Package {divoRce}

Title:	Diagnosing Separation Phenomena in Latent Polyhedral Categorical Response Models
Version:	1.0-2
Maintainer:	Thomas Rusch <thomas.rusch@wu.ac.at>
Description:	Utilities for checking and diagnosing separation phenomena (complete separation, quasi-complete separation, overlap) for latent polyhedral categorical response models including binary, nominal and ordinal data models with link construction as baseline-category, adjacent-category, cumulative, sequential (continuation-ratio), ordered stereotype and arbitrary link error distribution (including logit, probit, cauchit, cloglog, loglog, log amongst others) based on structure vectors as described in Sablica, Hornik, Rusch (2026) <doi:10.48550/arXiv.2610.08100> and Rusch, Sablica, Hornik (2026) <doi:10.48550/arXiv.2610.09951>. The package functionality includes a check for separation and a check for overlap with a linear program, a quick check for overlap, a sequential and a parallel check for overlap based on subsamples, detailed separation diagnostics such as identification of columns in the design matrix/structure vector matrix that lead to separation, identification of design matrix/structure vector matrix rows that lead to separation, the dimension of the recession cone and the structure vectors that are linearities. Calculations can be done with package 'rcdd' to employ arbitrary precision and various other linear program solvers can also be used via package 'ROI'. Implemented checks can be done before model fitting based on outcome and design matrix or structure vector matrix or via formula (pre-fit), or after model fitting for objects of class 'glm', 'multinom', 'polr', 'osm', 'clm', 'bracl', 'brmultinom'. Wrappers for other classes can be easily constructed by third parties via pre-fit functions.
Depends:	R (≥ 3.5.0)
Imports:	rcdd
Suggests:	clustord, detectseparation, MASS, nnet, ordinal, ROI
License:	GPL-2 | GPL-3
LazyData:	true
Encoding:	UTF-8
Config/roxygen2/version:	8.1.0
NeedsCompilation:	no
Packaged:	2026-10-08 11:38:25 UTC; trusch
Author:	Thomas Rusch [aut, cre], Lukas Sablica [aut], Kurt Hornik [aut]
Repository:	CRAN
Date/Publication:	2026-10-18 16:30:14 UTC

Untabeled alligator food choice data

Description

Untabeled alligator food choice data

Usage

data(Alligators)

Format

A data frame with 219 rows corresponding to captured alligator and 5 variables:

* 'foodchoice': primary food type, in volume, found in an alligator’s stomach, with levels 'fish', 'invertebrate','reptile', 'bird', 'other' * 'lake': lake of capture with levels 'Hancock', 'Oklawaha', 'Trafford', 'George'. * 'sex': sex of the alligator with levels 'Male' and 'Female' * 'size': size of the alligator with levels '<=2.3' meters long and '>2.3' meters long * 'freq': number of alligators for each foodchoice, lake, gender and size combination

Source

The alligators data set is analyzed in Agresti (2002, Subsection 7.1.2). These data are an untabeled version.

References

Agresti A (2002). *Categorical Data Analysis*. Wiley Series in Probability and Statistics. Wiley.

Willingness to Share Health Data of Drexler (2026)

Description

These data are a snapshot from a study on willingness to share health data in Austria. We look at the willingness to share data with a social health insurance provider for people with chronic conditions. The data is a random sample of 300 complete cases from the original 1260 observations and fully anonymized. We did the following data preparation steps over the original data: We reversed the polarity of the item variables by mapping the "worst" category to the lowest number and we also combined the two highest trust categories to trust category 4.

Usage

data(HDSS)

Format

A 300 x 5 data frame:

ID

An ID (not the original one from the study).

WSTSSHI

Item: Willingness to share personal health information with the social health insurance provider. An ordered factor with 1 indicating lowest willingness and 4 highest willingness.

knowledge

Item: Knowledge about health data. An ordinal scale from 1 to 4 with 1 being the lowest knowledge and 4 highest knowledge.

chronic

Number of chronic conditions (1 meaning "yes, one" 2 meaning "yes, many" and 3 meaning "none").

trustSHI

Item: Trust in the social health insurance provider. An ordinal scale from 1 to 4 with 1 being the lowest trust and 4 highest trust.

gender

A person's gender identification with levels "f" for female, "m" for male and "x" for neither.

Source

Drexler, S. (2026). Patient-reported and register-based indicators for system-wide primary care quality evaluation: An analysis of applicability, benefits, limitations, and mitigation strategies. Phd thesis, WU Vienna University of Economics and Business, Vienna, Austria.

Psychiatric Cases Classification based on GHQ of Silvapulle (1981)

Description

These data are from a psychiatric study of for 120 patients on the relation between the value of the score on the 12-item General Health Questionnaire (GHQ) and classification as a psychiatric case ("yes" or "no"). The patients attended as general practitioner's surgery and were administered the GHQ, resulting in a theoretical score between 0 and 12 (there were no cases or non-cases with GHQ scores of 11 or 12). Subsequently the patinets were given a full psychiatric examination by a psychiatrist who did not know the patient's GHQ score. The patient was classified by the psychiatrist as either a clinical case requiring psychiatric treatment (case="yes"), or as non-clinial (case="no"). The biological sex of the patients was also recorded.

Usage

data(Silvapulle)

Format

A 120 x 3 data frame:

sex

A factor with levels 'male' and 'female'.

ghq

The GHQ score on a scale from 0 to 12 (numeric).

case

Diagnosis as a clinical case ('yes') or not ('no').

Source

Silvapulle, M. J. (1981), "On the existence of maximum likelihood estimators for the binomial response model", J. Roy. Statist. Soc. B., 43, 310-313.

Check overlap

Description

This function checks for overlap by calling the appropriate low-level functions. It can be run with the linear program ('quick = FALSE', default), linear program 2 ('quick = TRUE'), on sequential subsets of data ('sequential = TRUE') or via multicore parallelization ('parallel = TRUE').

Usage

check_overlap(object, ...)

