DescTools (version 0.99.36)

Conf: Confusion Matrix And Associated Statistics

Description

Calculates a cross-tabulation of observed and predicted classes with associated statistics.

Usage

Conf(x, ...)

# S3 method for table Conf(x, pos = NULL, ...) # S3 method for matrix Conf(x, pos = NULL, ...) # S3 method for default Conf(x, ref, pos = NULL, na.rm = TRUE, ...)

# S3 method for rpart Conf(x, ...) # S3 method for multinom Conf(x, ...) # S3 method for glm Conf(x, cutoff = 0.5, ...) # S3 method for randomForest Conf(x, ...) # S3 method for svm Conf(x, ...) # S3 method for regr Conf(x, ...)

# S3 method for Conf plot(x, main = "Confusion Matrix", ...)

# S3 method for Conf print(x, digits = max(3, getOption("digits") - 3), ...)

Sens(x, ...) Spec(x, ...)

Arguments

x

a vector, normally a factor, of predicted classes or an object of following classes rpart, randomForest, svm, C50, glm, multinom, regr, lda, qda or table, resp. matrix. When a model is given, the predicted classes will be determined. A table or a matrix will be interpreted as a confusion matrix.

ref

a vector, normally a factor, of classes to be used as the reference. This is ignored if x is a table or matrix.

pos

a character string that defines the factor level corresponding to the "positive" results. Will be ignored for a \(n \times n\) table n > 2.

cutoff

used in logit models. The cutoff for changing classes.

main

overall title for the plot.

digits

controls the number of digits to print.

na.rm

a logical value indicating whether or not missing values should be removed. Defaults to FALSE.

further arguments to be passed to or from methods.

Value

a list with elements

table

the results of table on data and reference

positive

the positive result level

overall

a numeric vector with overall accuracy and Kappa statistic values

byClass

the sensitivity, specificity, positive predictive value, negative predictive value, prevalence, dection rate and detection prevalence for each class. For two class systems, this is calculated once using the positive argument

Details

The functions require the factors to have the same levels.

For two class problems, the sensitivity, specificity, positive predictive value and negative predictive value is calculated using the positive argument. Also, the prevalence of the "event" is computed from the data (unless passed in as an argument), the detection rate (the rate of true events also predicted to be events) and the detection prevalence (the prevalence of predicted events).

Suppose a \(2 \times 2\) table with notation

Reference
Predicted Event No Event
Event A B
No Event C D

The formulas used here are: $$Sensitivity = A/(A+C)$$ $$Specificity = D/(B+D)$$ $$Prevalence = (A+C)/(A+B+C+D)$$ $$PPV = (sensitivity * Prevalence)/((sensitivity*Prevalence) + ((1-specificity)*(1-Prevalence)))$$ $$NPV = (specificity * (1-Prevalence))/(((1-sensitivity)*Prevalence) + ((specificity)*(1-Prevalence)))$$ $$Detection Rate = A/(A+B+C+D)$$ $$Detection Prevalence = (A+B)/(A+B+C+D)$$ $$F-val Accuracy = 2 / (1/PPV + 1/Sensitivity)$$ $$Matthews Cor.-Coef = (A*D-B*C)/sqrt((A+B)*(A+C)*(D+B)*(D+C)) $$

See the references for discusions of the first five formulas.

For more than two classes, these results are calculated comparing each factor level to the remaining levels (i.e. a "one versus all" approach).

The overall accuracy and unweighted Kappa statistic are calculated. A p-value from McNemar's test is also computed using mcnemar.test (which can produce NA values with sparse tables).

The overall accuracy rate is computed along with a 95 percent confidence interval for this rate (using BinomCI) and a one-sided test to see if the accuracy is better than the "no information rate," which is taken to be the largest class percentage in the data.

The sensitivity is defined as the proportion of positive results out of the number of samples which were actually positive. When there are no positive results, sensitivity is not defined and a value of NA is returned. Similarly, when there are no negative results, specificity is not defined and a value of NA is returned. Similar statements are true for predictive values.

Confidence intervals for sensitivity, specificity etc. could be calculated as binomial confidence intervals (see BinomCI). BinomCI(A, A+C) yields the ci for sensitivity.

References

Kuhn, M. (2008) Building predictive models in R using the caret package Journal of Statistical Software, (http://www.jstatsoft.org/v28/i05/).

Powers, David M W (2011) Evaluation: From Precision, Recall and F-Measure to ROC, Informedness, Markedness & Correlation (PDF). Journal of Machine Learning Technologies 2 (1): 37-63.

Collett D (1999) Modelling Binary Data. Chapman & Hall/CRC, Boca Raton Florida, pp. 24.

Matthews, B. W. (1975) Comparison of the predicted and observed secondary structure of T4 phage lysozyme. Biochimica et Biophysica Acta (BBA) - Protein Structure 405 (2): 442-451. doi:10.1016/0005-2795(75)90109-9. PMID 1180967.

See Also

OddsRatio, RelRisk

Examples

Run this code
# NOT RUN {
# let tab be a confusion table
tab <- TextToTable("
   lo hi
lo 23 13
hi 10 18 ", dimnames=c("pred", "obs"))

Conf(tab, pos="hi")


pred <- Untable(tab)[,"pred"]
obs <- Untable(tab)[,"obs"]

Conf(x = pred, ref = obs)
Conf(x = pred, ref = obs, pos="hi")

Sens(tab)   # Sensitivity
Spec(tab)   # Specificity


tab <- TextToTable("
      terrible poor marginal clear
terrible       10    4        1     0
poor            5   10       12     2
marginal        2    4       12     5
clear           0    2        6    13
", dimnames=c("pred", "obs"))

Conf(tab)
# }

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