MVOPR (version 2.0.0)

MVOPR2: 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"
)

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`.

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".

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)