## Default S3 method:
check_overlap(object, ...)

## S3 method for class 'factor'
check_overlap(
  object,
  X,
  rational = FALSE,
  quick = FALSE,
  sequential = FALSE,
  parallel = FALSE,
  backend = c("rcdd", "ROI"),
  solver = NULL,
  nc = NULL,
  nss = NULL,
  ...
)

## S3 method for class 'logical'
check_overlap(
  object,
  X,
  rational = FALSE,
  quick = FALSE,
  sequential = FALSE,
  parallel = FALSE,
  backend = c("rcdd", "ROI"),
  solver = NULL,
  nc = NULL,
  nss = NULL,
  ...
)

## S3 method for class 'numeric'
check_overlap(
  object,
  X,
  rational = FALSE,
  quick = FALSE,
  sequential = FALSE,
  parallel = FALSE,
  backend = c("rcdd", "ROI"),
  solver = NULL,
  nc = NULL,
  nss = NULL,
  ...
)

## S3 method for class 'integer'
check_overlap(
  object,
  X,
  rational = FALSE,
  quick = FALSE,
  sequential = FALSE,
  parallel = FALSE,
  backend = c("rcdd", "ROI"),
  solver = NULL,
  nc = NULL,
  nss = NULL,
  ...
)

## S3 method for class 'character'
check_overlap(
  object,
  X,
  rational = FALSE,
  quick = FALSE,
  sequential = FALSE,
  parallel = FALSE,
  backend = c("rcdd", "ROI"),
  solver = NULL,
  nc = NULL,
  nss = NULL,
  ...
)

## S3 method for class 'matrix'
check_overlap(
  object,
  rational = FALSE,
  quick = FALSE,
  sequential = FALSE,
  parallel = FALSE,
  backend = c("rcdd", "ROI"),
  solver = NULL,
  nc = NULL,
  nss = NULL,
  ...
)

## S3 method for class 'formula'
check_overlap(
  object,
  data,
  model = NULL,
  rational = FALSE,
  contrasts = NULL,
  quick = FALSE,
  sequential = FALSE,
  parallel = FALSE,
  backend = c("rcdd", "ROI"),
  solver = NULL,
  ...
)

## S3 method for class 'osm'
check_overlap(
  object,
  rational = FALSE,
  backend = c("rcdd", "ROI"),
  solver = NULL,
  quick = FALSE,
  parallel = FALSE,
  sequential = FALSE,
  nss = NULL,
  nc = NULL,
  ...
)

## S3 method for class 'clm'
check_overlap(
  object,
  rational = FALSE,
  backend = c("rcdd", "ROI"),
  solver = NULL,
  quick = FALSE,
  parallel = FALSE,
  sequential = FALSE,
  nss = NULL,
  nc = NULL,
  ...
)

## S3 method for class 'polr'
check_overlap(
  object,
  rational = FALSE,
  backend = c("rcdd", "ROI"),
  solver = NULL,
  quick = FALSE,
  parallel = FALSE,
  sequential = FALSE,
  nss = NULL,
  nc = NULL,
  ...
)

## S3 method for class 'multinom'
check_overlap(
  object,
  rational = FALSE,
  backend = c("rcdd", "ROI"),
  solver = NULL,
  quick = FALSE,
  parallel = FALSE,
  sequential = FALSE,
  nss = NULL,
  nc = NULL,
  ...
)

## S3 method for class 'glm'
check_overlap(
  object,
  rational = FALSE,
  backend = c("rcdd", "ROI"),
  solver = NULL,
  quick = FALSE,
  parallel = FALSE,
  sequential = FALSE,
  nss = NULL,
  nc = NULL,
  ...
)

## S3 method for class 'bracl'
check_overlap(
  object,
  rational = FALSE,
  backend = c("rcdd", "ROI"),
  solver = NULL,
  quick = FALSE,
  parallel = FALSE,
  sequential = FALSE,
  nss = NULL,
  nc = NULL,
  ...
)

## S3 method for class 'brmultinom'
check_overlap(
  object,
  rational = FALSE,
  backend = c("rcdd", "ROI"),
  solver = NULL,
  quick = FALSE,
  parallel = parallel,
  sequential = sequential,
  nss = nss,
  nc = nc,
  ...
)

Arguments

Details

check_overlap is an S3 generic function. For developers: If a method should be provided for the generic, it is best to have that method create a matrix of structure vectors S and use the low-level function check_overlap_worker with it.

The formula method is for standard data frames and formulas that work the same way as when used with glm. It does not support extended formulas, and may not work for functions that do formula processing differently.

For a data frame or matrix given as rational numbers in the rcdd definition, this is recognized but the formula does not get expanded and is taken literally. Consequently:

• variables in formula must match exactly with the column names in data;

• factors need to be converted to dummies beforehand (which would not be possible in the rational format in any other way anyway).

Value

A logical, 'TRUE' is overlap is detected.

Examples

 # pre fit

## Binary data
data(csepdat1)
outc<-csepdat1$y
desma<-cbind("(Intercept)"=1,csepdat1[,2:ncol(csepdat1)])
check_overlap(outc, X = desma, model = "b")

# Nominal data 
# Baseline-category link
data(qcsepdatm)
check_overlap(y ~ x1 + x2, data = qcsepdatm, model = "bcl")

# Ordinal data
data(qcsepdato)
yo<-qcsepdato$y
Xo<-qcsepdato[,2:ncol(qcsepdato)]

# Sequential link
check_overlap(yo, Xo, model = "sl", rational = TRUE)

# Ordered stereotype
check_overlap(yo, Xo, model = "os", sequential = TRUE, nss =2)

# Adjacent-category link
check_overlap(yo, Xo, model= "acl", parallel = TRUE, nc = 1)

# Cumulative link
check_overlap(yo, Xo, model = "cl", quick = TRUE)


# post fit
m1 <- stats::glm(y~x1+x2,data=csepdat1,family=binomial())
check_overlap(m1)

Check separation

Description

General separation check function.

Usage

check_separation(object, ...)

