Andrew M. Jones 60512.6.3 Applications using finite mixtures
The common factor model was introduced earlier in this chapter in the context
of Aakviket al.’s (2005) evaluation of a Norwegian VR program (see equations
(12.8)–(12.10) above). Aakviket al.’s application takes a parametric approach and
assumes that the common factor is normally distributed. An alternative, semipara-
metric approach is to use a finite density and estimate a DFM. The DFM has two
main advantages over MSL. First, it is semiparametric and therefore more robust
than the parametric approach, which relies on strong distributional assumptions.
Also, in general, it is easier to compute, involving standard numerical methods for
maximum likelihood estimation or the use of the expectation maximization (EM)
algorithm, rather than computationally intensive Monte Carlo simulation (see,
e.g., Arcidianconoet al.,2007). However, in practice there can be problems with
identification, manifested in failure of convergence and problems with multiple
optima.
Like Aakviket al.(2005), Aakviket al.(2003) use a latent variable framework to
specify the impact of multidisciplinary treatment for back pain on the probability
of leaving sickness benefits. Using a structural model, based on latent variables,
allows them to define the ATE, the ATET and to allow for heterogeneous MTEs.
In this application the unobservables are modeled using a discrete factor structure
with distance to the nearest hospital used to identify the model. The estimates
show a positive effect of around 6 percentage points on the probability of leaving
sickness benefits.
Rous and Hotchkiss (2003) use data from 254 Texas counties on all reported births
in 1993 to explore the impact of prenatal care on birth weight. They estimate a
discrete factor model with three equations: a logit model for whether the pregnancy
is carried to full-term and linear regressions for a measure of prenatal care visits
and for birth weight. Travel distance to the nearest provider of abortions is used to
identify the first equation, the availability of obstetricians is used for the second and
the gender of the child for the third. The factor model shows evidence of adverse
selection effects. Piconeet al.(2003b) merge panel data from the US National
Long-Term Care Survey (NLTCS) for 1984–95 with the National Death Index to
investigate the impact of treatment intensity on survival rates and other health
outcomes. Their model involves a system of three equations for treatment intensity,
length of stay and health outcomes. These are assumed to have a common factor
structure which is estimated using a one-factor model. The selection of models
is based on the likelihood ratio (LR) statistic (Mroz, 1999) and 1,000 bootstrap
replications are used to avoid the problem of local optima. The model is identified
by excluding area data on the cost of capital, the Herfindahl index for hospital
concentration and a wage index from the mortality equation. The results suggest
that treatment intensity has a beneficial effect. Hamiltonet al.(2000) compare
US and Canadian data to see whether waiting time for surgery for hip fractures
influences the outcomes of the treatment, measured by length of stay and inpatient
mortality. They use discharge data for 20,995 patients admitted to acute hospitals
in Quebec and Massachusetts between 1990 and 1992 and estimate a competing