Table of Contents

• missLASSO
• DOWNLOAD AND INSTALLATION
• Input
• Dataset
• Output
• Contact
• Reference

missLASSO

missLASSO is a C++ software package that performs variable selection and estimation for the regression analysis of an outcome of interest against multiple types of features with missing data. We use a latent factor model to characterize the relationships across and within different types of features and to infer missing values from the observed data. Variable selection and estimation are performed by a penalized maximum likelihood approach and the estimator is computed using an EM algorithm.

DOWNLOAD AND INSTALLATION

Download

The latest version of missLASSO can be downloaded from github page.

Installation

missLASSO is an executable file. Users can run it on the Linux or Window environment using missLASSO.tar.gz or missLASSO.exe, respectively.

Linux Environment

1. Download missLASSO.tar.gz to a destinated directory
2. Go to the destinated directory:

   cd ./[destinated directory]
   

3. Extract missLASSO.tar.gz

   tar -xzvf missLASSO.tar.gz
   

4. Run missLASSO

   ./missLASSO [type] [method] [penaltyno] [sizeX] [r] [groupsize] [cv] [lambda] [dirname] [foldername] [filename]
   Example : C:\Users\Desktop\missLASSO>missLASSO type 0 method 1 penaltyno 0 sizeX 0 r 1,1,1 groupsize 50,50 cv 1 lambda TestLambda.csv foldername testing filename SampleDataset_1.csv 
   

Window Environment

1. Download missLASSO.exe to a destinated directory
2. Open command prompt and set the working directory

   cd ./[destinated directory]
   

3. Run missLASSO

   missLASSO [type] [method] [penaltyno] [sizeX] [r] [groupsize] [cv] [lambda] [dirname] [foldername] [filename]
   Example : C:\Users\Desktop\missLASSO>missLASSO type 0 method 1 penaltyno 0 sizeX 0 r 1,1,1,1 groupsize 30,30,30 cv 1 lambda TestLambda.csv foldername testing filename SampleDataset.csv 
   

Input

There are 13 arguments for the function:

Argument	Description	Value(s) / Format	Interpretation	Can be Omitted	Remark
type	Type of the outcome variable	0/1	0: Gaussian 1: Binary	✖	-
method	Method for handling missing data	0/1	0: Complete case analysis 1: Single imputation and the full likelihood approach	✖	-
penaltyno	Penalty type	0/1	0: Lasso 1: Adaptive lasso with marginal coefficients as weights	✖	-
sizeX	Number of covariates (not modeled by the factor model)	Integer ≥ 0		✖	-
r	Numbers of latent factors for different types of features		-	✖	seperate using ","; the first component is the number of common factors, and the later components correspond to the number of factors specific to a type
groupsize	Number of variables for each type of features		-	✖	seperate using ","
cv	Cross validation	0/1	0: Do not perform cross validation 1: Perform cross validation	✔	default is to perform cross validation
lambda	sequence of tuning parameter values	.csv file	-	✔	-
XyExclude	Indices of covariates that are to be excluded from the outcome model		-	✔	separated using ","; by default, all covariates are included
XsExclude	Indices of covariates that are to be excluded from the factor model		-	✔	separated using ","; by default, all covariates are included
dirname	Output directory	Any file path	-	✔	Relative path can be used Default: current working directory
foldername	Output folder name	Any name	-	✔	Default is Result
filename	Input dataset name	.csv file	-	✖	-

Dataset

The input dataset should be in .csv format and consist of 3 sets of input: outcome Y, covariates X, and potentially missing covariates S. The dataset is in the format of a n x (p+k+1)-matrix, where n is the sample size, p is the number of covariates, and k is the number of potentially missing covariates. The dataset should be in following format:

Outcome variable	1st covariate	2nd covariate	...	pth covariate	1st missing covariate	2nd missing covariate	...	kth missing covariate

A sample dataset can be downloaded from github page.

SampleDataset_1.csv is a dataset without covariate X and contains potentially missing covariate S only, with groupsize = 50,50.

SampleDataset_2.csv is a dataset with covariate X and potentially missing covariate S, with sizeX = 6, groupsize = 50,50,50.

Output

All results will be stored in an output folder. By default, the output folder is called "Result" under the current working directory. The output folder will contain the following .csv files:

Complete case analysis (method = 0)

1. Complete.csv
2. Complete-lambda.csv
3. Complete-loglikelihood.csv

Single imputation and full likelihood approach (method = 1)

1. Impute.csv
2. Impute-imploglikelihood.csv
3. Impute-lambda.csv
4. Impute-loglikelihood.csv
5. Impute-param.csv
6. Joint.csv
7. Joint-lambda.csv
8. Joint-loglikelihood.csv
9. Joint-param.csv

The descriptions of the output files are as follows:

File	Description
Complete.csv/Impute.csv/Joint.csv	Regression coefficients in the outcome model over all tuning parameter values considered. Let q be the number of tuning parameter values. The first q components of the output correspond to the numbers of nonzero coefficients under the tuning parameter values. Let m be the sum of the first q components of the output. The q+1-th to the q+m-th components correspond to the positions of the nonzero coefficients. The q+m+1-th to the q+2m-th components correspond to the values of the nonzero coefficients. For example, if q=3 and the output is 1,2,4,0,0,1,0,1,2,3,0.3,0.3,0.4,0.4,0.5,0.6,0.7, then for the first tuning parameter value, one variable is selected, the position is 0 (i.e., the first variable), and the coefficient is 0.3; for the second tuning parameter value, two variables are selected, the positions are (0,1), and the coefficients are (0.3,0.4); for the third tuning parameter, four variables are selected, the positions are (0,1,2,3), and the coefficients are (0.4,0.5,0.6,0.7).
Complete-lambda.csv/Impute-lambda.csv/Joint-lambda.csv	Sequence of lambda values considered. If cv=1, then the last component of the lambda sequence is that selected by cross validation.
Complete-loglikelihood.csv/Impute-loglikelihood.csv/Joint-loglikelihood.csv	Sequence of log-likelihood values, corresponding to the lambda values in the "-lambda.csv" files.
Impute-imploglikelihood.csv	loglikelihood value evaluated at the imputed data.
Joint-param.csv	All parameter estimates at the selected tuning parameter value. The parameter estimates are ordered as follows: $\beta$, $\alpha$, $\Gamma$ (intercept), $\Gamma$ (coefficients of covariates), $\Psi$, $\Sigma$ (diagonal elements), $\xi$ (error variance for the linear outcome model); refer to Wong et al. (2023) for the parameter names.

Contact

Wong Kin Yau, Alex <kin-yau.wong@polyu.edu.hk>

Reference

Wong, K. Y., Zeng, D., and Lin, D. Y. (2023), "Penalized regression for multiple types of many features with missing data," Statistica Sinica, 33, 633–662.