Package 'CFM'

Aids2 Dataset

Description

Australian AIDS survival data containing information on patients diagnosed with AIDS in Australia.

Usage

data(Aids2)

Format

A data frame with 2843 observations and 7 variables:

state

State in Australia: NSW, Other, QLD, VIC

sex

Sex of the patient

diag

Date of diagnosis

death

Date of death

status

Status at the end of the study: A (alive), D (dead)

T.categ

Transmission category

age

Age at diagnosis

Source

Australian National AIDS Registry

Examples

data(Aids2)
head(Aids2)
summary(Aids2)

---

Boundary Condition Dataset

Description

A dataset containing boundary condition data for computational fluid mechanics simulations.

Usage

data(bcdata)

Format

A data frame with variables:

time

Time variable (seconds)

pressure

Pressure values (Pa)

temperature

Temperature values (K)

velocity

Velocity components (m/s)

Source

Experimental measurements or numerical simulations

Examples

data(bcdata)
head(bcdata)
summary(bcdata)

---

Robust Censored Factor Model

Description

Implementation of robust censored factor model using robust PCA initialization for handling left-censored data.

Usage

censored_factor_model(
  X,
  m,
  max_iter = 100,
  tol = 1e-04,
  nugget = 1e-06,
  alpha = 0.75
)

Arguments

X	Data matrix (n x p)
m	Number of factors
max_iter	Maximum number of ECM iterations (default: 100)
tol	Convergence tolerance (default: 1e-4)
nugget	Numerical stability term (default: 1e-6)
alpha	Robustness parameter for MCD (default: 0.75)

Value

A list containing model results

---

Basic censored-factor data simulator

Description

Generates multivariate data that follow a latent factor structure with censored errors (Normal, Student-t or Logistic).

Usage

censored_factor_models(
  n,
  p,
  m,
  distribution = c("normal", "t", "logistic"),
  df = NULL,
  seed = NULL
)

Arguments

n	Sample size (> 0).
p	Number of observed variables (> 0).
m	Number of latent factors (< p).
distribution	Error distribution: "normal" (default), "t", "logistic".
df	Degrees of freedom when distribution = "t".
seed	Optional random seed.

Value

A list with components:

data	numeric n × p matrix of observations
loadings	p × m factor loadings matrix
uniqueness	p × p diagonal uniqueness matrix
KMO	KMO measure of sampling adequacy
Bartlett_p	p-value of Bartlett's test
distribution	error distribution used
seed	random seed

Examples

set.seed(2025)
obj <- censored_factor_models(200, 6, 2)
psych::KMO(obj$data)

---

Kernel Censored Factor Model

Description

Implementation of kernel-based censored factor model using kernel PCA initialization for nonlinear factor analysis with censored data.

Usage

censored_kernel_factor_model(
  X,
  m,
  kernel_type = "rbf",
  gamma = NULL,
  max_iter = 100,
  tol = 1e-04,
  nugget = 1e-06
)

Arguments

X	Data matrix (n x p)
m	Number of factors
kernel_type	Kernel type: "rbf" or "linear" (default: "rbf")
gamma	Gamma parameter for RBF kernel (default: 1/p)
max_iter	Maximum number of ECM iterations (default: 100)
tol	Convergence tolerance (default: 1e-4)
nugget	Numerical stability term (default: 1e-6)

Value

A list containing model results

---

Censored Factor Models Data Generation

Description

Generate multivariate data that follow a latent factor structure with censoring errors drawn from Normal, Student-t or Logistic distributions. Convenience wrapper around rcnorm, rct, and rclogis.

Usage

CFM(n, p, m, cens.dist = c("normal", "t", "logistic"), df = 5, seed = NULL)

Arguments

n	sample size ($n \times 1$ observations).
p	number of manifest variables.
m	number of latent factors.
cens.dist	censoring error distribution: "normal", "t", or "logistic".
df	degrees of freedom when cens.dist = "t".
seed	optional random seed for reproducibility.

Value

A named list with components:

data	numeric $n \times p$ matrix of observations.
F	factor scores matrix ($n \times m$).
A	factor loadings matrix ($p \times m$).
D	unique variances diagonal matrix ($p \times p$).

Examples

set.seed(2025)
# Normal censoring
obj <- CFM(n = 200, p = 10, m = 3, cens.dist = "normal")
head(obj$data)

# t-censoring with 6 d.f.
obj <- CFM(n = 300, p = 12, m = 4, cens.dist = "t", df = 6)
psych::KMO(obj$data)

---

Censored Factor Analysis via Principal Component (FanPC, pure R)

Description

Censored Factor Analysis via Principal Component (FanPC, pure R)

Usage

FanPC.CFM(
  data,
  m,
  A = NULL,
  D = NULL,
  p = NULL,
  cens.dist = c("normal", "t", "logistic"),
  df = NULL,
  cens.method = c("winsorise", "em"),
  cens_prop = 0.01,
  surv.obj = NULL,
  ctrl = NULL,
  verbose = NULL
)

Arguments

data	Numeric matrix or data frame of dimension $n \times p$.
m	Number of factors (< p).
A	Optional true loading matrix, used only for error calculation.
D	Optional true unique-variance diagonal matrix, used only for error calculation.
p	Number of variables (deprecated; detected automatically).
cens.dist	Error distribution, reserved for future use.
df	Degrees of freedom, reserved for future use.
cens.method	Censoring handling method; currently only "winsorise" is implemented. Defaults to "winsorise".
cens_prop	Winsorisation proportion, default 0.01.
surv.obj	Reserved for future use.
ctrl	Reserved for future use.
verbose	Reserved for future use.

Value

AF

Estimated loading matrix, p × m.

DF

Estimated unique-variance diagonal matrix, p × p.