## Default S3 method:
check_separation(object, ...)

## S3 method for class 'factor'
check_separation(
  object,
  X,
  model = NULL,
  rational = FALSE,
  quick = FALSE,
  backend = c("rcdd", "ROI"),
  solver = NULL,
  ...
)

## S3 method for class 'logical'
check_separation(
  object,
  X,
  model = NULL,
  rational = FALSE,
  quick = FALSE,
  backend = c("rcdd", "ROI"),
  solver = NULL,
  ...
)

## S3 method for class 'numeric'
check_separation(
  object,
  X,
  model = NULL,
  rational = FALSE,
  quick = FALSE,
  backend = c("rcdd", "ROI"),
  solver = NULL,
  ...
)

## S3 method for class 'integer'
check_separation(
  object,
  X,
  model = NULL,
  rational = FALSE,
  quick = FALSE,
  backend = c("rcdd", "ROI"),
  solver = NULL,
  ...
)

## S3 method for class 'character'
check_separation(
  object,
  X,
  model = NULL,
  rational = FALSE,
  quick = FALSE,
  backend = c("rcdd", "ROI"),
  solver = NULL,
  ...
)

## S3 method for class 'matrix'
check_separation(
  object,
  rational = FALSE,
  quick = FALSE,
  backend = c("rcdd", "ROI"),
  solver = NULL,
  ...
)

## S3 method for class 'formula'
check_separation(
  object,
  data,
  model = NULL,
  rational = FALSE,
  quick = FALSE,
  contrasts = NULL,
  backend = c("rcdd", "ROI"),
  solver = NULL,
  ...
)

## S3 method for class 'osm'
check_separation(
  object,
  rational = FALSE,
  backend = c("rcdd", "ROI"),
  solver = NULL,
  quick = FALSE,
  ...
)

## S3 method for class 'clm'
check_separation(
  object,
  rational = FALSE,
  backend = c("rcdd", "ROI"),
  solver = NULL,
  quick = FALSE,
  ...
)

## S3 method for class 'polr'
check_separation(
  object,
  rational = FALSE,
  backend = c("rcdd", "ROI"),
  solver = NULL,
  quick = FALSE,
  ...
)

## S3 method for class 'multinom'
check_separation(
  object,
  rational = FALSE,
  backend = c("rcdd", "ROI"),
  solver = NULL,
  quick = FALSE,
  ...
)

## S3 method for class 'glm'
check_separation(
  object,
  rational = FALSE,
  backend = c("rcdd", "ROI"),
  solver = NULL,
  quick = FALSE,
  ...
)

## S3 method for class 'bracl'
check_separation(
  object,
  rational = FALSE,
  backend = c("rcdd", "ROI"),
  solver = NULL,
  quick = FALSE,
  ...
)

## S3 method for class 'brmultinom'
check_separation(
  object,
  rational = FALSE,
  backend = c("rcdd", "ROI"),
  solver = NULL,
  quick = FALSE,
  ...
)

Arguments

Details

This function checks for (quasi-)complete separation by calling the appropriate low-level functions either with linear program 1 ('quick = FALSE'; default') or linear program 2 ('quick = TRUE').

check_separation is an S3 generic function.

For developers: If a method should be provided for the generic, it is best to have that method create a matrix of structure vectors S and use the generic with the matrix.

The formula method is for standard data frames and formulas that work the same way as when used with glm. It does not support extended formulas, and may not work for functions that do formula processing differently.

For a data frame or matrix given as rational numbers in the rcdd definition, this is recognized but the formula does not get expanded and is taken literally. Consequently:

• variables in formula must match exactly with the column names in data;

• factors need to be converted to dummies beforehand (which would not be possible in the rational format in any other way anyway).

Value

A logical, 'TRUE' is separation is detected.

Examples

 # pre fit

## Binary data
data(csepdat1)
outc<-csepdat1$y
desma<-cbind("(Intercept)"=1,csepdat1[,2:ncol(csepdat1)])
check_separation(outc, X = desma, model = "b")

# Nominal data 
# Baseline-category link
data(qcsepdatm)
y<-qcsepdatm$y
X<-cbind(1,qcsepdatm[,2:ncol(qcsepdatm)])
check_separation(y, X = X, model = "bcl")

# Ordinal data
data(qcsepdato)
yo<-qcsepdato$y
Xo<-qcsepdato[,2:ncol(qcsepdato)]

# Sequential link
check_separation(yo, Xo, model = "sl")

# Ordered stereotype
check_separation(yo, Xo, model = "os")

# Adjacent-category link
check_separation(yo, Xo, model= "acl")

# Cumulative link
check_separation(yo, Xo, model = "cl")


# post fit
m1 <- stats::glm(y~x1+x2,data=csepdat1,family=binomial())
check_separation(m1)

Toy data set with complete separation

Description

Toy data with binary reponse that exhibit complete separation.

Usage

data(csepdat1)

Format

A 10 x 3 data frame:

y

Binary response (factor)

x1

Numeric predictor

x2

Numeric predictor

Toy data set with complete separation

Description

Toy data with binary reponse that exhibit complete separation.

Usage

data(csepdat2)

Format

A 10 x 3 data frame:

y

Binary response (factor)

x1

Numeric predictor

x2

Numeric predictor

Toy data set with complete separation

Description

Toy data with multinomial response that exhibit complete separation.

Usage

data(csepdatm)

Format

A 10 x 3 data frame:

y

Categorical response (factor) with 3 levels

x1

Numeric predictor

x2

Numeric predictor

Toy data set with complete separation

Description

Toy data with ordinal response that exhibit complete separation.

Usage

data(csepdato)

Format

A 10 x 3 data frame:

y

Ordered response with 3 levels

x1

Numeric predictor

x2

Numeric predictor

Detailed separation diagnostic for all categorical outcomes.

Description

This function checks whether there is (quasi-) complete separation, which type if any, gives the dimension of the recession cone, lists the number of columns in the design matrix that give rise to the separation as well as the columns names and lists the rows in X/S for which we have separation.

