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Standardization (Z-scoring)

Source: R/standardize.R, R/unstandardize.R
standardize.Rd

Performs a standardization of data (z-scoring), i.e., centering and scaling, so that the data is expressed in terms of standard deviation (i.e., mean = 0, SD = 1) or Median Absolute Deviance (median = 0, MAD = 1). When applied to a statistical model, this function extracts the dataset, standardizes it, and refits the model with this standardized version of the dataset. The normalize() function can also be used to scale all numeric variables within the 0 - 1 range.

For model standardization, see standardize.default().

Usage

standardize(x, ...)

standardise(x, ...)

# S3 method for class 'numeric'
standardize(
  x,
  robust = FALSE,
  two_sd = FALSE,
  weights = NULL,
  reference = NULL,
  center = NULL,
  scale = NULL,
  verbose = TRUE,
  ...
)

# S3 method for class 'factor'
standardize(
  x,
  robust = FALSE,
  two_sd = FALSE,
  weights = NULL,
  force = FALSE,
  verbose = TRUE,
  ...
)

# S3 method for class 'data.frame'
standardize(
  x,
  select = NULL,
  exclude = NULL,
  robust = FALSE,
  two_sd = FALSE,
  weights = NULL,
  reference = NULL,
  center = NULL,
  scale = NULL,
  remove_na = c("none", "selected", "all"),
  force = FALSE,
  append = FALSE,
  ignore_case = FALSE,
  regex = FALSE,
  verbose = TRUE,
  ...
)

unstandardize(x, ...)

unstandardise(x, ...)

# S3 method for class 'numeric'
unstandardize(
  x,
  center = NULL,
  scale = NULL,
  reference = NULL,
  robust = FALSE,
  two_sd = FALSE,
  ...
)

# S3 method for class 'data.frame'
unstandardize(
  x,
  center = NULL,
  scale = NULL,
  reference = NULL,
  robust = FALSE,
  two_sd = FALSE,
  select = NULL,
  exclude = NULL,
  ignore_case = FALSE,
  regex = FALSE,
  verbose = TRUE,
  ...
)

Arguments

x

A (grouped) data frame, a vector or a statistical model (for unstandardize() cannot be a model).

...

Arguments passed to or from other methods.

robust

Logical, if TRUE, centering is done by subtracting the median from the variables and dividing it by the median absolute deviation (MAD). If FALSE, variables are standardized by subtracting the mean and dividing it by the standard deviation (SD).

two_sd

If TRUE, the variables are scaled by two times the deviation (SD or MAD depending on robust). This method can be useful to obtain model coefficients of continuous parameters comparable to coefficients related to binary predictors, when applied to the predictors (not the outcome) (Gelman, 2008).

weights

Can be NULL (for no weighting), or:

  • For model: if TRUE (default), a weighted-standardization is carried out.

  • For data.frames: a numeric vector of weights, or a character of the name of a column in the data.frame that contains the weights.

  • For numeric vectors: a numeric vector of weights.

reference

A data frame or variable from which the centrality and deviation will be computed instead of from the input variable. Useful for standardizing a subset or new data according to another data frame.

center, scale

  • For standardize():
    Numeric values, which can be used as alternative to reference to define a reference centrality and deviation. If scale and center are of length 1, they will be recycled to match the length of selected variables for standardization. Else, center and scale must be of same length as the number of selected variables. Values in center and scale will be matched to selected variables in the provided order, unless a named vector is given. In this case, names are matched against the names of the selected variables.

  • For unstandardize():
    center and scale correspond to the center (the mean / median) and the scale (SD / MAD) of the original non-standardized data (for data frames, should be named, or have column order correspond to the numeric column). However, one can also directly provide the original data through reference, from which the center and the scale will be computed (according to robust and two_sd). Alternatively, if the input contains the attributes center and scale (as does the output of standardize()), it will take it from there if the rest of the arguments are absent.

verbose

Toggle warnings and messages on or off.

force

Logical, if TRUE, forces recoding of factors and character vectors as well.

select

Variables that will be included when performing the required tasks. Can be either

  • a variable specified as a literal variable name (e.g., column_name),

  • a string with the variable name (e.g., "column_name"), a character vector of variable names (e.g., c("col1", "col2", "col3")), or a character vector of variable names including ranges specified via : (e.g., c("col1:col3", "col5")),

  • a formula with variable names (e.g., ~column_1 + column_2),

  • a vector of positive integers, giving the positions counting from the left (e.g. 1 or c(1, 3, 5)),

  • a vector of negative integers, giving the positions counting from the right (e.g., -1 or -1:-3),

  • one of the following select-helpers: starts_with(), ends_with(), contains(), a range using : or regex(""). starts_with(), ends_with(), and contains() accept several patterns, e.g starts_with("Sep", "Petal").

  • or a function testing for logical conditions, e.g. is.numeric() (or is.numeric), or any user-defined function that selects the variables for which the function returns TRUE (like: foo <- function(x) mean(x) > 3),

  • ranges specified via literal variable names, select-helpers (except regex()) and (user-defined) functions can be negated, i.e. return non-matching elements, when prefixed with a -, e.g. -ends_with(""), -is.numeric or -(Sepal.Width:Petal.Length). Note: Negation means that matches are excluded, and thus, the exclude argument can be used alternatively. For instance, select=-ends_with("Length") (with -) is equivalent to exclude=ends_with("Length") (no -). In case negation should not work as expected, use the exclude argument instead.

