Package 'BFM'

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)

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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)

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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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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)

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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)

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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)

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