Usage

diagnose_separation(object, ...)

## Default S3 method:
diagnose_separation(object, ...)

## S3 method for class 'factor'
diagnose_separation(
  object,
  X,
  model = NULL,
  rational = FALSE,
  backend = c("rcdd", "ROI"),
  solver = NULL,
  ...
)

## S3 method for class 'character'
diagnose_separation(
  object,
  X,
  model = NULL,
  rational = FALSE,
  backend = c("rcdd", "ROI"),
  solver = NULL,
  ...
)

## S3 method for class 'logical'
diagnose_separation(
  object,
  X,
  model = NULL,
  rational = FALSE,
  backend = c("rcdd", "ROI"),
  solver = NULL,
  ...
)

## S3 method for class 'numeric'
diagnose_separation(
  object,
  X,
  model = NULL,
  rational = FALSE,
  backend = c("rcdd", "ROI"),
  solver = NULL,
  ...
)

## S3 method for class 'integer'
diagnose_separation(
  object,
  X,
  model = NULL,
  rational = FALSE,
  backend = c("rcdd", "ROI"),
  solver = NULL,
  ...
)

## S3 method for class 'matrix'
diagnose_separation(
  object,
  rational = FALSE,
  backend = c("rcdd", "ROI"),
  solver = NULL,
  ...
)

## S3 method for class 'formula'
diagnose_separation(
  object,
  data,
  model = NULL,
  rational = FALSE,
  contrasts = NULL,
  backend = c("rcdd", "ROI"),
  solver = NULL,
  ...
)

## S3 method for class 'osm'
diagnose_separation(
  object,
  rational = FALSE,
  backend = c("rcdd", "ROI"),
  solver = NULL,
  ...
)

## S3 method for class 'clm'
diagnose_separation(
  object,
  rational = FALSE,
  backend = c("rcdd", "ROI"),
  solver = NULL,
  ...
)

## S3 method for class 'polr'
diagnose_separation(
  object,
  rational = FALSE,
  backend = c("rcdd", "ROI"),
  solver = NULL,
  ...
)

## S3 method for class 'multinom'
diagnose_separation(
  object,
  rational = FALSE,
  backend = c("rcdd", "ROI"),
  solver = NULL,
  ...
)

## S3 method for class 'glm'
diagnose_separation(
  object,
  rational = FALSE,
  backend = c("rcdd", "ROI"),
  solver = NULL,
  ...
)

## S3 method for class 'bracl'
diagnose_separation(
  object,
  rational = FALSE,
  backend = c("rcdd", "ROI"),
  solver = NULL,
  ...
)

## S3 method for class 'brmultinom'
diagnose_separation(
  object,
  rational = FALSE,
  backend = c("rcdd", "ROI"),
  solver = NULL,
  ...
)

Arguments

Details

diagnose_separation is an S3 generic function.

For developers: If a method should be provided for the generic, it is best to have that method create a matrix of structure vectors S and use the generic with the matrix.

The formula method is for standard data frames and formulas that work the same way as when used with glm. It does not support extended formulas, and may not work for functions that do formula processing differently.

For a data frame or matrix given as rational numbers in the rcdd definition, this is recognized but the formula does not get expanded and is taken literally. Consequently:

• variables in formula must match exactly with the column names in data;

• factors need to be converted to dummies beforehand (which would not be possible in the rational format in any other way anyway).

Value

an object of class 'sepmod' that is a list with the components:

• separation boolean whether there is separation ('TRUE' means separation)

• septype which type of separation (or not). A string of either "Overlap", "Quasi-Complete Separation" or "Complete Separation".

• reccdim dimension of recession cone

• offrows rows associated with separation

• nr.offcols number of columns of the design matrix that have separation

• offcols columns associated with separation

For model = "sl" an object of class 'sepmod_sl'. It is a list or the above lists with the elements corresponding to each category.

Examples

data(qcsepdatm)

## Binary data
data(csepdat1)
outc<-csepdat1$y
desma<-cbind("(Intercept)"=1,csepdat1[,2:ncol(csepdat1)])
c1<- diagnose_separation(outc, X = desma, model = "b")
print(c1)
print(c1, "full")

# Nominal data 
# Baseline-category link
data(qcsepdatm)
y<-qcsepdatm$y
X<-cbind(1,qcsepdatm[,2:ncol(qcsepdatm)])
diagnose_separation(y, X = X, model = "bcl")

# Ordinal data
data(qcsepdato)
yo<-qcsepdato$y
Xo<-qcsepdato[,2:ncol(qcsepdato)]

# Sequential link
diagnose_separation(yo, Xo, model = "sl")

# Ordered stereotype
diagnose_separation(yo, Xo, model = "os")

# Adjacent-category link
diagnose_separation(yo, Xo, model= "acl")

# Cumulative link
diagnose_separation(yo, Xo, model = "cl")

#post fit
if (require('nnet')) {
m1 <- nnet::multinom(y ~ x1 + x2, data = qcsepdatm)
diagnose_separation(m1)
}

Adapted Iris Dataset

Description

This dataset is an adaptation of the famous Iris dataset. The original dataset contains measurements of iris flowers from three different species. In this adaptation, the dataset has been modified to create an ordinal response variable based on petal length, categorizing it into three groups: Low, Medium, and High, so that it shows separation. The dataset consists of five predictor variables and one ordinal response variable.

Usage

data(iris2)

Format

A data frame with 150 rows and 6 coumns/variables:

y

An ordered factor representing the petal length category:

• Low: Petal length less than 2.5

• Medium: Petal length between 2.5 and 5.0

• High: Petal length greater than 5.0

Sepal.Length

Numeric. The length of the sepal in centimeters.

Sepal.Width

Numeric. The width of the sepal in centimeters.

Petal.Length

Numeric. The length of the petal in centimeters.

Petal.Width

Numeric. The width of the petal in centimeters.

Species

Categorical. The species of Iris.

