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Type:

Package

Title:

Least Squares, Logistic, and Cox-Regression with Ordered Predictors

Version:

1.0.8

Date:

2026-04-26

Maintainer:

Kaspar Rufibach <kaspar.rufibach@gmail.com>

Depends:

survival, eha, MASS

Imports:

stats

Description:

In biomedical studies, researchers are often interested in assessing the association between one or more ordinal explanatory variables and an outcome variable, at the same time adjusting for covariates of any type. The outcome variable may be continuous, binary, or represent censored survival times. In the absence of a precise knowledge of the response function, using monotonicity constraints on the ordinal variables improves efficiency in estimating parameters, especially when sample sizes are small. This package implements an active set algorithm that efficiently computes such estimators.

License:

GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]

LazyLoad:

yes

URL:

http://www.kasparrufibach.ch

NeedsCompilation:

Packaged:

2026-04-26 17:03:16 UTC; kaspa

Author:

Kaspar Rufibach

[aut, cre]

Repository:

CRAN

Date/Publication:

2026-04-26 17:20:02 UTC

Least Squares, Logistic, and Cox-Regression with Ordered Predictors

Description

Details

Package:	OrdFacReg
Type:	Package
Version:	1.0.8
Date:	2026-04-26
License:	GPL (>=2)
LazyLoad:	yes

Use this package to get estimates in least squares, logistic, or Cox-regression where coefficients corresponding to dummy variables of ordered factors are estimated to be in non-decreasing order and at least 0. The package offers an active set algorithm implemented in the functions ordFacReg for least squares and logistic regression and ordFacRegCox for Cox-regression.

Author(s)

Kaspar Rufibach (maintainer)
kaspar.rufibach@gmail.com
http://www.kasparrufibach.ch

References

Rufibach, K. (2010). An Active Set Algorithm to Estimate Parameters in Generalized Linear Models with Ordered Predictors. Comput. Statist. Data Anal., 54, 1442-1456.

Internal functions for ordered factor regression functions

Description

Internal functions for ordered factor regression functions.

Details

These functions are not intended to be called by users directly.

Abeta: Function A(\bold{\beta}) in Rufibach (2010) that collects the indices of the inequalities violated by \bold{\beta}.
constraintMats: Function that computes the matrices \bold{B} (collects the basis vectors given in Theorem 3.1 of Duembgen et al. (2007)) and \bold{V} (collects the vectors \bold{v}_i that make up the cone K in Section 3.1 of Duembgen et al. (2007)).
coxDeriv: Computes gradient of (pseudo-)log-likelihood function in Cox-regression.
coxLoglik: Computes value of (pseudo-)log-likelihood function in Cox-regression.
coxSubspace: Computes maximizer on subspace, denoted by \widetilde{\psi}(A) in Table 1 of Duembgen et al. (2007).
dummy: Generate a matrix of dummy variables corresponding to the levels of the inputed factor. The dummy variable corresponding to the lowest level of the factor is omitted.
expandBeta: After computation of \bold{\beta} on subspace “blow up” this vector again to original dimension.
indexDummy: Compute column numbers of the dummy variables of the ordered factor(s).
lmLSE: Compute value of least squares criterion and least squares estimate.
lmSS: Compute value of least squares criterion and its gradient.
logRegDeriv: Gradient of log-likelihood function in logistic regression.
logRegLoglik: Compute value of log-likelihood function in logistic regression.
logRegSubspace: Computes maximizer on subspace, denoted by \widetilde{\psi}(A) in Table 1 of Duembgen et al. (2007).
LSEsubspace: Computes maximizer on subspace, denoted by \widetilde{\psi}(A) in Table 1 of Duembgen et al. (2007).
maxStep: Compute maximal permissible steplength, denoted by t in Table 1 in Duembgen et al. (2007).
phi_jl: Function \phi in Rufibach (2010) that maps the original indices (i, j) to the inequality index i.
setminus: Remove elements in vector B from vector A.
shrinkBeta: Collapse \bold{\beta} according to the active constraints specified by the set A.

Author(s)

Kaspar Rufibach (maintainer)
kaspar.rufibach@gmail.com
http://www.kasparrufibach.ch

References

Duembgen, L., Huesler, A. and Rufibach, K. (2010). Active set and EM algorithms for log-concave densities based on complete and censored data. Technical report 61, IMSV, Univ. of Bern, available at https://arxiv.org/abs/0707.4643.

