Labour Force Participation of Married Women 1967-1971
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.
data(Heckman)
A 5-dimensional array resulting from cross-tabulating 5 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"
|
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.
Lindsey, J. K. (1993). Models for Repeated Measurements Oxford, UK: Oxford University Press, p. 185.
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
data(Heckman) # independence model mosaic(Heckman, shade=TRUE) # same, as a loglm() require(MASS) (heckman.mod0 <- loglm(~ e1971+e1970+e1969+e1968+e1967, data=Heckman)) 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)) 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)) 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)) mosaic(heckman.mod2, main="3rd order markov chain model")
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