MVOPR2 {MVOPR}R Documentation

Multi-View Orthogonal Projection Regression for two modalities

Description

Fit Multi-View Orthogonal Projection Regression for two modalities with Lasso, MCP, SCAD. The function is capable for linear, logistic, and poisson regression.

Usage

MVOPR2(
  M1,
  M2,
  Y,
  RRR_Control = list(Sparsity = TRUE, nrank = 10, ic.type = "GIC"),
  family = "gaussian",
  penalty = "lasso"
)

Arguments

M1

A numeric matrix (n x p) for the first modality.

M2

A numeric matrix (n x q) for the second modality. Assumes 'M2' is correlated to 'M1' via a low-rank matrix.

Y

A numeric response vector of length 'n', connected to 'M1' and 'M2'.

RRR_Control

A list to control the fitting for reduced rank regression.

Sparsity

Logical. If 'TRUE', performs Sparse Orthogonal Factor Regression (SOFAR); otherwise, a reduced-rank regression model is fitted.

nrank

Integer. Maximum rank to be searched for the reduced-rank model.

ic.type

Character. Model selection criterion: '"AIC"', '"BIC"', or '"GIC"'.

family

Either "gaussian", "binomial", or "poisson", depending on the response.

penalty

The penalty to be applied in the outcome model Y to M1 and M2. Either "MCP" (the default), "SCAD", or "lasso".

Value

A list containing:

fitY

Results for Outcome regression (Y~M1+M2). A fitted object from 'cv.ncvreg', which contains the penalized regression results for 'Y'.

fitM2

Results for reduced-rank regression (M2~M1).The fitted reduced-rank regression model from 'rrpack'.

CoefY

A vector of estimated regression coefficients for 'M1' and 'M2' on 'Y'.

coefM2

A matrix of estimated regression coefficients for 'M1' on 'M2'.

rank

An integer indicates the estimated rank of the reduced-rank regression.

P

A projection matrix used to extract the orthogonal components of 'M1'.

M1s

Transformed version of 'M1' after projection.

M2s

Transformed version of 'M2' after removing the effect of 'M1'.

References

Dai, Z., Huang, Y. J., & Li, G. (2025). Multi-View Orthogonal Projection Regression with Application in Multi-omics Integration. arXiv preprint arXiv:2503.16807. Available at <https://arxiv.org/abs/2503.16807>

Examples


## Simulation.1
p = 100; q = 100; n = 200
rank = 3

beta = c(rep(c(rep(1,5),rep(0,95)),2))
M1 = matrix(rnorm(p*n),n,p)

U = matrix(rnorm(rank*p),p,rank)
V = matrix(rnorm(rank*q),rank,q)
B = U %*% V
E = matrix(rnorm(q*n),n,q)
M2 = M1 %*% B + E
Y = cbind(M1,M2) %*% matrix(beta,p+q,1)

Fit = MVOPR2(M1,M2,Y,RRR_Control = list(Sparsity = FALSE))

## Result for variable selection
print(data.frame(Truecoef = beta,estimate = Fit$CoefY[2:(p+q+1)]))

## Plot the pathway and cv error in outcome model
oldpar <- par(mfrow = c(1, 2))
on.exit(par(oldpar))
plot(Fit$fitY$fit)
plot(Fit$fitY)



[Package MVOPR version 2.0.0 Index]