options(tinytex.verbose = TRUE) knitr::opts_chunk$set( collapse = TRUE, comment = "#>" ) library(latentcor)
R package latentcor
utilizes the powerful semi-parametric latent Gaussian copula models to estimate latent correlations between mixed data types. The package allows to estimate correlations between any of continuous/binary/ternary/zero-inflated (truncated) variable types. The underlying implementation takes advantage of fast multi-linear interpolation scheme with a clever choice of grid points that give the package a small memory footprint, and allows to use the latent correlations with sub-sampling and bootstrapping.
No R software package is currently available that allows accurate and fast correlation estimation from mixed variable data in a unifying manner. The R package latentcor
, introduced here, thus represents the first stand-alone R package for
computation of latent correlation that takes into account all variable types (continuous/binary/ordinal/zero-inflated), comes with an optimized memory footprint,
and is computationally efficient, essentially making latent correlation estimation almost as fast as rank-based correlation estimation.
First, we will generate a pair of variables with different types using a sample size $n=100$ which will serve as example data. Here first variable will be ternary, and second variable will be continuous.
simdata = gen_data(n = 100, types = c("ter", "con"))
The output of gen_data
is a list with 2 elements:
names(simdata)
X
: a matrix ($100\times 2$), the first column is the ternary variable; the second column is the continuous variable.X = simdata$X head(X, n = 6L)
plotX
: NULL (showplot = FALSE
, can be changed to display the plot of generated data ingen_data
input).simdata$plotX
Then we can estimate the latent correlation matrix based on these 2 variables using latentcor
function.
estimate = latentcor(X, types = c("ter", "con"))
The output of latentcor
is a list with several elements:
names(estimate)
zratios
is a list has the same length as the number of variables. Here the first element is a ($2\times1$) vector indicating the cumulative proportions for zeros and ones in the ternary variable (e.g. first element in vector is the proportion of zeros, second element in vector is the proportion of zeros and ones.) The second element of the list is NA for continuous variable.estimate$zratios
K
: Kendall $\tau$ ($\tau_{a}$) correlation matrix for these 2 variables. estimate$K
Rpointwise
: matrix of pointwise estimated correlations. Due to pointwise estimation, Rpointwise
is not guaranteed to be positive semi-definiteestimate$Rpointwise
R
: estimated final latent correlation matrix, this matrix is guaranteed to be strictly positive definite (through nearPD
projection and parameter nu
, see Mathematical framework for estimation) if use.nearPD = TRUE
.estimate$R
plotR
: NULL by default as showplot = FALSE
in latentcor
. Otherwise displays a heatmap of latent correlation matrix.estimate$plotR
We use the build-in dataset mtcars
:
head(mtcars, n = 6L)
Let's take a look at the unique values for each variable to determine the corresponding data type.
apply(mtcars, 2, table)
Then we can estimate the latent correlation matrix for all variables of mtcars
by using latentcor
function.
estimate_mtcars = latentcor(mtcars, types = c("con", "ter", "con", "con", "con", "con", "con", "bin", "bin", "ter", "con"))
Note that the determination of variable types can also be done automatically by latentcor
package using get_types
function:
estimate_mtcars = latentcor(mtcars, types = get_types(mtcars))
This function is run automatically inside latentcor
if the types
are not supplied by the user, however the automatic determination of types takes extra time, so we recommend to specify types
explicitly if they are known in advance.
The output of latentcor
for mtcars
:
names(estimate_mtcars)
zratios
: zratios for corresponding variables in mtcars
.estimate_mtcars$zratios
K
: Kendall $\tau$ ($\tau_{a}$) correlation matrix for variables in mtcars
. estimate_mtcars$K
Rpointwise
: matrix of pointwise estimated correlations for mtcars
.estimate_mtcars$Rpointwise
R
: estimated final latent correlation matrix for mtcars
.estimate_mtcars$R
plotR
: NULL by default as showplot = FALSE
in latentcor
. Otherwise displays a heatmap of latent correlation matrix for mtcars
(See heatmap of latent correlation (approx) for mtcars).estimate_mtcars$plotR
While latentcor
can determine the types of each variable automatically, it is recommended to call get_types
first and then supply types
explicitly to save the computation time, especially when using latentcor with sub-sampling (which we illustrate below).
First, we will generate variables with different types using a sample size $n=100$ which will serve as an example data for subsampling.
simdata2 = gen_data(n = 100, types = c(rep("ter", 3), "con", rep("bin", 3)))
To use the data with subsampling, we recommend to first run get_types
on the full data
types = get_types(simdata2$X) types
Then, when doing subsampling, we recommend to explicitly supply identified types to latentcor
. We illustrate using 10 subsamples, each of size 80.
start_time = proc.time() for (s in 1:10){ # Select a random subsample of size 80 subsample = sample(1:100, 80) # Estimate latent correlation on subsample specifying the types Rs = latentcor(simdata2$X[subsample, ], types = types) } proc.time() - start_time
Compared with
start_time = proc.time() for (s in 1:10){ # Select a random subsample of size 80 subsample = sample(1:100, 80) # Estimate latent correlation on subsample specifying the types Rs = latentcor(simdata2$X[subsample, ], types = get_types(simdata2$X)) } proc.time() - start_time
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