Rufibach, K. (2010). An Active Set Algorithm to Estimate Parameters in Generalized Linear Models with Ordered Predictors. Comput. Statist. Data Anal., 54, 1442-1456.

Compute least squares or logistic regression for ordered predictors

Description

This function computes estimates in least squares or logistic regression where coefficients corresponding to dummy variables of ordered factors are estimated to be in non-decreasing order and at least 0. An active set algorithm as described in Duembgen et al. (2007) is used.

Usage

ordFacReg(D, Z, fact, ordfact, ordering = NA, type = c("LS", "logreg"), 
    intercept = TRUE, display = 0, eps = 0)

Arguments

D

Response vector, either in R^n (least squares) or in \{0, 1\}^n (logistic).

Z

Matrix of predictors. Factors are coded with levels from 1 to j.

fact

Specify columns in Z that correspond to unordered factors.

ordfact

Specify columns in Z that correspond to ordered factors.

ordering

Vector of the same length as ordfact. Specifies ordering of ordered factors: "i" means that the coefficients of the corresponding ordered factor are estimated in non-decreasing order and "d" means non-increasing order. See the examples below for details.

type

Specify type of response variable.

intercept

If TRUE, an intercept (= column of all 1's) is added to the design matrix.

display

If display == 1 progress of the algorithm is output.

eps

Quantity to which the criterion in the Basic Procedure 2 in Duembgen et al. (2007) is compared.

Details

For a detailed description of the problem and the algorithm we refer to Rufibach (2010).

Value

L

Value of the criterion function at the maximum.

beta

Computed regression coefficients.

A

Set A of active constraints.

design.matrix

Design matrix that was generated.

Author(s)

Kaspar Rufibach (maintainer)
kaspar.rufibach@gmail.com
http://www.kasparrufibach.ch

References

Rufibach, K. (2010). An Active Set Algorithm to Estimate Parameters in Generalized Linear Models with Ordered Predictors. Comput. Statist. Data Anal., 54, 1442-1456.

Examples


## ========================================================
## To illustrate least squares estimation, we generate the same data
## that was used in Rufibach (2010), Table 1.
## ========================================================

## --------------------------------------------------------
## initialization
## --------------------------------------------------------
n <- 200
Z <- NULL
intercept <- FALSE

## --------------------------------------------------------
## quantitative variables
## --------------------------------------------------------
n.q <- 3
set.seed(14012009)
if (n.q > 0){for (i in 1:n.q){Z <- cbind(Z, rnorm(n, mean = 1, sd = 2))}}

## --------------------------------------------------------
## unordered factors
## --------------------------------------------------------
un.levels <- 3
for (i in 1:length(un.levels)){Z <- cbind(Z, sample(rep(1:un.levels[i], 
    each = ceiling(n / un.levels)))[1:n])}
fact <- n.q + 1:length(un.levels)

## --------------------------------------------------------
## ordered factors
## --------------------------------------------------------
levels <- 8
for (i in 1:length(un.levels)){Z <- cbind(Z, sample(rep(1:levels[i], 
    each = ceiling(n / levels)))[1:n])}
ordfact <- n.q + length(un.levels) + 1:length(levels)

## --------------------------------------------------------
## generate data matrices
## --------------------------------------------------------
Y <- prepareData(Z, fact, ordfact, ordering = NA, intercept)$Y

## --------------------------------------------------------
## generate response
## --------------------------------------------------------
D <- apply(Y * matrix(c(rep(c(2, -3, 0), each = n), rep(c(1, 1), each = n), 
    rep(c(0, 2, 2, 2, 2, 5, 5), each = n)), ncol = ncol(Y)), 1, sum) + 
    rnorm(n, mean = 0, sd = 4)

## --------------------------------------------------------
## compute estimates
## --------------------------------------------------------
res1 <- lmLSE(D, Y)
res2 <- ordFacReg(D, Z, fact, ordfact, ordering = "i", type = "LS", intercept, 
    display = 1, eps = 0)
b1 <- res1$beta
g1 <- lmSS(b1, D, Y)$dL
b2 <- res2$beta
g2 <- lmSS(b2, D, Y)$dL
Ls <- c(lmSS(b1, D, Y)$L, lmSS(b2, D, Y)$L)
names(Ls) <- c("LSE", "ordFact") 
disp <- cbind(1:length(b1), round(cbind(b1, g1, cumsum(g1)), 4), 
    round(cbind(b2, g2, cumsum(g2)), 4))

