Labour Force Participation of Married Women 1967-1971
Heckman.Rd
1583 married women were surveyed over the years 1967-1971, recording whether or not they were employed in the labor force.
The data, originally from Heckman & Willis (1977) provide an example of modeling longitudinal categorical data, e.g., with markov chain models for dependence over time.
Usage
data(Heckman)
Format
A 5-dimensional \(2^5\) array resulting from cross-tabulating 5 binary variables for 1583 observations. The variable names and their levels are:
No | Name | Levels |
1 | e1971 | "71Yes", "No" |
2 | e1970 | "70Yes", "No" |
3 | e1969 | "69Yes", "No" |
4 | e1968 | "68Yes", "No" |
5 | e1967 | "67Yes", "No" |
Details
Lindsey (1993) fits an initial set of logistic regression models examining the dependence of
employment in 1971 (e1971
) on successive subsets of the previous years,
e1970
, e1969
, ... e1967
.
Alternatively, one can examine markov chain models of first-order (dependence on previous year), second-order (dependence on previous two years), etc.
Source
Lindsey, J. K. (1993). Models for Repeated Measurements Oxford, UK: Oxford University Press, p. 185.
References
Heckman, J.J. & Willis, R.J. (1977). "A beta-logistic model for the analysis of sequential labor force participation by married women." Journal of Political Economy, 85: 27-58
Examples
data(Heckman)
# independence model
mosaic(Heckman, shade=TRUE)
# same, as a loglm()
require(MASS)
(heckman.mod0 <- loglm(~ e1971+e1970+e1969+e1968+e1967, data=Heckman))
#> Call:
#> loglm(formula = ~e1971 + e1970 + e1969 + e1968 + e1967, data = Heckman)
#>
#> Statistics:
#> X^2 df P(> X^2)
#> Likelihood Ratio 3824.863 26 0
#> Pearson 8747.019 26 0
mosaic(heckman.mod0, main="Independence model")
# first-order markov chain: bad fit
(heckman.mod1 <- loglm(~ e1971*e1970 + e1970*e1969 +e1969*e1968 + e1968*e1967, data=Heckman))
#> Call:
#> loglm(formula = ~e1971 * e1970 + e1970 * e1969 + e1969 * e1968 +
#> e1968 * e1967, data = Heckman)
#>
#> Statistics:
#> X^2 df P(> X^2)
#> Likelihood Ratio 210.2251 22 0
#> Pearson 254.8971 22 0
mosaic(heckman.mod1, main="1st order markov chain model")
# second-order markov chain: bad fit
(heckman.mod2 <- loglm(~ e1971*e1970*e1969 + e1970*e1969*e1968 +e1969*e1968*e1967, data=Heckman))
#> Call:
#> loglm(formula = ~e1971 * e1970 * e1969 + e1970 * e1969 * e1968 +
#> e1969 * e1968 * e1967, data = Heckman)
#>
#> Statistics:
#> X^2 df P(> X^2)
#> Likelihood Ratio 62.67163 16 1.845162e-07
#> Pearson 75.99393 16 8.698373e-10
mosaic(heckman.mod2, main="2nd order markov chain model")
# third-order markov chain: fits OK
(heckman.mod3 <- loglm(~ e1971*e1970*e1969*e1968 + e1970*e1969*e1968*e1967, data=Heckman))
#> Call:
#> loglm(formula = ~e1971 * e1970 * e1969 * e1968 + e1970 * e1969 *
#> e1968 * e1967, data = Heckman)
#>
#> Statistics:
#> X^2 df P(> X^2)
#> Likelihood Ratio 9.023246 8 0.3403388
#> Pearson 8.155529 8 0.4184270
mosaic(heckman.mod2, main="3rd order markov chain model")