Source

The original Iris dataset is available as data(iris) in R

Examples

# View the structure of the dataset
str(iris2)

Linearities

Description

This function calculates the linearities in the negative structure vector matrix X*, so the row vectors for which there is no separation. If this is an empty set or of length 0, then we have overlap.

Usage

linearities(
  y,
  X,
  S,
  rational = FALSE,
  model = c("b", "bcl", "acl", "os", "sl", "cl")
)

Arguments

Value

a list with elements $lins which lists the row vectors that are linearities for any category and $index which gives the row index of the linearities. If there is complete separation they are both empty set. If their length/row dimension is number of categories*dim(X)[1], there is overlap. Anything in between is quasi-complete separation.

This function is meant to set up a response variable and a design matrix from a formula-data combination for the pre-fit separation check functions.

Description

This function is meant to set up a response variable and a design matrix from a formula-data combination for the pre-fit separation check functions.

Usage

make_yx(formula, data, contrasts = NULL)

Arguments

Details

For standard data frames and formulas this function returns a list with the first element being the response variable (as specified by the left hand side of the formula) and the second element being a design matrix corresponding to the right hand side of the formula and the given optional contrasts. The design matrix is created in exactly the same way as in glm. For a data frame/matrix given as rational numbers in the rcdd definition, it returns a list with the first element being the response variable in rational format (as specified by the left hand side of the formula) and the second element being the character matrix in rational format corresponding to the right hand side of the formula. Note that in the latter the formula does not get expanded and is taken literally, so e.g. variables in formula must match exactly with the column names in data, or factors need to be converted to dummies before that (wouldn't be possible in the rational format in any other way anyway).

Value

A list with two elements, $y being the response variable (as specified by the left hand side of the formula) and the second element $X being a design matrix corresponding to the right hand side of the formula.

Examples

## standard data frame
data(nsduh2019)
frml <- her_lifetime ~ alc_agefirst + demog_age_cat6 + demog_sex
mk <- make_yx(frml,nsduh2019)
str(mk)

## rational structure
yr <- as.character(as.numeric(mk$y))
Xr <- apply(mk$X,2,as.character)
datr1 <- data.frame(yr,Xr) #data frame with rational data
frmlr1 <- yr~X.Intercept.+ alc_agefirst + demog_sexFemale
mkr1 <- make_yx(frmlr1,datr1)
str(mkr1)

datr2 <- cbind(yr,Xr) #character matrix with rational data  
frmlr2 <- yr~(Intercept) + alc_agefirst #note the intercept column is labeled differently here 
mkr2 <- make_yx(frmlr2,datr2)
str(mkr2)

A snapshot of the NSDUH 2019 data

Description

These data are from Nahhas (2024) to illustrate quasi-complete separation in his book Introduction to Regression Methods for Public Health Using R.

Usage

data(nsduh2019)

Format

A 843 x 4 data frame:

her_lifetime

A binary factor of heroin consumption in a person's lifetime ('No' and 'Yes').

alc_agefirst

Age at first use of alcohol.

demog_age_cat6

Current age category of the person.

demog_sex

Sex of the person "Male" or ""Female".

Source

Nahhas R. (2024). Introduction to Regression Methods for Public Health Using R. Chapman & Hall.

Voters in Ohio

Description

This is a cleaned-up and anonymized random snapshot (N=6544) of the data set used in Rusch, Lee, Hornik, Jank and Zeileis (2013).

Usage

data(ohiovoters)

Format

A 6544 x 83 data frame including: * gender : Factor w/ 2 levels "F" for female,"M" for male * partyAffiliation : Factor w/ 3 levels "D" for Democrat,"R" for Republican,"U" for unaffiliated/independent * partyMix : Factor w/ 8 levels "unknown" for unkown,"allR" for all are Republican, "allD" all are Democr#' ats, "noneRorD" none are Republican or Democrat, "noneD" none are Democrat, "onlyRorD" only #' Republican or Democrat, "noneR" none are Republican, "allRorDorLegal" all are either Republi#' can or Democrats or any other legal value (e.g., other party affiliation; describes the hous#' ehold composition in terms of party affiliation * householdHead : Factor w/ 2 levels "H" for household head,"M" for household member * householdRank : Factor w/ 3 levels "3+" < "2" < "1" rank in the household * income : Factor w/ 12 levels Level of estimated household income from census or estimated using demog#' raphic and census data. "A" - Under 15,000; "B" - 15,000-24,999; "C" - 25,000-34,999; "D" #' - 35,000-49,999; "E"- 50,000-74,999; "F" - 75,000-99,999; "G" - 100,000-124,999; "H" - 125,0#' 00-149,999; "I" - 150,000-174,999; "J" - 175,000-199,999; "K" - 200,000-249,999; "L"- 250,00#' 0+ * homeOwner : Factor w/ 5 levels "1" renter,"A" renter,"B" probable renter,"C" probable homeowner,"D" home#' owner (note: it is not clear how 1 is different from A) * mailOrder : Factor w/ 2 levels "0" no ,"1" yes; indicates mail order buyer * compOwner : Factor w/ 2 levels "0"no ,"1" yes; owns a computer * educationLevel : Factor w/ 7 levels "A","B","C","D","E","F","G" after ISCED (http://www.unesco.org/education/#' information/nfsunesco/doc/isced_1997.htm; A=0 and G=6) * donateXXX : Factor w/ 2 levels "0" no,"1" yes, donated to cause XXX (arts, politics, children, animals, hea#' lth, poverty, environment, religion) * fec_XX_YY : Factor w/ 2 levels "0" for no,"1" for yes; federal contributor in years XX and YY * dontPhone : Factor w/ 3 levels "N" for no ,"U" for unknown,"Y" for yes; person is on the federal do not call list * ageD : age in days * cnt : number of attended elections * genXX : Factor w/ 2 levels "0" for no,"1" for yes; attended general elections in year XX * priXX : Factor w/ 2 levels "0" for no,"1" for yes; attended primary elections in year XX * othXX : Factor w/ 2 levels "0" for no,"1" for yes; attended other elections in year XX * pppXX : Factor w/ 2 levels "0" for no,"1" for yes; attended presidential primary elections in year XX (is the priXX variable for years with presidential elections) * cntEligible : Number of election the person was eligible to vote * percentAttended : cnt/cntEligible * ageY : age in years (ageD/365.25) * pProb : predicted probabilities from the y~s|e model * pNodes : predicted node number * ageC : Factor w/ 4 levels; age category * incC : Factor w/ 3 levels "< 35k" less than 35,000 USD a year, "35k-75k" 35,001 to 75,000 USD per y#' ear ">75k more than 75,000 USD per year"; income categories * eduC : Factor w/ 3 levels "primary" primary education,"secondary" secondary education,"postsec" pos#' tsecondary eucation; education categories (collapsed educationLevel) * pSegs : Factor w/ 7 levels; predicted segment number