If NULL, selects all columns. Patterns that found no matches are silently ignored, e.g. extract_column_names(iris, select = c("Species", "Test")) will just return "Species".

exclude

See select, however, column names matched by the pattern from exclude will be excluded instead of selected. If NULL (the default), excludes no columns.

remove_na

How should missing values (NA) be treated: if "none" (default): each column's standardization is done separately, ignoring NAs. Else, rows with NA in the columns selected with select / exclude ("selected") or in all columns ("all") are dropped before standardization, and the resulting data frame does not include these cases.

append

Logical or string. If TRUE, standardized variables get new column names (with the suffix "_z") and are appended (column bind) to x, thus returning both the original and the standardized variables. If FALSE, original variables in x will be overwritten by their standardized versions. If a character value, standardized variables are appended with new column names (using the defined suffix) to the original data frame.

ignore_case

Logical, if TRUE and when one of the select-helpers or a regular expression is used in select, ignores lower/upper case in the search pattern when matching against variable names.

regex

Logical, if TRUE, the search pattern from select will be treated as regular expression. When regex = TRUE, select must be a character string (or a variable containing a character string) and is not allowed to be one of the supported select-helpers or a character vector of length > 1. regex = TRUE is comparable to using one of the two select-helpers, select = contains("") or select = regex(""), however, since the select-helpers may not work when called from inside other functions (see 'Details'), this argument may be used as workaround.

Value

The standardized object (either a standardize data frame or a statistical model fitted on standardized data).

Note

When x is a vector or a data frame with remove_na = "none"), missing values are preserved, so the return value has the same length / number of rows as the original input.

Selection of variables - the select argument

For most functions that have a select argument (including this function), the complete input data frame is returned, even when select only selects a range of variables. That is, the function is only applied to those variables that have a match in select, while all other variables remain unchanged. In other words: for this function, select will not omit any non-included variables, so that the returned data frame will include all variables from the input data frame.

See also

See center() for grand-mean centering of variables, and makepredictcall.dw_transformer() for use in model formulas.

Other transform utilities: normalize(), ranktransform(), rescale(), reverse()

Other standardize: standardize.default()

Examples

d <- iris[1:4, ]

# vectors
standardise(d$Petal.Length)
#> [1]  0.000000  0.000000 -1.224745  1.224745
#> (center: 1.4, scale = 0.082)
#> 

# Data frames
# overwrite
standardise(d, select = c("Sepal.Length", "Sepal.Width"))
#>   Sepal.Length Sepal.Width Petal.Length Petal.Width Species
#> 1    1.2402159   1.3887301          1.4         0.2  setosa
#> 2    0.3382407  -0.9258201          1.4         0.2  setosa
#> 3   -0.5637345   0.0000000          1.3         0.2  setosa
#> 4   -1.0147221  -0.4629100          1.5         0.2  setosa

# append
standardise(d, select = c("Sepal.Length", "Sepal.Width"), append = TRUE)
#>   Sepal.Length Sepal.Width Petal.Length Petal.Width Species Sepal.Length_z
#> 1          5.1         3.5          1.4         0.2  setosa      1.2402159
#> 2          4.9         3.0          1.4         0.2  setosa      0.3382407
#> 3          4.7         3.2          1.3         0.2  setosa     -0.5637345
#> 4          4.6         3.1          1.5         0.2  setosa     -1.0147221
#>   Sepal.Width_z
#> 1     1.3887301
#> 2    -0.9258201
#> 3     0.0000000
#> 4    -0.4629100

# append, suffix
standardise(d, select = c("Sepal.Length", "Sepal.Width"), append = "_std")
#>   Sepal.Length Sepal.Width Petal.Length Petal.Width Species Sepal.Length_std
#> 1          5.1         3.5          1.4         0.2  setosa        1.2402159
#> 2          4.9         3.0          1.4         0.2  setosa        0.3382407
#> 3          4.7         3.2          1.3         0.2  setosa       -0.5637345
#> 4          4.6         3.1          1.5         0.2  setosa       -1.0147221
#>   Sepal.Width_std
#> 1       1.3887301
#> 2      -0.9258201
#> 3       0.0000000
#> 4      -0.4629100

# standardizing with reference center and scale
d <- data.frame(
  a = c(-2, -1, 0, 1, 2),
  b = c(3, 4, 5, 6, 7)
)

# default standardization, based on mean and sd of each variable
standardize(d) # means are 0 and 5, sd ~ 1.581139
#>            a          b
#> 1 -1.2649111 -1.2649111
#> 2 -0.6324555 -0.6324555
#> 3  0.0000000  0.0000000
#> 4  0.6324555  0.6324555
#> 5  1.2649111  1.2649111

# standardization, based on mean and sd set to the same values
standardize(d, center = c(0, 5), scale = c(1.581, 1.581))
#>            a          b
#> 1 -1.2650221 -1.2650221
#> 2 -0.6325111 -0.6325111
#> 3  0.0000000  0.0000000
#> 4  0.6325111  0.6325111
#> 5  1.2650221  1.2650221

# standardization, mean and sd for each variable newly defined
standardize(d, center = c(3, 4), scale = c(2, 4))
#>      a     b
#> 1 -2.5 -0.25
#> 2 -2.0  0.00
#> 3 -1.5  0.25
#> 4 -1.0  0.50
#> 5 -0.5  0.75

# standardization, taking same mean and sd for each variable
standardize(d, center = 1, scale = 3)
#>            a         b
#> 1 -1.0000000 0.6666667
#> 2 -0.6666667 1.0000000
#> 3 -0.3333333 1.3333333
#> 4  0.0000000 1.6666667
#> 5  0.3333333 2.0000000