`FitBinormalRoc.Rd`

Fit the binormal model-predicted ROC curve for a dataset. This is the R equivalent of ROCFIT or RSCORE

`FitBinormalRoc(dataset, trt = 1, rdr = 1)`

- dataset
The ROC dataset

- trt
The desired modality, default is 1

- rdr
The desired reader, default is 1

The returned value is a list with the following elements:

- a
The mean of the diseased distribution; the non-diseased distribution is assumed to have zero mean

- b
The standard deviation of the non-diseased distribution. The diseased distribution is assumed to have unit standard deviation

- zetas
The binormal model cutoffs, zetas or thresholds

- AUC
The binormal model fitted ROC-AUC

- StdAUC
The standard deviation of AUC

- NLLIni
The initial value of negative LL

- NLLFin
The final value of negative LL

- ChisqrFitStats
The chisquare goodness of fit results

- covMat
The covariance matrix of the parameters

- fittedPlot
A ggplot2 object containing the fitted operating characteristic along with the empirical operating points. Use

`print()`

to display the object

In the binormal model ratings (more accurately the latent decision variables) from diseased cases are sampled from \(N(a,1)\) while ratings for non-diseased cases are sampled from \(N(0,b^2)\). To avoid clutter error bars are only shown for the lowest and uppermost operating points. An FROC dataset is internally converted to a highest rating inferred ROC dataset. To many bins containing zero counts will cause the algorithm to fail; so be sure to bin the data appropriately to fewer bins, where each bin has at least one count.

Dorfman DD, Alf E (1969) Maximum-Likelihood Estimation of Parameters of Signal-Detection Theory and Determination of Confidence Intervals - Rating-Method Data, Journal of Mathematical Psychology 6, 487-496.

Grey D, Morgan B (1972) Some aspects of ROC curve-fitting: normal and logistic models. Journal of Mathematical Psychology 9, 128-139.

```
# \donttest{
## Test with an included ROC dataset
retFit <- FitBinormalRoc(dataset02);## print(retFit$fittedPlot)
## Test with an included FROC dataset; it needs to be binned
## as there are more than 5 discrete ratings levels
binned <- DfBinDataset(dataset05, desiredNumBins = 5, opChType = "ROC")
retFit <- FitBinormalRoc(binned);## print(retFit$fittedPlot)
## Test with single interior point data
fp <- c(rep(1,7), rep(2, 3))
tp <- c(rep(1,5), rep(2, 5))
dataset <- Df2RJafrocDataset(fp, tp)
retFit <- FitBinormalRoc(dataset);## print(retFit$fittedPlot)
## Test with two interior data points
fp <- c(rep(1,7), rep(2, 5), rep(3, 3))
tp <- c(rep(1,3), rep(2, 5), rep(3, 7))
dataset <- Df2RJafrocDataset(fp, tp)
retFit <- FitBinormalRoc(dataset);## print(retFit$fittedPlot)
## Test with TONY data for which chisqr can be calculated
ds <- DfFroc2Roc(dataset01)
retFit <- FitBinormalRoc(ds, 2, 3);## print(retFit$fittedPlot)
## retFit$ChisqrFitStats
## Test with included degenerate ROC data
retFit <- FitBinormalRoc(datasetDegenerate);## print(retFit$fittedPlot)
#> Warning: Data is degenerate; binormal model cannot fit it unambiguously: use CBM or RSM method
# }
```