Source

Rusch, Lee, Hornik, Jank, Zeileis (2013). Influencing elections with statistics: Targeting voters with logistic regression trees. The Annals of Applied Statistics, 7(3), pp. 1612-1639. doi: 10.1214/13-AOAS648

Toy data set with overlap.

Description

Toy data with binary response that exhibit overlap and thus existence of MLE.

Usage

data(ovldat1)

Format

A 10 x 3 data frame:

y

Binary response (factor)

x1

Numeric predictor

x2

Numeric predictor

Toy data set with overlap.

Description

Toy data with binary response that exhibit overlap and existence of MLE.

Usage

data(ovldat2)

Format

A 10 x 3 data frame:

y

Binary response (factor)

x1

Numeric predictor

x2

Numeric predictor

Toy data set with overlap.

Description

Toy data with categorical response that exhibit overlap and thus existence of MLE.

Usage

data(ovldatm)

Format

A 10 x 3 data frame:

y

Categorical response (factor) with 3 levels

x1

Numeric predictor

x2

Numeric predictor

Toy data set with overlap.

Description

Toy data with ordered response that exhibit overlap.

Usage

data(ovldato)

Format

A 10 x 3 data frame:

y

Ordered response with 3 levels

x1

Numeric predictor

x2

Numeric predictor

Print method for sepmod classes

Description

Print method for sepmod classes

Usage

## S3 method for class 'sepmod'
print(x, info = c("minimal", "full"), ...)

Arguments

Value

No return value, called for side effects. Returns the input object 'x' invisibly.

Print method for sepmod_sl classes

Description

Print method for sepmod_sl classes

Usage

## S3 method for class 'sepmod_sl'
print(x, info = c("minimal", "full"), ...)

Arguments

Value

No return value, called for side effects. Returns the input object 'x' invisibly.

Toy data set with quasi-complete separation

Description

Toy data with binary reponse that exhibit quasi-complete separation.

Usage

data(qcsepdat1)

Format

A 10 x 3 data frame:

y

Binary response (factor)

x1

Numeric predictor

x2

Numeric predictor

Toy data set with quasi-complete separation

Description

Toy data with binary reponse that exhibit quasi-complete separation.

Usage

data(qcsepdat2)

Format

A 10 x 3 data frame:

y

Binary response (factor)

x1

Numeric predictor

x2

Numeric predictor

Toy data set with quasi-complete separation

Description

Toy data with categorical response that exhibit quasi-complete separation.

Usage

data(qcsepdatm)

Format

A 10 x 3 data frame:

y

Categorical response (factor) with 3 levels

x1

Numeric predictor

x2

Numeric predictor

Toy data set with quasi-complete separation

Description

Toy data with ordered response that exhibit quasi-complete separation.

Usage

data(qcsepdato)

Format

A 10 x 3 data frame:

y

Ordered response with 3 levels

x1

Numeric predictor

x2

Numeric predictor

Recession cone calculation

Description

This function calculates the dimension of the recession cone and returns the recession cone.

Usage

recession_cone(object, ...)

## Default S3 method:
recession_cone(object, ...)

## S3 method for class 'factor'
recession_cone(object, X, model = NULL, rational = FALSE, ...)

## S3 method for class 'character'
recession_cone(object, X, model = NULL, rational = FALSE, ...)

## S3 method for class 'logical'
recession_cone(object, X, model = NULL, rational = FALSE, ...)

## S3 method for class 'numeric'
recession_cone(object, X, model = NULL, rational = FALSE, ...)

## S3 method for class 'integer'
recession_cone(object, X, model = NULL, rational = FALSE, ...)

## S3 method for class 'matrix'
recession_cone(object, rational = FALSE, ...)

## S3 method for class 'formula'
recession_cone(
  object,
  data,
  model = NULL,
  rational = FALSE,
  contrasts = NULL,
  ...
)

## S3 method for class 'osm'
recession_cone(object, rational = FALSE, ...)

## S3 method for class 'clm'
recession_cone(object, rational = FALSE, ...)

## S3 method for class 'polr'
recession_cone(object, rational = FALSE, ...)

## S3 method for class 'multinom'
recession_cone(object, rational = FALSE, ...)

## S3 method for class 'glm'
recession_cone(object, rational = FALSE, ...)

## S3 method for class 'bracl'
recession_cone(object, rational = FALSE, ...)

## S3 method for class 'brmultinom'
recession_cone(object, rational = FALSE, ...)

Arguments

Details

Note that in case of non full column rank, the 'reccdim' value is the dimension of the recession cone due to separation plus the number of columns that are linear dependent.

The formula method is for standard data frames and formulas that work the same way as when used with glm. It does not support extended formulas, and may not work for functions that do formula processing differently.

For a data frame or matrix given as rational numbers in the rcdd definition, this is recognized but the formula does not get expanded and is taken literally. Consequently:

• variables in formula must match exactly with the column names in data;

• factors need to be converted to dummies beforehand (which would not be possible in the rational format in any other way anyway).

Value

A list with the components:

• cone being the recession cone,

• reccdim being the dimensions of the recession cone

• index the row index of the structure vectors that are not linearities.

