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Smooth a non-positive definite correlation matrix to make it positive definite

Source: R/cor_smooth.R
cor_smooth.Rd

Make correlations positive definite using psych::cor.smooth. If smoothing is done, inferential statistics (p-values, confidence intervals, etc.) are removed, as they are no longer valid.

Usage

cor_smooth(x, method = "psych", verbose = TRUE, ...)

is.positive_definite(x, tol = 10^-12, ...)

is_positive_definite(x, tol = 10^-12, ...)

Arguments

x

A correlation matrix.

method

Smoothing method. Can be psych (will use psych::cor.smooth()), hj (Jorjani et al., 2003) or lrs (Schaeffer, 2014). For the two last, will use mbend::bend() (check its documentation for details).

verbose

Set to FALSE to silence the function.

...

Other arguments to be passed to or from other functions.

tol

The minimum eigenvalue to be considered as acceptable.

Examples

set.seed(123)
data <- as.matrix(mtcars)
# Make missing data so pairwise correlation matrix is non-positive definite
data[sample(seq_len(352), size = 60)] <- NA
data <- as.data.frame(data)
x <- correlation(data)
is.positive_definite(x)
#> [1] FALSE

smoothed <- cor_smooth(x)
#> mpg - cyl: -0.85 -> -0.82
#> 
#> mpg - disp: no change (-0.82)
#> 
#> mpg - hp: no change (-0.76)
#> 
#> mpg - drat: no change (0.58)
#> 
#> mpg - wt: no change (-0.84)
#> 
#> mpg - qsec: no change (0.32)
#> 
#> mpg - vs: no change (0.64)
#> 
#> mpg - am: 0.55 -> 0.54
#> 
#> mpg - gear: no change (0.42)
#> 
#> mpg - carb: no change (-0.57)
#> 
#> cyl - disp: 0.92 -> 0.89
#> 
#> cyl - hp: 0.88 -> 0.82
#> 
#> cyl - drat: -0.66 -> -0.64
#> 
#> cyl - wt: 0.80 -> 0.78
#> 
#> cyl - qsec: -0.47 -> -0.43
#> 
#> cyl - vs: -0.80 -> -0.76
#> 
#> cyl - am: -0.74 -> -0.66
#> 
#> cyl - gear: -0.66 -> -0.64
#> 
#> cyl - carb: no change (0.54)
#> 
#> disp - hp: no change (0.77)
#> 
#> disp - drat: no change (-0.57)
#> 
#> disp - wt: 0.88 -> 0.87
#> 
#> disp - qsec: -0.45 -> -0.43
#> 
#> disp - vs: no change (-0.74)
#> 
#> disp - am: -0.58 -> -0.56
#> 
#> disp - gear: no change (-0.52)
#> 
#> disp - carb: no change (0.56)
#> 
#> hp - drat: no change (-0.41)
#> 
#> hp - wt: 0.62 -> 0.60
#> 
#> hp - qsec: no change (-0.65)
#> 
#> hp - vs: no change (-0.71)
#> 
#> hp - am: -0.22 -> -0.23
#> 
#> hp - gear: no change (-0.14)
#> 
#> hp - carb: 0.65 -> 0.64
#> 
#> drat - wt: no change (-0.66)
#> 
#> drat - qsec: no change (-0.19)
#> 
#> drat - vs: no change (0.22)
#> 
#> drat - am: 0.74 -> 0.73
#> 
#> drat - gear: no change (0.71)
#> 
#> drat - carb: no change (-0.06)
#> 
#> wt - qsec: -0.09 -> -0.10
#> 
#> wt - vs: no change (-0.56)
#> 
#> wt - am: -0.72 -> -0.71
#> 
#> wt - gear: -0.64 -> -0.63
#> 
#> wt - carb: 0.50 -> 0.50
#> 
#> qsec - vs: no change (0.73)
#> 
#> qsec - am: -0.35 -> -0.32
#> 
#> qsec - gear: -0.13 -> -0.14
#> 
#> qsec - carb: -0.63 -> -0.61
#> 
#> vs - am: 0.20 -> 0.20
#> 
#> vs - gear: no change (0.32)
#> 
#> vs - carb: -0.69 -> -0.68
#> 
#> am - gear: 0.81 -> 0.79
#> 
#> am - carb: -0.24 -> -0.22
#> 
#> gear - carb: no change (0.03)
#>