Potency of two herbicides

Data are from an experiment, comparing the potency of the two herbicides glyphosate and bentazone in white mustard Sinapis alba.

Usage

data(S.alba)

Format

A data frame with 68 observations on the following 3 variables.

Dose

a numeric vector containing the dose in g/ha.

Herbicide

a factor with levels Bentazone Glyphosate (the two herbicides applied).

DryMatter

a numeric vector containing the response (dry matter in g/pot).

Details

The lower and upper limits for the two herbicides can be assumed identical, whereas slopes and ED50 values are different (in the log-logistic model).

Source

Christensen, M. G. and Teicher, H. B., and Streibig, J. C. (2003) Linking fluorescence induction curve and biomass in herbicide screening, Pest Management Science, 59, 1303–1310.

Examples

library(drc)

## Fitting a log-logistic model with
##  common lower and upper limits
S.alba.LL.4.1 <- drm(DryMatter~Dose, Herbicide, data=S.alba, fct = LL.4(),
pmodels=data.frame(Herbicide,1,1,Herbicide)) 
summary(S.alba.LL.4.1)
#> 
#> Model fitted: Log-logistic (ED50 as parameter) (4 parms)
#> 
#> Parameter estimates:
#> 
#>                Estimate Std. Error t-value   p-value    
#> b:Bentazone    5.046141   1.040135  4.8514 8.616e-06 ***
#> b:Glyphosate   2.390218   0.495959  4.8194 9.684e-06 ***
#> c:(Intercept)  0.716559   0.089245  8.0291 3.523e-11 ***
#> d:(Intercept)  3.854861   0.076255 50.5519 < 2.2e-16 ***
#> e:Bentazone   28.632355   2.038098 14.0486 < 2.2e-16 ***
#> e:Glyphosate  66.890545   5.968819 11.2067 < 2.2e-16 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> Residual standard error:
#> 
#>  0.3705151 (62 degrees of freedom)

## Applying the optimal transform-both-sides Box-Cox transformation
## (using the initial model fit)  
S.alba.LL.4.2 <- boxcox(S.alba.LL.4.1, method = "anova") 

summary(S.alba.LL.4.2)
#> 
#> Model fitted: Log-logistic (ED50 as parameter) (4 parms)
#> 
#> Parameter estimates:
#> 
#>                Estimate Std. Error t-value   p-value    
#> b:Bentazone    4.838636   0.927240  5.2183 2.216e-06 ***
#> b:Glyphosate   1.944311   0.236471  8.2222 1.630e-11 ***
#> c:(Intercept)  0.682591   0.028768 23.7270 < 2.2e-16 ***
#> d:(Intercept)  3.862611   0.106186 36.3760 < 2.2e-16 ***
#> e:Bentazone   28.396147   1.874598 15.1479 < 2.2e-16 ***
#> e:Glyphosate  65.573335   5.618945 11.6700 < 2.2e-16 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> Residual standard error:
#> 
#>  0.1558947 (62 degrees of freedom)
#> 
#> Non-normality/heterogeneity adjustment through Box-Cox transformation
#> 
#> Estimated lambda: 0.101 
#> Confidence interval for lambda: [-0.126, 0.331] 
#> 

## Plotting fitted regression curves together with the data
plot(S.alba.LL.4.2)