For model = "sl" 'cone' is the recession cone over all categories, 'reccdim' the dimension of the largest recession cone of any category and 'index' the row index of the structure vectors that are not linearities over all categories.

Examples

## Binary data
data(csepdat1)
outc<-csepdat1$y
desma<-cbind("(Intercept)"=1,csepdat1[,2:ncol(csepdat1)])
recession_cone(outc, X = desma, model = "b")

# Nominal data 
# Baseline-category link
data(qcsepdatm)
y<-qcsepdatm$y
X<-cbind(1,qcsepdatm[,2:ncol(qcsepdatm)])
recession_cone(y, X = X, model = "bcl")

# Ordinal data
data(qcsepdato)
yo<-qcsepdato$y
Xo<-qcsepdato[,2:ncol(qcsepdato)]

# Sequential link
recession_cone(yo, Xo, model = "sl")

# Ordered stereotype
recession_cone(yo, Xo, model = "os")

# Adjacent-category link
recession_cone(yo, Xo, model= "acl")

# Cumulative link
recession_cone(yo, Xo, model = "cl")

# post fit
if (require('ordinal')) {
m1 <- ordinal::clm(y~x1+x2, data = qcsepdato)
recession_cone(m1)
}

Identify separation columns

Description

This function identifies the columns in a design matrix/structure vector matrix that are responsible for separation. It calls lower level functions if given an argument or chooses based on the response type.

Usage

separation_columns(object, ...)

## Default S3 method:
separation_columns(object, ...)

## S3 method for class 'factor'
separation_columns(
  object,
  X,
  model = NULL,
  rational = FALSE,
  backend = c("rcdd", "ROI"),
  solver = NULL,
  ...
)

## S3 method for class 'character'
separation_columns(
  object,
  X,
  model = NULL,
  rational = FALSE,
  backend = c("rcdd", "ROI"),
  solver = NULL,
  ...
)

## S3 method for class 'logical'
separation_columns(
  object,
  X,
  model = NULL,
  rational = FALSE,
  backend = c("rcdd", "ROI"),
  solver = NULL,
  ...
)

## S3 method for class 'numeric'
separation_columns(
  object,
  X,
  model = NULL,
  rational = FALSE,
  backend = c("rcdd", "ROI"),
  solver = NULL,
  ...
)

## S3 method for class 'integer'
separation_columns(
  object,
  X,
  model = NULL,
  rational = FALSE,
  backend = c("rcdd", "ROI"),
  solver = NULL,
  ...
)

## S3 method for class 'matrix'
separation_columns(
  object,
  rational = FALSE,
  backend = c("rcdd", "ROI"),
  solver = NULL,
  ...
)

## S3 method for class 'formula'
separation_columns(
  object,
  data,
  model = NULL,
  rational = FALSE,
  contrasts = NULL,
  backend = c("rcdd", "ROI"),
  solver = NULL,
  ...
)

## S3 method for class 'osm'
separation_columns(
  object,
  rational = FALSE,
  backend = c("rcdd", "ROI"),
  solver = NULL,
  ...
)

## S3 method for class 'clm'
separation_columns(
  object,
  rational = FALSE,
  backend = c("rcdd", "ROI"),
  solver = NULL,
  ...
)

## S3 method for class 'polr'
separation_columns(
  object,
  rational = FALSE,
  backend = c("rcdd", "ROI"),
  solver = NULL,
  ...
)

## S3 method for class 'multinom'
separation_columns(
  object,
  rational = FALSE,
  backend = c("rcdd", "ROI"),
  solver = NULL,
  ...
)

## S3 method for class 'glm'
separation_columns(
  object,
  rational = FALSE,
  backend = c("rcdd", "ROI"),
  solver = NULL,
  ...
)

## S3 method for class 'bracl'
separation_columns(
  object,
  rational = FALSE,
  backend = c("rcdd", "ROI"),
  solver = NULL,
  ...
)

## S3 method for class 'brmultinom'
separation_columns(
  object,
  rational = FALSE,
  backend = c("rcdd", "ROI"),
  solver = NULL,
  ...
)

Arguments

Details

separation_columns is an S3 generic function.

For developers: If a method should be provided for the generic, it is best to have that method create a matrix of structure vectors S and use the generic with the matrix.

The formula method is for standard data frames and formulas that work the same way as when used with glm. It does not support extended formulas, and may not work for functions that do formula processing differently.

For a data frame or matrix given as rational numbers in the rcdd definition, this is recognized but the formula does not get expanded and is taken literally. Consequently:

• variables in formula must match exactly with the column names in data;

• factors need to be converted to dummies beforehand (which would not be possible in the rational format in any other way anyway).

Value

A list with the components:

• ls the solution vector of the linear program

• offcols the names of the columns that show separation

• colnrs the index number of the columns that show separation

• separated a logical vector of whetehr the colum shows separation

For model = "sl" it is a list of these lists for each category.

Examples

#' ## Binary data
data(csepdat1)
outc<-csepdat1$y
desma<-cbind("(Intercept)"=1,csepdat1[,2:ncol(csepdat1)])
separation_columns(outc, X = desma, model = "b")

# Nominal data 
# Baseline-category link
data(qcsepdatm)
y<-qcsepdatm$y
X<-cbind(1,qcsepdatm[,2:ncol(qcsepdatm)])
separation_columns(y, X = X, model = "bcl")

# Ordinal data
data(qcsepdato)
yo<-qcsepdato$y
Xo<-qcsepdato[,2:ncol(qcsepdato)]

# Sequential link
separation_columns(yo, Xo, model = "sl")

# Ordered stereotype
separation_columns(yo, Xo, model = "os")

# Adjacent-category link
separation_columns(yo, Xo, model= "acl")

# Cumulative link
separation_columns(yo, Xo, model = "cl")


# post fit
if (require('clustord')) {
m1 <- clustord::osm(y~x1+x2, data = qcsepdato)
separation_columns(m1)
}

Identify separation rows

Description

This function identifies the rows in a design matrix/structure vector matrix that are associated for separation. It calls lower level functions if given an argument or chooses based on the response type.

