# Estimation of ED values using model-averaging

### Description

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

### Usage

1 2 3 |

### 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

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 | ```
## 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!
``` |