)  
maED(ryegrass.m1, 
list(LL.5(), LN.4(), W1.4(), W2.4(), FPL.4(-1,1), FPL.4(-2,3), FPL.4(-0.5,0.5)), 
c(10, 50, 90), "buckland")

## With confidence intervals according to Kang et al. (2000)
maED(ryegrass.m1, 
list(LL.5(), LN.4(), W1.4(), W2.4(), FPL.4(-1,1), FPL.4(-2,3), FPL.4(-0.5,0.5)), 
c(10, 50, 90), "kang")

## Comparing to model-averaged ED values with simple linear regression included
maED(ryegrass.m1, 
list(LL.5(), LN.4(), W1.4(), W2.4(), FPL.4(-1,1), FPL.4(-2,3), FPL.4(-0.5,0.5)), 
c(10, 50, 90), interval = "buckland", linreg = TRUE)



## Example with a model fit involving two compounds/curves
S.alba.m1 <- drm(DryMatter~Dose, Herbicide, data=S.alba, fct = LL.4(),
pmodels=data.frame(Herbicide,1,1,Herbicide)) 

## Model-averaged ED50 for both compounds
maED(S.alba.m1, list(LL.3(), LN.4()), 50)

## Model-averaged ED50 only for one compound (glyphosate)
maED(S.alba.m1, list(LL.3(), LN.4()), 50, clevel="Glyphosate")

## With confidence intervals
maED(S.alba.m1, list(LL.3(), LN.4()), 50, interval="buckland")

## For comparison model-specific confidence intervals
ED(S.alba.m1, 50, interval="delta")  # wider!

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