<!-- badges: end -->

latentcor: Latent Correlation for Mixed Types of Data

latentcor is an R package for estimation of latent correlations with mixed data types (continuous, binary, truncated, and ternary) under the latent Gaussian copula model. For references on the estimation framework, see

• Fan, J., Liu, H., Ning, Y., and Zou, H. (2017), “High Dimensional Semiparametric Latent Graphical Model for Mixed Data.” JRSS B. Continuous/binary types.

• Quan X., Booth J.G. and Wells M.T."Rank-based approach for estimating correlations in mixed ordinal data." arXiv Ternary type.

• Yoon G., Carroll R.J. and Gaynanova I. (2020). “Sparse semiparametric canonical correlation analysis for data of mixed types”. Biometrika. Truncated type for zero-inflated data.

• Yoon G., Müller C.L. and Gaynanova I. (2021). “Fast computation of latent correlations” JCGS. Approximation method of computation, see vignette for details.

Statement of Need

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.

Multi-linear interpolation: Earlier versions of latentcor used multi-linear interpolation based on functionality of R package chebpol written by Simen Gaure. This functionality is needed for faster computations of latent correlations with approximation method. However, chebpol was removed from CRAN on 2022-02-07. The current version of latentcor reuses the multi-linear interpolation part of the chebpol (provided under Artistic-2 license) integrated directly within latentcor. To cite multi-linear interpolation only, please use original chebpol.

Accuracy: The approximation method for ternary/ternary, truncated(zero-inflated)/ternary, and ternary/binary cases are less accurate close to boundary (zero proportions) due to size limitations of CRAN packages on the pre-stored grid. If higher accuracy is desired and original method is computationally prohibitive, latencor is also available as Python package with Github development python version

Installation

To use latentcor, you need to install R. To enhance your user experience, you may use some IDE for it (e.g. RStudio).

The development version of latentcor is available on GitHub. You can download it with the help of the devtools package in R as follow:

r install.packages("devtools") devtools::install_github("https://github.com/mingzehuang/latentcor", build_vignettes = TRUE) The stable release version latentcor is available on CRAN. You can download it in R as follow:

r install.packages("latentcor")

Example

A simple example estimating latent correlation is shown below.

```r library(latentcor)

Generate two variables of sample size 100

The first variable is ternary (pi0 = 0.3, pi1 = 0.5, pi2 = 1-0.3-0.5 = 0.2)

The second variable is continuous.

No copula transformation is applied.

X = gen_data(n = 1000, types = c("ter", "con"), XP = list(c(0.3, .5), NA))$X

Estimate latent correlation matrix with the original method

latentcor(X = X, types = c("ter", "con"), method = "original")$R

Estimate latent correlation matrix with the approximation method

latentcor(X = X, types = c("ter", "con"))$R

Speed improvement by approximation method compared with original method

library(microbenchmark) microbenchmark(latentcor(X, types = c("ter", "con"), method = "original"), latentcor(X, types = c("ter", "con")))

Unit: milliseconds

min lq mean median uq max neval

5.3444 5.8301 7.033555 6.06740 6.74975 20.8878 100

1.5049 1.6245 2.009371 1.73805 1.99820 5.0027 100

This is run on Windows 10 with Intel(R) Core(TM) i5-4570 CPU @ 3.20GHz 3.20 GHz

Heatmap for latent correlation matrix.

latentcor(X = X, types = c("ter", "con"), showplot = TRUE)$plotR `` Another example with themtcars` dataset.

```r library(latentcor)

Use build-in dataset mtcars

X = mtcars

Check variable types for manual determination

apply(mtcars, 2, table)

Or use built-in get_types function to get types suggestions

get_types(mtcars)

Estimate latent correlation matrix with original method

latentcor(mtcars, types = c("con", "ter", "con", "con", "con", "con", "con", "bin", "bin", "ter", "con"), method = "original")$R

Estimate latent correlation matrix with approximation method

latentcor(mtcars, types = c("con", "ter", "con", "con", "con", "con", "con", "bin", "bin", "ter", "con"))$R

Speed improvement by approximation method compared with original method

library(microbenchmark) microbenchmark(latentcor(mtcars, types = types, method = "original"), latentcor(mtcars, types = types, method = "approx"))

Unit: milliseconds

min lq mean median uq max neval

201.9872 215.6438 225.30385 221.5364 226.58330 411.4940 100

71.8457 75.1681 82.42531 80.1688 84.77845 238.3793 100

This is run on Windows 10 with Intel(R) Core(TM) i5-4570 CPU @ 3.20GHz 3.20 GHz

Heatmap for latent correlation matrix with approximation method.

latentcor(mtcars, types = c("con", "ter", "con", "con", "con", "con", "con", "bin", "bin", "ter", "con"), showplot = TRUE)$plotR ```

Interactive heatmap see: interactive heatmap of latent correlations (approx) for mtcars

Community Guidelines

1. Contributions and suggestions to the software are always welcome. Please consult our contribution guidelines prior to submitting a pull request.
2. Report issues or problems with the software using github’s issue tracker.
3. Contributors must adhere to the Code of Conduct.

Acknowledgments

We thank Dr. Grace Yoon for providing implementation details of the mixedCCA R package.