Given a frequency table of predictions versus target values, calculate numerous statistics of interest.
calc_stats(tabble, prevalence = NULL, positive, ...)A frequency table created with table
Prevalence value. Default is NULL
Positive class
Other, not currently used
A tibble with (at present) columns for sensitivity, specificity, PPV, NPV, F1 score, detection rate, detection prevalence, balanced accuracy, FDR, FOR, FPR, FNR. For more than 2 classes, these statistics are provided for each class.
Used within confusion_matrix to calculate various confusion matrix
metrics. This is called by confusion_matrix, but if this is all you
want you can simply supply the table.
Suppose a 2x2 table with notation
| target | ||
| Predicted | Event | No Event |
| Event | A | B |
| No Event | C | D |
The formulas used here are:
$$Sensitivity = A/(A+C)$$
$$Specificity = D/(B+D)$$
$$Prevalence = (A+C)/(A+B+C+D)$$
$$Positive Predictive Value = (sensitivity * prevalence)/((sensitivity*prevalence) + ((1-specificity)*(1-prevalence)))$$
$$Negative Predictive Value = (specificity * (1-prevalence))/(((1-sensitivity)*prevalence) + ((specificity)*(1-prevalence)))$$ $$Detection Rate = A/(A+B+C+D)$$
$$Detection Prevalence = (A+B)/(A+B+C+D)$$
$$Balanced Accuracy = (sensitivity+specificity)/2$$
$$Precision = A/(A+B)$$
$$Recall = A/(A+C)$$
$$F1 = harmonic mean of precision and recall = (1+beta^2)*precision*recall/((beta^2 * precision)+recall)$$
where beta = 1 for this function.
$$False Discovery Rate = 1 - Positive Predictive Value$$
$$False Omission Rate = 1 - Negative Predictive Value$$
$$False Positive Rate = 1 - Specificity$$
$$False Negative Rate = 1 - Sensitivity$$
$$D' = qnorm(Sensitivity) - qnorm(1 - Specificity)$$
$$AUC ~= pnorm(D'/sqrt(2))$$
See the references for discussions of the first five formulas. Abbreviations:
Different names are used for the same statistics.
This function is called by confusion_matrix, but if this is all you
want, you can simply supply the table to this function.
Kuhn, M. (2008), "Building predictive models in R using the caret package, " Journal of Statistical Software, (https://www.jstatsoft.org/article/view/v028i05).
Altman, D.G., Bland, J.M. (1994) "Diagnostic tests 1: sensitivity and specificity", British Medical Journal, vol 308, 1552.
Altman, D.G., Bland, J.M. (1994) "Diagnostic tests 2: predictive values," British Medical Journal, vol 309, 102.
Velez, D.R., et. al. (2008) "A balanced accuracy function for epistasis modeling in imbalanced datasets using multifactor dimensionality reduction.," Genetic Epidemiology, vol 4, 306.