gkwreg (version 2.1.6)

FoodExpenditure: Proportion of Household Income Spent on Food

Description

Cross-section data on annual food expenditure and annual income for a random sample of households in a large U.S. city. The dataset models the proportion of income spent on food as a function of total income and household size.

Usage

FoodExpenditure

Format

A data frame with 38 observations on 3 variables:

food

numeric. Annual food expenditure in U.S. dollars.

income

numeric. Annual household income in U.S. dollars.

persons

numeric. Number of persons in the household.

Details

This classic econometric dataset was taken from Griffiths et al. (1993, Table 15.4) who cite Leser (1963) as the original source. The data are used to model Engel curves, which describe how household expenditure on a particular good or service varies with household income.

The response variable of interest is typically food/income, the proportion of income spent on food, which follows beta distribution properties as it is bounded between 0 and 1.

References

Cribari-Neto, F., and Zeileis, A. (2010). Beta Regression in R. Journal of Statistical Software, 34(2), 1--24. tools:::Rd_expr_doi("10.18637/jss.v034.i02")

Ferrari, S.L.P., and Cribari-Neto, F. (2004). Beta Regression for Modeling Rates and Proportions. Journal of Applied Statistics, 31(7), 799--815.

Griffiths, W.E., Hill, R.C., and Judge, G.G. (1993). Learning and Practicing Econometrics. New York: John Wiley and Sons.

Leser, C.E.V. (1963). Forms of Engel Functions. Econometrica, 31(4), 694--703.

Examples

# \donttest{
require(gkwreg)
require(gkwdist)

data(FoodExpenditure)
FoodExpenditure$prop <- FoodExpenditure$food / FoodExpenditure$income

# Example 1: Basic Kumaraswamy regression
# Proportion spent on food decreases with income (Engel's law)
# Larger households spend more on food
fit_kw <- gkwreg(prop ~ income + persons,
  data = FoodExpenditure,
  family = "kw"
)
summary(fit_kw)

# Interpretation:
# - Alpha: Negative income effect (Engel's law)
#   Positive household size effect
# - Beta: Constant precision (homoscedastic model)

# Example 2: Heteroscedastic model
# Variability in food proportion may differ by income and household size
fit_kw_hetero <- gkwreg(
  prop ~ income + persons |
    income + persons,
  data = FoodExpenditure,
  family = "kw"
)
summary(fit_kw_hetero)

# Interpretation:
# - Beta: Precision varies with both income and household size
#   Wealthier or larger households may show different spending variability

# Test for heteroscedasticity
anova(fit_kw, fit_kw_hetero)

# Example 3: Exponentiated Kumaraswamy for extreme spending patterns
# Some households may have unusual food spending (very frugal or lavish)
fit_ekw <- gkwreg(
  prop ~ income + persons | # alpha
    persons | # beta: household size affects precision
    income, # lambda: income affects extremity
  data = FoodExpenditure,
  family = "ekw"
)
summary(fit_ekw)

# Interpretation:
# - Lambda: Income level affects tail behavior
#   Rich households may show more extreme (unusual) spending patterns

# Visualization: Engel curve
plot(prop ~ income,
  data = FoodExpenditure,
  xlab = "Annual Income ($)", ylab = "Proportion Spent on Food",
  main = "Engel Curve for Food Expenditure"
)
# Add fitted values
FoodExpenditure$fitted_kw <- fitted(fit_kw)
points(FoodExpenditure$income, FoodExpenditure$fitted_kw,
  col = "blue", pch = 19, cex = 0.8
)
legend("topright",
  legend = c("Observed", "Fitted"),
  col = c("black", "blue"), pch = c(1, 19)
)
# }