Package {BFM}

Type: Package
Title: Beta Factor Model
Version: 0.2.11
Author: Guangbao Guo [aut, cre], Jiahui Feng [aut]
Maintainer: Guangbao Guo <ggb11111111@163.com>
Description: Provides tools for factor analysis in financial and econometric settings under Beta factor models. It includes functions to simulate factor-model data with Beta-distributed idiosyncratic components (e.g., standard Beta, scaled Beta, and truncated Beta distributions) and to conduct model diagnostic assessments such as likelihood ratio tests for factor number selection and goodness-of-fit tests for Beta distribution assumptions. Estimation routines encompass maximum likelihood estimation for finite-dimensional Beta factor models, regularized Beta factor analysis for high-dimensional datasets, and shrinkage-based estimation for robust Beta factor loading recovery in noisy or incomplete data environments. The package's methodological framework is detailed in Guo G. (2023) <doi:10.1007/s00180-022-01270-z>.
License: MIT + file LICENSE
Encoding: UTF-8
Depends: R (≥ 3.5.0)
Suggests: testthat (≥ 3.0.0), spelling, betareg, zoib
NeedsCompilation: no
LazyData: true
RoxygenNote: 7.3.3
Imports: MASS, psych, stats
Language: en-US
Packaged: 2026-05-12 12:44:40 UTC; Administrator
Repository: CRAN
Date/Publication: 2026-05-18 18:20:13 UTC

California Alcohol Use Data

Description

A county-level monthly alcohol use dataset from California students (grades 7-11, 2008-2010). The response variable Percentage is a proportion (0 < Percentage < 1), suitable for zero-inflated beta regression.

Usage

AlcoholUse

Format

A data frame with multiple rows and variables:

Percentage

numeric: percentage of students who drank alcohol

Grade

factor: student grade level

Gender

factor: student gender

MedDays

numeric: mid-point of days bucket

Days

numeric: days bucket

County

factor: county identifier

A data frame with 44 rows and 4 variables:

accuracy

numeric: proportion of correct responses in a reading task

accuracy1

numeric: transformed accuracy measure

dyslexia

factor: dyslexia status (levels: "yes", "no")

iq

numeric: IQ score

Source

http://www.kidsdata.org Reading Skills Data

A dataset from Smithson and Verkuilen (2006) on reading accuracy, dyslexia status, and IQ scores. The response variable accuracy is a proportion (0 < accuracy < 1), suitable for beta regression.

Smithson, M. & Verkuilen, J. (2006). A better lemon squeezer? Maximum-likelihood regression with beta-distributed dependent variables. https://psycnet.apa.org/doi/10.1037/1082-989X.11.1.54

Examples

data(AlcoholUse)
str(AlcoholUse)

The BFM function is to generate Beta Factor Models data.

Description

The function supports various distribution types for generating the data.

Usage

BFM(n, p, m, mub, phib, distribution_type)

Arguments

n

Sample size.

p

Sample dimensionality.

m

Number of factors.

mub

Mean parameter for Beta distribution (numeric vector or scalar, 0 < mub < 1).

phib

Precision parameter for Beta distribution (positive numeric vector or scalar).

distribution_type

Type of Beta distribution.

Value

A list containing:

data

Generated BFM data matrix (n rows, p columns).

A

A matrix representing the factor loadings.

D

Diagonal matrix of unique variances.

kmo

Kaiser-Meyer-Olkin sampling adequacy measure.

bartlett

Bartlett's test of sphericity.

Examples

n <- 1000
p <- 10
m <- 5
mub <- runif(p, 0.2, 0.8)
phib <- runif(p, 5, 30)
dist_type <- "Elliptical Distribution"
X <- BFM(n, p, m, mub, phib, dist_type)

Household Food Expenditure Data

Description

A dataset from Griffiths, Hill, and Judge (1993) on household food expenditure, income, and household size. The response variable food is a proportion (0 < food < 1), suitable for beta regression.

Usage

FoodExpenditure

Format

A data frame with 38 rows and 3 variables:

food

numeric: proportion of household income spent on food

income

numeric: household income (in thousands of dollars)

persons

numeric: number of persons living in the household

Source

Griffiths, W. E., Hill, R. C., & Judge, G. G. (1993). Learning and Practicing Econometrics. Wiley.

Examples

data(FoodExpenditure)
str(FoodExpenditure)

Gasoline Yield Data from Prater (1956)

Description

A dataset containing 32 observations on gasoline yield under different experimental conditions. The response variable yield is a proportion (0 < yield < 1), making it suitable for beta regression.

Usage

GasolineYield

Format

A data frame with 32 rows and 6 variables:

yield

numeric: proportion of crude oil converted to gasoline

batch

factor: 10 unique batches of crude oil

temp

numeric: temperature (Fahrenheit)

gravity

numeric: crude oil gravity

pressure

numeric: pressure

temp10

numeric: temperature (scaled)

Source

Prater (1956), as cited in Ferrari and Cribari-Neto (2004) Beta Regression for Modelling Rates and Proportions https://www.jstor.org/stable/4110074

Examples

data(GasolineYield, package = "betareg")
str(GasolineYield)

Reading Skills Data

Description

A dataset from Smithson and Verkuilen (2006) on reading accuracy, dyslexia status, and IQ scores. The response variable accuracy is a proportion (0 < accuracy < 1), suitable for beta regression.

Usage

ReadingSkills

Format

A data frame with 44 rows and 4 variables:

accuracy

numeric: proportion of correct responses in a reading task

accuracy1

numeric: transformed accuracy measure

dyslexia

factor: dyslexia status (levels: "yes", "no")

iq

numeric: IQ score

Source

Smithson, M. & Verkuilen, J. (2006). A better lemon squeezer? Maximum-likelihood regression with beta-distributed dependent variables. https://psycnet.apa.org/doi/10.1037/1082-989X.11.1.54

Examples

data(ReadingSkills)
str(ReadingSkills)

Calculate Errors for Factor Analysis Estimates

Description

This function calculates the Mean Squared Error (MSE) and relative error for factor loadings and uniqueness estimates.

Usage

calculate_errors(data, A, D, estimation_results)

Arguments

data

Matrix of BFM data.

A

Matrix of true factor loadings.

D

Matrix of true uniquenesses (diagonal matrix).

estimation_results

A list containing A_hat (estimated loadings) and D_hat (estimated uniquenesses).

Value

A named vector containing:

MSEA

Mean Squared Error for factor loadings.

MSED

Mean Squared Error for uniqueness estimates.

LSA

Relative error for factor loadings.

LSD

Relative error for uniqueness estimates.

Examples

set.seed(123)
n <- 10
p <- 5
A <- matrix(runif(p * p, -1, 1), nrow = p)
D <- diag(runif(p, 1, 2))
data <- matrix(runif(n * p), nrow = n)
estimation_results <- list(A_hat = A, D_hat = D)
errors <- calculate_errors(data, A, D, estimation_results)
print(errors)

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