plmmr is a package for fitting
Penalized Linear
Mixed Models in R.
This package was created for the purpose of fitting penalized regression
models to high dimensional data in which the observations are correlated
in some complex way. For instance, this kind of data arises often in the
context of genetics (e.g., GWAS dealing with population
structure/family structure).
For more information on the theoretical context of penalized regression, check out these online course notes; the section on ridge regression may be a good place to start.
The novelties of plmmr are:
Integration: plmmr combines the
functionality of several packages in order to do quality control, model
fitting/analysis, and data visualization all in one package. For
example, if you have GWAS data, plmmr will take you from
PLINK files all the way to a list of SNPs for downstream
analysis.
Accessibility: plmmr can be run
from an R session on a typical desktop or laptop computer.
The user does not need access to a supercomputer or have experience with
the command line in order to fit models plmmr.
Handling correlation: plmmr uses a
transformation that (1) measures correlation among samples and (2) uses
this correlation measurement to improve predictions (via the best linear
unbiased predictor, or BLUP). This means that in plmm(),
there’s no need to filter data down to a ‘maximum subset of unrelated
samples.’
In many applications of high dimensional data analysis, the dataset
is too large to read into R – the session will crash for lack of memory.
This is particularly common when analyzing data from genome-wide
association studies (GWAS). To analyze such large datasets,
plmmr is equipped to analyze data using
filebacking - a strategy that lets R ‘point’ to a file on disk,
rather than reading the file into the R session. Many other packages use
this technique - bigstatsr and biglasso are two
examples of packages that use the filebacking technique. The package
that plmmr uses to create and store filebacked objects is
bigmemory.
The filebacked computation relies on the biglasso package by Yaohui
Zeng et al. and on bigalgebra by
Michael Kane et al. For processing PLINK files, we use
methods from the bigsnpr package by Florian Privé.
At this time, the package is designed for linear regression only – that is, we are considering only continuous (numeric) outcomes. We maintain that treating binary outcomes as numeric values is appropriate in some contexts, as described by Hastie et al. in the Elements of Statistical Learning, chapter 4. In the future, we would like to extend this package to handle dichotomous outcomes via logistic regression; the theoretical work underlying this is an open problem.
Since we are focused on penalized regression in this package,
plmmr offers 3 choices of penalty: the minimax concave
(MCP), the smoothly clipped absolute deviation (SCAD), and the least
absolute shrinkage and selection operator (LASSO). The implementation of
these penalties is built on the concepts/techniques provided in the ncvreg package.
We distinguish between the data attributes ‘big’ and ‘high dimensional.’ ‘Big’ describes the amount of space data takes up on a computer, while ‘high dimensional’ describes a context where the ratio of features (also called ‘variables’ or ‘predictors’) to observations (e.g., samples) is high. For instance, data with 100 samples and 100 variables is high dimensional, but not big. By contrast, data with 10 million observations and 100 variables is big, but not high dimensional.
plmmr is optimized for data that are high dimensional –
the methods we are using to estimate relatedness among observations
perform best when there are a high number of features relative to the
number of observations.
plmmr is also designed to accommodate data that is too
large to analyze in-memory. We accommodate such data through
file-backing (as described above). Our current analysis pipeline works
well for data files up to about 40 Gb in size. In practice, this means
that plmmr is equipped to analyze GWAS data, but not
biobank-sized data.
plmmr currently works with three types of data
input:
Data that is stored in-memory as a matrix or data frame
Data that is stored in PLINK files
Data that is stored in delimited files
plmmr currently includes three example data sets, one
for each type of data input.
The admix data is our example of matrix input data.
admix is a small data set (197 observations, 100 SNPs) that
describes individuals of different ancestry groups. The outcome of
admix is simulated to include population structure effects
(i.e. race/ethnicity have an impact on the SNP associations).
This data set is available as whenever library(plmmr) is
called. An example analysis with the admix data is
available in
vignette('matrix_data', package = "plmmr").
The penncath_lite data is our example of PLINK input
data. penncath_lite (data on coronary artery disease from
the PennCath
study) is a high dimensional data set (1401 observations, 4217 SNPs)
with several health outcomes as well as age and sex information. The
features in this data set represent a small subset of a much larger GWAS
data set (the original data has over 800K SNPs). For for information on
this data set, refer to the original
publication. An example analysis with the penncath_lite
data is available in
vignette('plink_files', package = "plmmr").
The colon2 data is our example of delimited-file
input data. colon2 is a variation of the colon
data included in the biglasso package.
colon2 has 62 observations and 2,001 features representing
a study of colon disease. 2000 features are original to the data, and
the ‘sex’ feature is simulated. An example analysis with the
colon2 data is available in
vignette('delim_files', package = "plmmr").