Usage

separation_rows(object, ...)

## Default S3 method:
separation_rows(object, ...)

## S3 method for class 'factor'
separation_rows(object, X, model = NULL, rational = FALSE, ...)

## S3 method for class 'character'
separation_rows(object, X, model = NULL, rational = FALSE, ...)

## S3 method for class 'logical'
separation_rows(object, X, model = NULL, rational = FALSE, ...)

## S3 method for class 'numeric'
separation_rows(object, X, model = NULL, rational = FALSE, ...)

## S3 method for class 'integer'
separation_rows(object, X, model = NULL, rational = FALSE, ...)

## S3 method for class 'matrix'
separation_rows(object, rational = FALSE, ...)

## S3 method for class 'formula'
separation_rows(
  object,
  data,
  model = NULL,
  rational = FALSE,
  contrasts = NULL,
  ...
)

## S3 method for class 'osm'
separation_rows(object, rational = FALSE, ...)

## S3 method for class 'clm'
separation_rows(object, rational = FALSE, ...)

## S3 method for class 'polr'
separation_rows(object, rational = FALSE, ...)

## S3 method for class 'multinom'
separation_rows(object, rational = FALSE, ...)

## S3 method for class 'glm'
separation_rows(object, rational = FALSE, ...)

## S3 method for class 'bracl'
separation_rows(object, rational = FALSE, ...)

## S3 method for class 'brmultinom'
separation_rows(object, rational = FALSE, ...)

Arguments

Details

separation_rows is S3 generic. For developers: If a method should be provided for the generic, it is best to have that method create a matrix of structure vectors S and use the low-level function seprows_worker with it.

The formula method is for standard data frames and formulas that work the same way as when used with glm. It does not support extended formulas, and may not work for functions that do formula processing differently.

For a data frame or matrix given as rational numbers in the rcdd definition, this is recognized but the formula does not get expanded and is taken literally. Consequently:

• variables in formula must match exactly with the column names in data;

• factors need to be converted to dummies beforehand (which would not be possible in the rational format in any other way anyway).

Value

A list with the components:

• offrows the submatrix of the matrix (X,y) with the rows responsible for separation

• index the index of the rows responsible for separation

For model = "sl" it is a list of these lists for each category.

Examples

## Binary data
data(csepdat1)
outc<-csepdat1$y
desma<-cbind("(Intercept)"=1,csepdat1[,2:ncol(csepdat1)])
separation_rows(outc, X = desma, model = "b")

# Nominal data 
# Baseline-category link
data(qcsepdatm)
y<-qcsepdatm$y
X<-cbind(1,qcsepdatm[,2:ncol(qcsepdatm)])
separation_rows(y, X = X, model = "bcl")

# Ordinal data
data(qcsepdato)
yo<-qcsepdato$y
Xo<-qcsepdato[,2:ncol(qcsepdato)]

# Sequential link
separation_rows(yo, Xo, model = "sl")

# Ordered stereotype
separation_rows(yo, Xo, model = "os")

# Adjacent-category link
separation_rows(yo, Xo, model= "acl")

# Cumulative link
separation_rows(yo, Xo, model = "cl")

# post fit
if (require('MASS')) {
m1 <- MASS::polr(y~x1+x2, data = qcsepdato)
separation_rows(m1)
}

Structure Vector S3 Generic

Description

Generic function to compute structure vectors from different types of inputs.

Method for structure_vectors when the input is a formula and data frame.

Usage

structure_vectors(x, ...)

## Default S3 method:
structure_vectors(
  x,
  X,
  model = c("b", "bcl", "acl", "os", "sl", "cl"),
  label = TRUE,
  rational = FALSE,
  ...
)

## S3 method for class 'formula'
structure_vectors(
  x,
  data,
  contrasts = NULL,
  model = NULL,
  label = TRUE,
  rational = FALSE,
  ...
)

Arguments

Details

structure_vectors is an S3 generic function.

The formula method is for standard data frames and formulas that work the same way as when used with glm. It does not support extended formulas, and may not work for functions that do formula processing differently.

For a data frame or matrix given as rational numbers in the rcdd definition, this is recognized but the formula does not get expanded and is taken literally. Consequently:

• variables in formula must match exactly with the column names in data;

• factors need to be converted to dummies beforehand (which would not be possible in the rational format in any other way anyway).

Value

A structure vector matrix with or without labeled rows and columns. For model = "sl", a list of structure vector matrices, where each list element corresponds sequentially to the categories of y, starting with the lowest and ending with the (K-1)-th category. At each category k, we consider all observations with category k or higher for the structure vector matrix.

Examples

data(qcsepdato)
yo<-qcsepdato$y
Xo<-qcsepdato[,2:ncol(qcsepdato)]

# Sequential link (default method and no labelling) 
structure_vectors(yo, Xo, model = "sl", label = FALSE)

# Ordered stereotype (formula method)
structure_vectors(y ~ x1 + x2, data = qcsepdato, model = "os")

All people of age 3 in the Kaggle Titanic data set

Description

This data set contains the subset of people in the Titanic data sets that were aged 3. It shows various separation types depending on the model fitted.

Usage

data(titanic3)

Format

A 6 x 12 data frame:

passengerId

ID of the passenger

Survived

Survived? (1=yes, 0=no)

Pclass

Passenger Class (1=upper, 2=middle, 3=lower).

Name

Name.

Sex

Sex of the person.

Age

Age of the person. All are 3 yrs.

SibSp

Number of siblings or spouses on board the ship.

Parch

Number of parents or children on board the ship.

Ticket

Ticket number

.

Fare

Passenger fare.

Cabin

Cabin number.

Embarked

Port of embarkation (C=Cherbourg, Q=Queenstown, S=Southampton).

Source

Will Cukierski. Titanic - Machine Learning from Disaster. https://kaggle.com/competitions/titanic, 2012. Kaggle.

Examples

with(titanic3,ftable(Survived~Sex+Pclass))