Income distribution (percentages) in the Northeast US
Income distribution (percentages) in the Northeast US in 1960 and 1970 adopted from McCullagh (1980).
income
yearyear.
pctpercentage of population in income class per year.
incomeincome groups. The unit is thousands of constant (1973) US dollars.
Data are adopted from McCullagh (1980).
McCullagh, P. (1980) Regression Models for Ordinal Data. Journal of the Royal Statistical Society. Series B (Methodological), Vol. 42, No. 2., pp. 109-142.
print(income)
## Convenient table:
(tab <- xtabs(pct ~ year + income, income))
## small rounding error in 1970:
rowSums(tab)
## compare link functions via the log-likelihood:
links <- c("logit", "probit", "cloglog", "loglog", "cauchit")
sapply(links, function(link) {
clm(income ~ year, data=income, weights=pct, link=link)$logLik })
## a heavy tailed (cauchy) or left skew (cloglog) latent distribution
## is fitting best.
## The data are defined as:
income.levels <- c(0, 3, 5, 7, 10, 12, 15)
income <- paste(income.levels, c(rep("-", 6), "+"),
c(income.levels[-1], ""), sep = "")
income <-
data.frame(year=factor(rep(c("1960", "1970"), each = 7)),
pct = c(6.5, 8.2, 11.3, 23.5, 15.6, 12.7, 22.2,
4.3, 6, 7.7, 13.2, 10.5, 16.3, 42.1),
income=factor(rep(income, 2), ordered=TRUE,
levels=income))Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.