Package 'MVOPR'

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)

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Multi-View Orthogonal Projection Regression for three modalities

Description

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

Usage

MVOPR3(
  M1,
  M2,
  M3,
  Y,
  RRR_Control = list(Sparsity = TRUE, nrank = 10, ic.type = "GIC"),
  family = "gaussian",
  penalty = "lasso"
)

Arguments

M1	A numeric matrix (n x p1) for the first modality.
M2	A numeric matrix (n x p2) for the second modality. Assumes 'M2' is correlated to 'M1' via a low-rank matrix.
M3	A numeric matrix (n x p3) for the third modality. Assumes 'M3' is correlated to 'M1' and 'M2' via a low-rank matrix.
Y	A numeric response vector of length 'n', connected to 'M1', 'M2', and 'M3'.
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

A fitted object from 'cv.ncvreg', containing the penalized regression results for 'Y'.

fitM2

The fitted reduced-rank regression ('sofar' or 'rrr' object) for 'M2' given 'M1'.

fitM3

The fitted reduced-rank regression ('sofar' or 'rrr' object) for 'M3' given 'M1' and 'M2'.

CoefY

A vector of estimated regression coefficients for 'Y'.

coefM2

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

coefM3

A matrix of estimated regression coefficients for 'M3' given 'M1' and 'M2'.

rank1

An integer indicating the estimated rank of the reduced-rank regression for 'M2'.

rank2

An integer indicating the estimated rank of the reduced-rank regression for 'M3'.

P1

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

P2

A projection matrix used to extract the orthogonal components of 'E2', which is the error term in the regression for 'M2' given 'M1'.

M1s

A transformed version of 'M1' after projection.

M2s

A transformed version of 'M2' after removing the effect of 'M1' and projecting to the orthogonal space.

M3s

A transformed version of 'M3' after removing the effects of 'M1' and 'M2'.

#' @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: three modalities
p1 = 50; p2 = 50; p3 = 50; n = 200
rank = 2

beta = c(rep(c(rep(1,5),rep(0,45)),3))
M1 = matrix(rnorm(p1*n),n,p1)

U1 = matrix(rnorm(rank*p1),p1,rank)
V1 = matrix(runif(rank*p2,-0.1,0.1),rank,p2)
B1 = U1 %*% V1

U2 = matrix(rnorm(rank*p1),p1,rank)
V2 = matrix(runif(rank*p2,-0.1,0.1),rank,p3)
B2 = U2 %*% V2

U3 = matrix(rnorm(rank*p2),p2,rank)
V3 = matrix(runif(rank*p2,-0.1,0.1),rank,p3)
B3 = U3 %*% V3

E1 = matrix(rnorm(p2*n),n,p2)
E2 = matrix(rnorm(p3*n),n,p3)

M2 = M1 %*% B1 + E1
M3 = M1 %*% B2 + M2 %*% B3 + E2
Y = cbind(M1,M2,M3) %*% matrix(beta,p1+p2+p3,1)

## Fit MVOPR with Lasso
Fit1 = MVOPR3(M1,M2,M3,Y,RRR_Control = list(Sparsity = FALSE),penalty = 'lasso')

## Fit MVOPR with MCP
Fit2 = MVOPR3(M1,M2,M3,Y,RRR_Control = list(Sparsity = FALSE),penalty = 'MCP')

## Fit MVOPR with SCAD
Fit3 = MVOPR3(M1,M2,M3,Y,RRR_Control = list(Sparsity = FALSE),penalty = 'SCAD')

## Compare the variable selection between Lasso, MCP, SCAD
print(data.frame(Lasso = Fit1$CoefY[2:151],MCP = Fit2$CoefY[2:151],SCAD = Fit3$CoefY[2:151],beta))

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