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Detect outliers

Source: R/outliers.R
detect_outlr.Rd

Applies one or more outlier detection methods to a given signal variable, and optionally aggregates the outputs to create a consensus result. See the outliers vignette for examples.

detect_outlr_rm detects outliers based on a distance from the rolling median specified in terms of multiples of the rolling interquartile range (IQR).

detect_outlr_stl detects outliers based on a seasonal-trend decomposition using LOESS (STL).

Usage

detect_outlr(
  x = seq_along(y),
  y,
  methods = tibble::tibble(method = "rm", args = list(list()), abbr = "rm"),
  combiner = c("median", "mean", "none")
)

detect_outlr_rm(
  x = seq_along(y),
  y,
  n = 21,
  log_transform = FALSE,
  detect_negatives = FALSE,
  detection_multiplier = 2,
  min_radius = 0,
  replacement_multiplier = 0
)

detect_outlr_stl(
  x = seq_along(y),
  y,
  n_trend = 21,
  n_seasonal = 21,
  n_threshold = 21,
  seasonal_period,
  seasonal_as_residual = FALSE,
  log_transform = FALSE,
  detect_negatives = FALSE,
  detection_multiplier = 2,
  min_radius = 0,
  replacement_multiplier = 0
)

Arguments

x

Design points corresponding to the signal values y. Default is seq_along(y) (that is, equally-spaced points from 1 to the length of y).

y

Signal values.

methods

A tibble specifying the method(s) to use for outlier detection, with one row per method, and the following columns:

  • method: Either "rm" or "stl", or a custom function for outlier detection; see details for further explanation.

  • args: Named list of arguments that will be passed to the detection method.

  • abbr: Abbreviation to use in naming output columns with results from this method.

combiner

String, one of "median", "mean", or "none", specifying how to combine results from different outlier detection methods for the thresholds determining whether a particular observation is classified as an outlier, as well as a replacement value for any outliers. If "none", then no summarized results are calculated. Note that if the number of methods (number of rows) is odd, then "median" is equivalent to a majority vote for purposes of determining whether a given observation is an outlier.

n

Number of time steps to use in the rolling window. Default is 21. This value is centrally aligned. When n is an odd number, the rolling window extends from (n-1)/2 time steps before each design point to (n-1)/2 time steps after. When n is even, then the rolling range extends from n/2-1 time steps before to n/2 time steps after.

log_transform

Should a log transform be applied before running outlier detection? Default is FALSE. If TRUE, and zeros are present, then the log transform will be padded by 1.

detect_negatives

Should negative values automatically count as outliers? Default is FALSE.

detection_multiplier

Value determining how far the outlier detection thresholds are from the rolling median, which are calculated as (rolling median) +/- (detection multiplier) * (rolling IQR). Default is 2.

min_radius

Minimum distance between rolling median and threshold, on transformed scale. Default is 0.

replacement_multiplier

Value determining how far the replacement values are from the rolling median. The replacement is the original value if it is within the detection thresholds, or otherwise it is rounded to the nearest (rolling median) +/- (replacement multiplier) * (rolling IQR). Default is 0.

n_trend

Number of time steps to use in the rolling window for trend. Default is 21.

n_seasonal

Number of time steps to use in the rolling window for seasonality. Default is 21. Can also be the string "periodic". See s.window in stats::stl.

n_threshold

Number of time steps to use in rolling window for the IQR outlier thresholds.

seasonal_period

Integer specifying period of "seasonality". For example, for daily data, a period 7 means weekly seasonality. It must be strictly larger than 1. Also impacts the size of the low-pass filter window; see l.window in stats::stl.

seasonal_as_residual

Boolean specifying whether the seasonal(/weekly) component should be treated as part of the residual component instead of as part of the predictions. The default, FALSE, treats them as part of the predictions, so large seasonal(/weekly) components will not lead to flagging points as outliers. TRUE may instead consider the extrema of large seasonal variations to be outliers; n_seasonal and seasonal_period will still have an impact on the result, though, by impacting the estimation of the trend component.

Value

An tibble with number of rows equal to length(y) and columns giving the outlier detection thresholds (lower and upper) and replacement values from each detection method (replacement).

Details

Each outlier detection method, one per row of the passed methods tibble, is a function that must take as its first two arguments x and y, and then any number of additional arguments. The function must return a tibble with the number of rows equal to length(y), and with columns lower, upper, and replacement, representing lower and upper bounds for what would be considered an outlier, and a posited replacement value, respectively.

