Use of weighted results in surprising behaviour in the estimate

[joethorley]

library(ssdtools)
#> Please replace the following in your scripts:
#> - `ssdtools::boron_data` with `ssddata::ccme_boron`
#> - `ssdtools::ccme_data` with `ssddata::ccme_data`
library(ssddata)

data <- ssddata::ccme_boron

data$Weight <- 1
data$Weight[rank(data$Conc) > 6] <- 1/10

fitall <- ssd_fit_dists(data, dists="lnorm")
ssd_hc(fitall)
#> # A tibble: 1 × 10
#>   dist    percent   est    se   lcl   ucl    wt method     nboot pboot
#>   <chr>     <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <chr>      <int> <dbl>
#> 1 average       5  1.68    NA    NA    NA     1 parametric     0    NA

fit1 <- ssd_fit_dists(subset(data, Weight == 1), dists="lnorm")
ssd_hc(fit1)
#> # A tibble: 1 × 10
#>   dist    percent   est    se   lcl   ucl    wt method     nboot pboot
#>   <chr>     <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <chr>      <int> <dbl>
#> 1 average       5  1.04    NA    NA    NA     1 parametric     0    NA

fit1w <- ssd_fit_dists(subset(data, Weight == 1), dists="lnorm", weight = "Weight")
ssd_hc(fit1w)
#> # A tibble: 1 × 10
#>   dist    percent   est    se   lcl   ucl    wt method     nboot pboot
#>   <chr>     <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <chr>      <int> <dbl>
#> 1 average       5  1.04    NA    NA    NA     1 parametric     0    NA

fitallw10 <- ssd_fit_dists(data, dists="lnorm", weight = "Weight")
ssd_hc(fitallw10)
#> # A tibble: 1 × 10
#>   dist    percent   est    se   lcl   ucl    wt method     nboot pboot
#>   <chr>     <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <chr>      <int> <dbl>
#> 1 average       5 0.547    NA    NA    NA     1 parametric     0    NA

^{Created on 2024-01-22 with reprex v2.1.0}

[joethorley]

The last value with all the unequally weighted data appears to be incorrect.

[joethorley]

However the calculations are correct.

As David Fox confirmed

I can further confirm that the introduction of weights in the log-likelihood function has been done correctly. I have validated this several ways: (i) writing my own code in R; (ii) performing the calculations outside of R with different mathematical/statistical software; (iii) and comparing with fitdistrplus.

I believe the matter of SSD weighting is still an unresolved issue because what ssdtools (and fitdistrplus) are doing is not what ecotoxciologists want or expect.

[joethorley]

We will turn off this functionality until a better solution is found.

[atillmanns]

I disagree with what David Fox has written above. Weighting the data in a tail end of a distribution will likely increase the length of the tails. This is because these data points will be the focus of fitting the distribution. This could be useful if the species in the tails are of great importance and if there are few data points to represent the class of taxa that are found to be sensitive. In this case it would be a useful too to have to weight the distribution more on these species so an estimate can be made that will be protective of that group of species. I do not think this function should be removed as it is not erroneous. It just does not behave similar to weighting when it is done in a regression. I therefore think this functionality should not be removed.

[beckyfisher]

One potential resolution for this is to leave the weighting function based on log-likelihood available, but include a section in the technical details vignette explaining that the current implementation is correct, but that this may result in unexpected behavior. Text from the Phase III report should make a good starting point for this vignette update.

[atillmanns]

I agree. I think we just need to explain what weighting the tails means when fitting distributions using MDL and how this can be useful for ecotoxicologists.