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Compute exact accuracy metrics based on probabilities.

Source: R/comp_accu.R
comp_accu_prob.Rd

comp_accu_prob computes a list of exact accuracy metrics from a sufficient and valid set of 3 essential probabilities (prev, and sens or its complement mirt, and spec or its complement fart).

Usage

comp_accu_prob(
  prev = prob$prev,
  sens = prob$sens,
  mirt = NA,
  spec = prob$spec,
  fart = NA,
  tol = 0.01,
  w = 0.5
)

Arguments

prev

The condition's prevalence prev (i.e., the probability of condition being TRUE).

sens

The decision's sensitivity sens (i.e., the conditional probability of a positive decision provided that the condition is TRUE). sens is optional when its complement mirt is provided.

mirt

The decision's miss rate mirt (i.e., the conditional probability of a negative decision provided that the condition is TRUE). mirt is optional when its complement sens is provided.

spec

The decision's specificity value spec (i.e., the conditional probability of a negative decision provided that the condition is FALSE). spec is optional when its complement fart is provided.

fart

The decision's false alarm rate fart (i.e., the conditional probability of a positive decision provided that the condition is FALSE). fart is optional when its complement spec is provided.

tol

A numeric tolerance value for is_complement. Default: tol = .01.

w

The weighting parameter w (from 0 to 1) for computing weighted accuracy wacc. Default: w = .50 (i.e., yielding balanced accuracy bacc).

Notes:

  • Accuracy metrics describe the correspondence of decisions (or predictions) to actual conditions (or truth).

    There are several possible interpretations of accuracy:

    1. as probabilities (i.e., acc being the proportion of correct classifications, or the ratio dec_cor/N),

    2. as frequencies (e.g., as classifying a population of N individuals into cases of dec_cor vs. dec_err),

    3. as correlations (e.g., see mcc in accu).

  • Computing exact accuracy values based on probabilities (by comp_accu_prob) may differ from accuracy values computed from (possibly rounded) frequencies (by comp_accu_freq).

    When frequencies are rounded to integers (see the default of round = TRUE in comp_freq and comp_freq_prob) the accuracy metrics computed by comp_accu_freq correspond to these rounded values. Use comp_accu_prob to obtain exact accuracy metrics from probabilities.

Value

A list accu containing current accuracy metrics.

Details

Currently computed accuracy metrics include:

  1. acc: Overall accuracy as the proportion (or probability) of correctly classifying cases or of dec_cor cases:

    (a) from prob: acc = (prev x sens) + [(1 - prev) x spec]

    (b) from freq: acc = dec_cor/N = (hi + cr)/(hi + mi + fa + cr)

    When frequencies in freq are not rounded, (b) coincides with (a).

    Values range from 0 (no correct prediction) to 1 (perfect prediction).

  2. wacc: Weighted accuracy, as a weighted average of the sensitivity sens (aka. hit rate HR, TPR, power or recall) and the the specificity spec (aka. TNR) in which sens is multiplied by a weighting parameter w (ranging from 0 to 1) and spec is multiplied by w's complement (1 - w):

    wacc = (w * sens) + ((1 - w) * spec)

    If w = .50, wacc becomes balanced accuracy bacc.

  3. mcc: The Matthews correlation coefficient (with values ranging from -1 to +1):

    mcc = ((hi * cr) - (fa * mi)) / sqrt((hi + fa) * (hi + mi) * (cr + fa) * (cr + mi))

    A value of mcc = 0 implies random performance; mcc = 1 implies perfect performance.

    See Wikipedia: Matthews correlation coefficient for additional information.

  4. f1s: The harmonic mean of the positive predictive value PPV (aka. precision) and the sensitivity sens (aka. hit rate HR, TPR, power or recall):

    f1s = 2 * (PPV * sens) / (PPV + sens)

    See Wikipedia: F1 score for additional information.

Note that some accuracy metrics can be interpreted as probabilities (e.g., acc) and some as correlations (e.g., mcc).

Also, accuracy can be viewed as a probability (e.g., the ratio of or link between dec_cor and N) or as a frequency type (containing dec_cor and dec_err).

comp_accu_prob computes exact accuracy metrics from probabilities. When input frequencies were rounded (see the default of round = TRUE in comp_freq and comp_freq_prob) the accuracy metrics computed by comp_accu correspond these rounded values.

References

Consult Wikipedia: Confusion matrix for additional information.

See also

accu for all accuracy metrics; comp_accu_freq computes accuracy metrics from frequencies; num for basic numeric parameters; freq for current frequency information; txt for current text settings; pal for current color settings; popu for a table of the current population.

Other metrics: acc, accu, comp_acc(), comp_accu_freq(), comp_err(), err

Other functions computing probabilities: comp_FDR(), comp_FOR(), comp_NPV(), comp_PPV(), comp_acc(), comp_accu_freq(), comp_comp_pair(), comp_complement(), comp_complete_prob_set(), comp_err(), comp_fart(), comp_mirt(), comp_ppod(), comp_prob(), comp_prob_freq(), comp_sens(), comp_spec()

Examples

comp_accu_prob()  # => accuracy metrics for prob of current scenario
#> $acc
#> [1] 0.775
#> 
#> $w
#> [1] 0.5
#> 
#> $wacc
#> [1] 0.8
#> 
#> $mcc
#> [1] 0.5303301
#> 
#> $f1s
#> [1] 0.6538462
#> 
comp_accu_prob(prev = .2, sens = .5, spec = .5)  # medium accuracy, but cr > hi.
#> $acc
#> [1] 0.5
#> 
#> $w
#> [1] 0.5
#> 
#> $wacc
#> [1] 0.5
#> 
#> $mcc
#> [1] 0
#> 
#> $f1s
#> [1] 0.2857143
#> 

