606 Panel Data Methods
risks model for delay before surgery and post-surgery length of stay. They use the
Heckman–Singer specification for the common heterogeneity with two mass points
(Heckman and Singer, 1984). Day of week of admission is used as an instrument for
delay until surgery. The raw data show a strong relationship between delays and
outcomes, but this disappears once unobserved frailty is taken into account. The
higher observed inpatient mortality in Quebec is attributed to the longer length of
stay rather than poorer outcomes: the longer the patients remain in hospital, the
more likely they are to die there rather than at home.
Other applications of the discrete factor model include Bhattacharyaet al.(2003),
who model the impact of public and private insurance on HIV-related mortality.
Melloet al.(2002) use a discrete factor specification for a two-equation model
of health plan choice, whether to join a Medicare HMO, and various measures
of subsequent health care utilization applied to data from the Medicare Current
Beneficiary Survey for 1993–96. A similar model of HMO enrollment and subse-
quent hospital use by Kanet al.(2003) finds evidence of strong selection effects
when a discrete factor specification is used to deal with unobservables. Rous and
Hotchkiss (2003) use the Nepal Living Standards Survey for 1996 in a model of
choice of health care provider, levels of expenditure and health outcomes with a
two-factor specification to allow for community and household effects. Holmes
(2005) combines a multinomial logit model with a discrete factor specification to
evaluate the US National Health Service Corps (NHSC) program that was designed
to encourage doctors to locate in underserviced areas.
The discrete factor model allows for a common factor in the intercept of each
equation. In contrast, the LCM allows all of the parameters to vary across the
latent classes. Clark and Etilé (2006) use the latent class framework to approximate
the continuous distribution of the individual effects in a dynamic random effects
bivariate probit model. They apply the model to data on smoking among couples in
the BHPS and use the simulated annealing version of the EM algorithm to estimate
the model. Atellaet al.(2004) develop a latent class model for the joint decisions of
consulting three types of physician. The authors assume that, within a latent class,
each decision can be modeled by an independent probit, so the joint distribution
of the three binary outcomes is a product of probits.
12.6.4 Applications using copulas
The copula approach leads to closed forms and avoids the need for numerical
integration. It also circumvents the problem of the limited menu of parametric
specifications of multivariate distributions that are available, especially when nor-
mality is an unsuitable assumption, for example, when dealing with highly skewed
data.
Although copulas are not mentioned explicitly, Prieger (2002) proposes an exten-
sion of the sample selection model that is built around the FGM copula. This
is applied to data from the 1996 wave of the MEPS. The outcome equation is a
duration model for hospital length of stay and the selection equation measures
whether the individual had an inpatient stay or not during the survey period.