For convenience, the outlier detection method can be specified (in the method column of methods) by a string "rm", shorthand for detect_outlr_rm(), which detects outliers via a rolling median; or by "stl", shorthand for detect_outlr_stl(), which detects outliers via an STL decomposition.

The STL decomposition is computed using stats::stl(). Once computed, the outlier detection method is analogous to the rolling median method in detect_outlr_rm(), except with the fitted values and residuals from the STL decomposition taking the place of the rolling median and residuals to the rolling median, respectively.

The last set of arguments, log_transform through replacement_multiplier, are exactly as in detect_outlr_rm().

Examples

detection_methods <- dplyr::bind_rows(
  dplyr::tibble(
    method = "rm",
    args = list(list(
      detect_negatives = TRUE,
      detection_multiplier = 2.5
    )),
    abbr = "rm"
  ),
  dplyr::tibble(
    method = "stl",
    args = list(list(
      detect_negatives = TRUE,
      detection_multiplier = 2.5,
      seasonal_period = 7
    )),
    abbr = "stl_seasonal"
  ),
  dplyr::tibble(
    method = "stl",
    args = list(list(
      detect_negatives = TRUE,
      detection_multiplier = 2.5,
      seasonal_period = 7,
      seasonal_as_residual = TRUE
    )),
    abbr = "stl_reseasonal"
  )
)

x <- covid_incidence_outliers %>%
  dplyr::select(geo_value, time_value, cases) %>%
  as_epi_df() %>%
  group_by(geo_value) %>%
  mutate(outlier_info = detect_outlr(
    x = time_value, y = cases,
    methods = detection_methods,
    combiner = "median"
  )) %>%
  unnest(outlier_info)
# Detect outliers based on a rolling median
covid_incidence_outliers %>%
  dplyr::select(geo_value, time_value, cases) %>%
  as_epi_df() %>%
  group_by(geo_value) %>%
  mutate(outlier_info = detect_outlr_rm(
    x = time_value, y = cases
  ))
#> An `epi_df` object, 730 x 4 with metadata:
#> * geo_type  = state
#> * time_type = day
#> * as_of     = 2021-10-28
#> 
#> # A tibble: 730 × 4
#> # Groups:   geo_value [2]
#>    geo_value time_value cases outlier_info$lower $upper $replacement
#>  * <chr>     <date>     <dbl>              <dbl>  <dbl>        <dbl>
#>  1 fl        2020-06-01   667               530   2010           667
#>  2 nj        2020-06-01   486               150.   840.          486
#>  3 fl        2020-06-02   617               582.  1992.          617
#>  4 nj        2020-06-02   658               210.   771.          658
#>  5 fl        2020-06-03  1317               635   1975          1317
#>  6 nj        2020-06-03   541               270    702           541
#>  7 fl        2020-06-04  1419               713   1909          1419
#>  8 nj        2020-06-04   478               174.   790.          478
#>  9 fl        2020-06-05  1305               553   2081          1305
#> 10 nj        2020-06-05   825               118.   838.          825
#> # ℹ 720 more rows
# Detects outliers based on a seasonal-trend decomposition using LOESS
covid_incidence_outliers %>%
  dplyr::select(geo_value, time_value, cases) %>%
  as_epi_df() %>%
  group_by(geo_value) %>%
  mutate(outlier_info = detect_outlr_stl(
    x = time_value, y = cases,
    seasonal_period = 7 # weekly seasonality for daily data
  ))
#> An `epi_df` object, 730 x 4 with metadata:
#> * geo_type  = state
#> * time_type = day
#> * as_of     = 2021-10-28
#> 
#> # A tibble: 730 × 4
#> # Groups:   geo_value [2]
#>    geo_value time_value cases outlier_info$lower $upper $replacement
#>  * <chr>     <date>     <dbl>              <dbl>  <dbl>        <dbl>
#>  1 fl        2020-06-01   667             -1193.  1233.          667
#>  2 nj        2020-06-01   486               281.   762.          486
#>  3 fl        2020-06-02   617              -691.  1890.          617
#>  4 nj        2020-06-02   658               317.   891.          658
#>  5 fl        2020-06-03  1317              -144.  2396.         1317
#>  6 nj        2020-06-03   541               292.   809.          541
#>  7 fl        2020-06-04  1419               260.  2696.         1419
#>  8 nj        2020-06-04   478               315.   792.          478
#>  9 fl        2020-06-05  1305               548.  2950.         1305
#> 10 nj        2020-06-05   825               382.   835.          825
#> # ℹ 720 more rows