# Extreme cases:
comp_accu_prob(prev = NaN, sens = NaN, spec = NaN)  # returns list of NA values
#> Warning: Please enter a valid set of essential probabilities.
#> $acc
#> [1] NA
#> 
#> $w
#> [1] 0.5
#> 
#> $wacc
#> [1] NA
#> 
#> $mcc
#> [1] NA
#> 
#> $f1s
#> [1] NA
#> 
comp_accu_prob(prev = 0, sens = NaN, spec = 1)      # returns list of NA values
#> Warning: Please enter a valid set of essential probabilities.
#> $acc
#> [1] NA
#> 
#> $w
#> [1] 0.5
#> 
#> $wacc
#> [1] NA
#> 
#> $mcc
#> [1] NA
#> 
#> $f1s
#> [1] NA
#> 
comp_accu_prob(prev = 0, sens = 0, spec = 1)     # perfect acc = 1, but f1s is NaN
#> Warning: accu$mcc: A denominator of 0 was corrected to 1, resulting in mcc = 0.
#> $acc
#> [1] 1
#> 
#> $w
#> [1] 0.5
#> 
#> $wacc
#> [1] 0.5
#> 
#> $mcc
#> [1] 0
#> 
#> $f1s
#> [1] NaN
#> 
comp_accu_prob(prev = .5, sens = .5, spec = .5)  # random performance
#> $acc
#> [1] 0.5
#> 
#> $w
#> [1] 0.5
#> 
#> $wacc
#> [1] 0.5
#> 
#> $mcc
#> [1] 0
#> 
#> $f1s
#> [1] 0.5
#> 
comp_accu_prob(prev = .5, sens = 1,  spec = 1)   # perfect accuracy
#> $acc
#> [1] 1
#> 
#> $w
#> [1] 0.5
#> 
#> $wacc
#> [1] 1
#> 
#> $mcc
#> [1] 1
#> 
#> $f1s
#> [1] 1
#> 
comp_accu_prob(prev = .5, sens = 0,  spec = 0)   # zero accuracy, but f1s is NaN
#> $acc
#> [1] 0
#> 
#> $w
#> [1] 0.5
#> 
#> $wacc
#> [1] 0
#> 
#> $mcc
#> [1] -1
#> 
#> $f1s
#> [1] NaN
#> 
comp_accu_prob(prev = 1,  sens = 1,  spec = 0)   # perfect, but see wacc (0.5) and mcc (0)
#> Warning: accu$mcc: A denominator of 0 was corrected to 1, resulting in mcc = 0.
#> $acc
#> [1] 1
#> 
#> $w
#> [1] 0.5
#> 
#> $wacc
#> [1] 0.5
#> 
#> $mcc
#> [1] 0
#> 
#> $f1s
#> [1] 1
#> 

# Effects of w:
comp_accu_prob(prev = .5, sens = .6, spec = .4, w = 1/2)  # equal weights to sens and spec
#> $acc
#> [1] 0.5
#> 
#> $w
#> [1] 0.5
#> 
#> $wacc
#> [1] 0.5
#> 
#> $mcc
#> [1] 0
#> 
#> $f1s
#> [1] 0.5454545
#> 
comp_accu_prob(prev = .5, sens = .6, spec = .4, w = 2/3)  # more weight on sens: wacc up
#> $acc
#> [1] 0.5
#> 
#> $w
#> [1] 0.6666667
#> 
#> $wacc
#> [1] 0.5333333
#> 
#> $mcc
#> [1] 0
#> 
#> $f1s
#> [1] 0.5454545
#> 
comp_accu_prob(prev = .5, sens = .6, spec = .4, w = 1/3)  # more weight on spec: wacc down
#> $acc
#> [1] 0.5
#> 
#> $w
#> [1] 0.3333333
#> 
#> $wacc
#> [1] 0.4666667
#> 
#> $mcc
#> [1] 0
#> 
#> $f1s
#> [1] 0.5454545
#> 

# Contrasting comp_accu_freq and comp_accu_prob:
# (a) comp_accu_freq (based on rounded frequencies):
freq1 <- comp_freq(N = 10, prev = 1/3, sens = 2/3, spec = 3/4)   # => rounded frequencies!
accu1 <- comp_accu_freq(freq1$hi, freq1$mi, freq1$fa, freq1$cr)  # => accu1 (based on rounded freq).
# accu1

# (b) comp_accu_prob (based on probabilities):
accu2 <- comp_accu_prob(prev = 1/3, sens = 2/3, spec = 3/4)      # => exact accu (based on prob).
# accu2
all.equal(accu1, accu2)  # => 4 differences!
#> [1] "Component “acc”: Mean relative difference: 0.03174603" 
#> [2] "Component “wacc”: Mean relative difference: 0.02586207"
#> [3] "Component “mcc”: Mean relative difference: 0.1306675"  
#> [4] "Component “f1s”: Mean relative difference: 0.07692308" 
#
# (c) comp_accu_freq (exact values, i.e., without rounding):
freq3 <- comp_freq(N = 10, prev = 1/3, sens = 2/3, spec = 3/4, round = FALSE)
accu3 <- comp_accu_freq(freq3$hi, freq3$mi, freq3$fa, freq3$cr)  # => accu3 (based on EXACT freq).
# accu3
all.equal(accu2, accu3)  # => TRUE (qed).
#> [1] TRUE