MSESigmaA

Mean squared error of loadings (if A is provided).

MSESigmaD

Mean squared error of unique variances (if D is provided).

LSigmaA

Relative error of loadings (if A is provided).

LSigmaD

Relative error of unique variances (if D is provided).

Examples

library(CFM)
obj <- CFM(n = 500, p = 10, m = 2, cens.dist = "normal")
res <- FanPC.CFM(obj$data, m = 2, A = obj$A, D = obj$D, cens.method = "winsorise")
print(res$MSESigmaA)

---

Incremental Censored Factor Model

Description

Implementation of incremental censored factor model for streaming data with left-censored observations. Processes data in batches.

Usage

incremental_censored_factor_model(
  batch_data,
  m,
  max_iter = 100,
  tol = 1e-04,
  nugget = 1e-06
)

Arguments

batch_data	List of data matrices (batches)
m	Number of factors
max_iter	Maximum number of ECM iterations (default: 100)
tol	Convergence tolerance (default: 1e-4)
nugget	Numerical stability term (default: 1e-6)

Value

A list containing model results

---

PC2 for censored factor models (Top-2 principal components, pure R)

Description

PC2 for censored factor models (Top-2 principal components, pure R)

Usage

PC2.CFM(
  data,
  m,
  A = NULL,
  D = NULL,
  p = NULL,
  cens.dist = c("normal", "t", "logistic"),
  df = NULL,
  cens.method = c("winsorise", "em"),
  cens_prop = 0.01,
  surv.obj = NULL,
  ctrl = NULL,
  verbose = NULL
)

Arguments

data	Numeric matrix or data frame of dimension $n \times p$.
m	Number of factors (< p).
A	Optional true loading matrix, used only for error calculation.
D	Optional true unique-variance diagonal matrix, used only for error calculation.
p	Number of variables (deprecated; detected automatically).
cens.dist	Error distribution, reserved for future use.
df	Degrees of freedom, reserved for future use.
cens.method	Censoring handling method; currently only "winsorise" is implemented. Defaults to "winsorise".
cens_prop	Winsorisation proportion, default 0.01.
surv.obj	Reserved for future use.
ctrl	Reserved for future use.
verbose	Reserved for future use.

Value

AF

Estimated loading matrix, p × 2.

DF

Estimated unique-variance diagonal matrix, p × p.

MSESigmaA

Mean squared error of loadings (if A is provided).

MSESigmaD

Mean squared error of unique variances (if D is provided).

LSigmaA

Relative error of loadings (if A is provided).

LSigmaD

Relative error of unique variances (if D is provided).

Examples

library(CFM)
obj <- CFM(n = 500, p = 12, m = 2, cens.dist = "normal")
res <- PC2.CFM(obj$data, A = obj$A, D = obj$D)
print(res$MSESigmaA)

---

PPC2 for censored factor models (Top-2 principal components, pure R)

Description

PPC2 for censored factor models (Top-2 principal components, pure R)

Usage

PPC2.CFM(
  data,
  m,
  A = NULL,
  D = NULL,
  p = NULL,
  cens.dist = c("normal", "t", "logistic"),
  df = NULL,
  cens.method = c("winsorise", "em"),
  cens_prop = 0.01,
  surv.obj = NULL,
  ctrl = NULL,
  verbose = NULL
)

Arguments

data	Numeric matrix or data frame of dimension $n \times p$.
m	Number of factors (< p).
A	Optional true loading matrix, used only for error calculation.
D	Optional true unique-variance diagonal matrix, used only for error calculation.
p	Number of variables (deprecated; detected automatically).
cens.dist	Error distribution, reserved for future use.
df	Degrees of freedom, reserved for future use.
cens.method	Censoring handling method; currently only "winsorise" is implemented. Defaults to "winsorise".
cens_prop	Winsorisation proportion, default 0.01.
surv.obj	Reserved for future use.
ctrl	Reserved for future use.
verbose	Reserved for future use.

Value

AF

Estimated loading matrix, p × 2.

DF

Estimated unique-variance diagonal matrix, p × p.

MSESigmaA

Mean squared error of loadings (if A is provided).

MSESigmaD

Mean squared error of unique variances (if D is provided).

LSigmaA

Relative error of loadings (if A is provided).

LSigmaD

Relative error of unique variances (if D is provided).

Examples

library(CFM)
obj <- CFM(n = 500, p = 12, m = 2, cens.dist = "normal")
res <- PPC2.CFM(obj$data, A = obj$A, D = obj$D, cens.method = "winsorise")
print(res$MSESigmaA)

---

Weighted Censored Factor Model

Description

Implementation of weighted censored factor model with weighted PCA initialization for handling left-censored data with observation weights.

Usage

weighted_censored_factor_model(
  X,
  m,
  weights = NULL,
  max_iter = 100,
  tol = 1e-04,
  nugget = 1e-06
)

Arguments

X	Data matrix (n x p)
m	Number of factors
weights	Observation weights vector of length n (optional)
max_iter	Maximum number of ECM iterations (default: 100)
tol	Convergence tolerance (default: 1e-4)
nugget	Numerical stability term (default: 1e-6)

Value

A list containing model results

---

Yoghurt Dataset

Description

A dataset containing experimental or survey data related to yogurt.

Usage

data(yoghurt)

Format

A data frame with the following columns:

adult

Description of adult variable

fadult

Description of fadult variable

left

Description of left variable

right

Description of right variable

Details

This dataset contains experimental data collected from yogurt-related studies. The specific meaning of each variable should be documented based on the original study.

Source

Original data source should be specified here.

Examples

# Load the data
data(yoghurt)

# Examine data structure
str(yoghurt)

# View first few rows
head(yoghurt)

# Basic summary statistics
summary(yoghurt)

---