## --------------------------------------------------------
## display results
## --------------------------------------------------------
disp
Ls

## ========================================================
## Artificial data is used to illustrate logistic regression.
## ========================================================

## --------------------------------------------------------
## initialization
## --------------------------------------------------------
set.seed(1977)
n <- 500
Z <- NULL
intercept <- FALSE

## --------------------------------------------------------
## quantitative variables
## --------------------------------------------------------
n.q <- 2
if (n.q > 0){for (i in 1:n.q){Z <- cbind(Z, rnorm(n, rgamma(2, 2, 1)))}}

## --------------------------------------------------------
## unordered factors
## --------------------------------------------------------
un.levels <- c(8, 2)
for (i in 1:length(un.levels)){Z <- cbind(Z, sample(round(runif(n, 0, 
    un.levels[i] - 1)) + 1))}
fact <- n.q + 1:length(un.levels)

## --------------------------------------------------------
## ordered factors
## --------------------------------------------------------
levels <- c(2, 4, 10)
for (i in 1:length(levels)){Z <- cbind(Z, sample(round(runif(n, 0, 
    levels[i] - 1)) + 1))}
ordfact <- n.q + length(un.levels) + 1:length(levels)

## --------------------------------------------------------
## generate response
## --------------------------------------------------------
D <- sample(c(rep(0, n / 2), rep(1, n/2)))

## --------------------------------------------------------
## generate design matrix
## --------------------------------------------------------
Y <- prepareData(Z, fact, ordfact, ordering = NA, intercept)$Y

## --------------------------------------------------------
## compute estimates
## --------------------------------------------------------
res1 <- matrix(glm.fit(Y, D, family = binomial(link = logit))$coefficients, ncol = 1)
res2 <- ordFacReg(D, Z, fact, ordfact, ordering = NA, type = "logreg", 
    intercept = intercept, display = 1, eps = 0)
b1 <- res1
g1 <- logRegDeriv(b1, D, Y)$dL
b2 <- res2$beta
g2 <- logRegDeriv(b2, D, Y)$dL
Ls <- unlist(c(logRegLoglik(res1, D, Y), res2$L))
names(Ls) <- c("MLE", "ordFact") 
disp <- cbind(1:length(b1), round(cbind(b1, g1, cumsum(g1)), 4), 
    round(cbind(b2, g2, cumsum(g2)), 4))

## --------------------------------------------------------
## display results
## --------------------------------------------------------
disp
Ls

## --------------------------------------------------------
## compute estimates when the third ordered factor should
## have *decreasing* estimated coefficients
## --------------------------------------------------------
res3 <- ordFacReg(D, Z, fact, ordfact, ordering = c("i", "i", "d"), 
    type = "logreg", intercept = intercept, display = 1, eps = 0)
b3 <- res3$beta
g3 <- logRegDeriv(b3, D, Y)$dL
Ls <- unlist(c(logRegLoglik(res1, D, Y), res2$L, res3$L))
names(Ls) <- c("MLE", "ordFact ddd", "ordFact iid") 
disp <- cbind(1:length(b1), round(cbind(b1, b2, b3), 4))

## --------------------------------------------------------
## display results
## --------------------------------------------------------
disp
Ls

Compute Cox-regression for ordered predictors

Description

This function computes estimates in Cox-regression where coefficients corresponding to dummy variables of ordered factors are estimated to be in non-decreasing order and at least 0. An active set algorithm as described in Duembgen et al. (2007) is used.

Usage

ordFacRegCox(ttf, tf, Z, fact, ordfact, ordering = NA, intercept = TRUE, 
    display = 0, eps = 0)

Arguments

ttf

Survival times.

tf

Censoring indicator (1 = event, 0 = censored).

Z

Matrix of predictors. Factors are coded with levels from 1 to j.

fact

Specify columns in Z that correspond to unordered factors.

ordfact

Specify columns in Z that correspond to ordered factors.

ordering

intercept

If TRUE, an intercept (= column of all 1's) is added to the design matrix.

display

If display == 1 progress of the algorithm is output.

eps

Quantity to which the criterion in the Basic Procedure 2 in Duembgen et al. (2007) is compared.

Details

For a detailed description of the problem and the algorithm we refer to Rufibach (2010).

Value

L

Value of the criterion function at the maximum.

beta

Computed regression coefficients.

A

Set A of active constraints.

design.matrix

Design matrix that was generated.

