collapse (version 1.7.5)

fvar-fsd: Fast (Grouped, Weighted) Variance and Standard Deviation for Matrix-Like Objects

Description

fvar and fsd are generic functions that compute the (column-wise) variance and standard deviation of x, (optionally) grouped by g and/or frequency-weighted by w. The TRA argument can further be used to transform x using its (grouped, weighted) variance/sd.

Usage

fvar(x, …)
fsd(x, …)
# S3 method for default
fvar(x, g = NULL, w = NULL, TRA = NULL, na.rm = TRUE,
     use.g.names = TRUE, stable.algo = TRUE, …)
# S3 method for default
fsd(x, g = NULL, w = NULL, TRA = NULL, na.rm = TRUE,
    use.g.names = TRUE, stable.algo = TRUE, …)
# S3 method for matrix
fvar(x, g = NULL, w = NULL, TRA = NULL, na.rm = TRUE,
     use.g.names = TRUE, drop = TRUE, stable.algo = TRUE, …)
# S3 method for matrix
fsd(x, g = NULL, w = NULL, TRA = NULL, na.rm = TRUE,
    use.g.names = TRUE, drop = TRUE, stable.algo = TRUE, …)
# S3 method for data.frame
fvar(x, g = NULL, w = NULL, TRA = NULL, na.rm = TRUE,
     use.g.names = TRUE, drop = TRUE, stable.algo = TRUE, …)
# S3 method for data.frame
fsd(x, g = NULL, w = NULL, TRA = NULL, na.rm = TRUE,
    use.g.names = TRUE, drop = TRUE, stable.algo = TRUE, …)
# S3 method for grouped_df
fvar(x, w = NULL, TRA = NULL, na.rm = TRUE,
     use.g.names = FALSE, keep.group_vars = TRUE, keep.w = TRUE,
     stable.algo = TRUE, …)
# S3 method for grouped_df
fsd(x, w = NULL, TRA = NULL, na.rm = TRUE,
    use.g.names = FALSE, keep.group_vars = TRUE, keep.w = TRUE,
    stable.algo = TRUE, …)

Arguments

x

a numeric vector, matrix, data frame or grouped data frame (class 'grouped_df').

g

a factor, GRP object, atomic vector (internally converted to factor) or a list of vectors / factors (internally converted to a GRP object) used to group x.

w

a numeric vector of (non-negative) weights, may contain missing values.

TRA

an integer or quoted operator indicating the transformation to perform: 1 - "replace_fill" | 2 - "replace" | 3 - "-" | 4 - "-+" | 5 - "/" | 6 - "%" | 7 - "+" | 8 - "*" | 9 - "%%" | 10 - "-%%". See TRA.

na.rm

logical. Skip missing values in x. Defaults to TRUE and implemented at very little computational cost. If na.rm = FALSE a NA is returned when encountered.

use.g.names

logical. Make group-names and add to the result as names (default method) or row-names (matrix and data frame methods). No row-names are generated for data.table's.

drop

matrix and data.frame method: Logical. TRUE drops dimensions and returns an atomic vector if g = NULL and TRA = NULL.

keep.group_vars

grouped_df method: Logical. FALSE removes grouping variables after computation.

keep.w

grouped_df method: Logical. Retain summed weighting variable after computation (if contained in grouped_df).

stable.algo

logical. TRUE (default) use Welford's numerically stable online algorithm. FALSE implements a faster but numerically unstable one-pass method. See Details.

…

arguments to be passed to or from other methods.

Value

fvar returns the variance of x, grouped by g, or (if TRA is used) x transformed by its variance, grouped by g. fsd computes the standard deviation of x in like manor.

Details

Welford's online algorithm used by default to compute the variance is well described here (the section Weighted incremental algorithm also shows how the weighted variance is obtained by this algorithm).

If stable.algo = FALSE, the variance is computed in one-pass as (sum(x^2)-n*mean(x)^2)/(n-1), where sum(x^2) is the sum of squares from which the expected sum of squares n*mean(x)^2 is subtracted, normalized by n-1 (Bessel's correction). This is numerically unstable if sum(x^2) and n*mean(x)^2 are large numbers very close together, which will be the case for large n, large x-values and small variances (catastrophic cancellation occurs, leading to a loss of numeric precision). Numeric precision is however still maximized through the internal use of long doubles in C++, and the fast algorithm can be up to 4-times faster compared to Welford's method.

The weighted variance is computed with frequency weights as (sum(x^2*w)-sum(w)*weighted.mean(x,w)^2)/(sum(w)-1). If na.rm = TRUE, missing values will be removed from both x and w i.e. utilizing only x[complete.cases(x,w)] and w[complete.cases(x,w)].

Missing-value removal as controlled by the na.rm argument is done very efficiently by simply skipping the values (thus setting na.rm = FALSE on data with no missing values doesn't give extra speed). Large performance gains can nevertheless be achieved in the presence of missing values if na.rm = FALSE, since then the corresponding computation is terminated once a NA is encountered and NA is returned.

This all seamlessly generalizes to grouped computations, which are performed in a single pass (without splitting the data) and therefore extremely fast.

When applied to data frames with groups or drop = FALSE, fvar/fsd preserves all column attributes (such as variable labels) but does not distinguish between classed and unclassed object (thus applying fvar/fsd to a factor column will give a 'malformed factor' error). The attributes of the data frame itself are also preserved.

References

Welford, B. P. (1962). Note on a method for calculating corrected sums of squares and products. Technometrics. 4 (3): 419-420. doi:10.2307/1266577.

See Also

Fast Statistical Functions, Collapse Overview

Examples

# NOT RUN {
## default vector method
fvar(mtcars$mpg)                            # Simple variance (all examples also hold for fvar!)
fsd(mtcars$mpg)                             # Simple standard deviation
fsd(mtcars$mpg, w = mtcars$hp)              # Weighted sd: Weighted by hp
fsd(mtcars$mpg, TRA = "/")                  # Simple transformation: scaling (See also ?fscale)
fsd(mtcars$mpg, mtcars$cyl)                 # Grouped sd
fsd(mtcars$mpg, mtcars$cyl, mtcars$hp)      # Grouped weighted sd
fsd(mtcars$mpg, mtcars$cyl, TRA = "/")      # Scaling by group
fsd(mtcars$mpg, mtcars$cyl, mtcars$hp, "/") # Group-scaling using weighted group sds

## data.frame method
fsd(iris)                           # This works, although 'Species' is a factor variable
fsd(mtcars, drop = FALSE)           # This works, all columns are numeric variables
fsd(iris[-5], iris[5])              # By Species: iris[5] is still a list, and thus passed to GRP()
fsd(iris[-5], iris[[5]])            # Same thing much faster: fsd recognizes 'Species' is a factor
head(fsd(iris[-5], iris[[5]], TRA = "/")) # Data scaled by species (see also fscale)

## matrix method
m <- qM(mtcars)
fsd(m)
fsd(m, mtcars$cyl) # etc..
# }
# NOT RUN {
 <!-- % No code relying on suggested package -->
## method for grouped data frames - created with dplyr::group_by or fgroup_by
library(dplyr)
mtcars %>% group_by(cyl,vs,am) %>% fsd()
mtcars %>% group_by(cyl,vs,am) %>% fsd(keep.group_vars = FALSE) # Remove grouping columns
mtcars %>% group_by(cyl,vs,am) %>% fsd(hp)      # Weighted by hp
mtcars %>% group_by(cyl,vs,am) %>% fsd(hp, "/") # Weighted scaling transformation
# }