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Flag outliers with robust Z-scores

Source: R/flag_z.R
flag_z.Rd

Identifies potential outliers in a numeric vector based on a moving window robust Z-score approach. The robust Z-score is computed using a biweight scale estimate centered on the median.

Usage

flag_z(x, width = 5, threshold = 3, return_z = FALSE)

Arguments

x

Numeric vector to check for outliers.

width

Odd integer giving the moving-window width. Defaults to 5.

threshold

Numeric threshold for the absolute Z-score above which a value is flagged. Defaults to 3.

return_z

Logical. If TRUE, return both Z-scores and flags. If FALSE, return only flags. Defaults to FALSE.

Value

If return_z = TRUE, a list with:

z

A numeric vector of robust Z-scores (with NA where not computable).

flag

A character vector of the same length as x, with "Z" where an outlier is detected and NA otherwise.

If return_z = FALSE, only the flag vector is returned.

Details

For each value in x, a window of length width centered on that value is extracted. The function:

  • Computes the median of the window.

  • Calculates residuals from the median and MAD-based scale.

  • Estimates a robust scale using the Tukey biweight midvariance with tuning constant c = 9 (Mosteller & Tukey 1977; Lax 1985): $$s^2 = n \cdot \frac{\sum r_i^2 (1 - u_i^2)^4}{\left[\sum (1 - u_i^2)(1 - 5 u_i^2)\right]^2}$$ where \(u_i = r_i / (c \cdot \mathrm{MAD})\) and the sums run over \(|u_i| < 1\).

  • Computes a Z-score as \((x_i - \text{median}) / s\).

If the absolute value of the Z-score exceeds threshold, the value is flagged with "Z".

NA values are ignored in the window statistics but retained in output positions.

References

Mosteller, F. and Tukey, J. W. (1977). Data Analysis and Regression. Addison-Wesley.

Lax, D. A. (1985). Robust estimators of scale: Finite-sample performance in long-tailed symmetric distributions. Journal of the American Statistical Association, 80(391), 736–741.

See also

stats::mad(), stats::median()

Examples

x <- c(1, 2, 1.5, 1.2, 100, 1.1, 1.3, 1.4)
flag_z(x)
#> [1] NA  "Z" NA  NA  "Z" NA  NA  NA 
flag_z(x, return_z = TRUE)
#> $z
#> [1]  -1.1941900   3.7088929   0.0000000  -0.7372456 577.2180895  -1.4041012
#> [7]  -1.1403570   0.7428716
#> 
#> $flag
#> [1] NA  "Z" NA  NA  "Z" NA  NA  NA 
#>