Author(s)

Kaspar Rufibach (maintainer)
kaspar.rufibach@gmail.com
http://www.kasparrufibach.ch

References

Rufibach, K. (2010). An Active Set Algorithm to Estimate Parameters in Generalized Linear Models with Ordered Predictors. Comput. Statist. Data Anal., 54, 1442-1456.

Examples


## ========================================================
## Artificial data is used to illustrate Cox-regression.
## ========================================================

## --------------------------------------------------------
## initialization
## --------------------------------------------------------
set.seed(1977)
n <- 500
Z <- NULL
intercept <- FALSE

## --------------------------------------------------------
## quantitative variables
## --------------------------------------------------------
n.q <- 2
if (n.q > 0){for (i in 1:n.q){Z <- cbind(Z, rnorm(n, rgamma(2, 2, 1)))}}

## --------------------------------------------------------
## unordered factors
## --------------------------------------------------------
un.levels <- c(8, 2)[2]
for (i in 1:length(un.levels)){Z <- cbind(Z, sample(round(runif(n, 0, 
    un.levels[i] - 1)) + 1))}
fact <- n.q + 1:length(un.levels)

## --------------------------------------------------------
## ordered factors
## --------------------------------------------------------
levels <- c(4, 5, 10)
for (i in 1:length(levels)){Z <- cbind(Z, sample(round(runif(n, 0, 
    levels[i] - 1)) + 1))}
ordfact <- n.q + length(un.levels) + 1:length(levels)

## --------------------------------------------------------
## generate response
## --------------------------------------------------------
ttf <- rexp(n)
tf <- round(runif(n))

## --------------------------------------------------------
## generate design matrix
## --------------------------------------------------------
Y <- prepareData(Z, fact, ordfact, ordering = NA, intercept)$Y

## --------------------------------------------------------
## compute estimates
## --------------------------------------------------------
res1 <- eha::coxreg.fit(Y, Surv(ttf, tf), max.survs = length(tf), 
    strats = rep(1, length(tf)))$coefficients
res2 <- ordFacRegCox(ttf, tf, Z, fact, ordfact, ordering = NA, 
    intercept = intercept, display = 1, eps = 0)
b1 <- matrix(res1, ncol = 1)
g1 <- coxDeriv(b1, ttf, tf, Y)$dL
b2 <- res2$beta
g2 <- coxDeriv(b2, ttf, tf, Y)$dL
Ls <- c(coxLoglik(b1, ttf, tf, Y)$L, res2$L)
names(Ls) <- c("MLE", "ordFact") 
disp <- cbind(1:length(b1), round(cbind(b1, g1, cumsum(g1)), 4), 
    round(cbind(b2, g2, cumsum(g2)), 4))

## --------------------------------------------------------
## display results
## --------------------------------------------------------
disp
Ls

Prepare input data to be used in active set algorithm

Description

This function takes a matrix consisting of quantitative variables, unordered, and ordered factors and generates the corresponding matrix of dummy variables, and some further quantities that are used by the active set algorithm in ordFacReg and ordFacRegCox.

Usage

prepareData(Z, fact = NA, ordfact, ordering = NA, intercept = TRUE)

Arguments

Z

Matrix with quantitative variables in the first c columns, unordered factors in the next columns, and finally unordered factors. The latter two need to have levels from 1 to j.

fact

Specify columns in Z that correspond to unordered factors.

ordfact

Specify columns in Z that correspond to ordered factors.

ordering

intercept

If TRUE, an intercept (= column of all 1's) is added to the design matrix.

Value

Quantities that are used by the active set algorithm. The names of the objects roughly correspond to those in Rufibach (2010).

Author(s)

Kaspar Rufibach (maintainer)
kaspar.rufibach@gmail.com
http://www.kasparrufibach.ch

References

Rufibach, K. (2010). An Active Set Algorithm to Estimate Parameters in Generalized Linear Models with Ordered Predictors. Comput. Statist. Data Anal., 54, 1442-1456.

Least Squares, Logistic, and Cox-Regression with Ordered Predictors

Description

Details

Author(s)

References

See Also

Internal functions for ordered factor regression functions

Description

Details

Author(s)

References

See Also

Compute least squares or logistic regression for ordered predictors

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

Compute Cox-regression for ordered predictors

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

Prepare input data to be used in active set algorithm

Description

Usage

Arguments

Value

Author(s)

References

See Also