Palgrave Handbook of Econometrics: Applied Econometrics

808 Computational Considerations in Microeconometrics

regularity conditions, in practice such an application is subject to qualifications,
especially in small samples or if the model is overfitted, so that one or more mixture
components are small. This increases the appeal of variance calculation using the
bootstrap (see McLachlan and Peel, 2000, Ch. 2.16).

15.5.2.2 FM of count models

Finite mixtures can be applied to continuous, discrete, or censored data (see
McLachlan and Peel, 2000). Although the methods have not yet become common
in widely used econometrics software, there are many examples in the literature.
In the remainder of this section, we illustrate the potential richness of this model-
ing approach using an application to a count data regression (see Deb and Trivedi,
1997, 2002).
The dataset consists of 3,064 observations, where the dependent variable is
number of doctor visits (DOCVIS). The predictors are age (AGE), squared age
(AGE2), years of education (EDUC), a dichotomous indicator of activity limita-
tion (ACTLIM), total number of chronic conditions (TOTCHR), and a dichotomous
indicator of private health insurance status (PRIVATE). Table 15.5 shows results
obtained using standard gradient methods of maximizing the likelihood. Poisson
regression results appear in the first column. Typically this model gives a poor fit
to the data because it imposes the assumption of equidispersion (E[y|x]=var(y|x)),

Table 15.5 Poisson NB2 mixture models for DOCVIS

(1) POISSON (2) POISSON (FM2) (3) NB2 (FM2)

Coef. Std. error Coef. Std. error Coef. Std. error

Component 1

AGE 0.299 0.0662 0.352 0.0953 0.446 0.162

AGE2 −0.198 0.0441 −0.232 0.0638 −0.290 0.107

EDUC 0.0288 0.00539 0.0299 0.00712 0.0417 0.0119

ACTLIM 0.160 0.0414 0.0701 0.0582 −0.0554 0.147

TOTCHR 0.259 0.0130 0.338 0.0174 0.527 0.0693

PRIVATE 0.154 0.0374 0.225 0.0582 0.400 0.114

Intercept −10.34 2.474 −13.18 3.537 −17.59 6.141

Component 2

AGE 0.219 0.107 0.272 0.0878

AGE2 −0.145 0.0720 −0.181 0.0586

EDUC 0.0204 0.00747 0.0228 0.00707)

ACTLIM 0.137 0.0592 0.201 0.0500

TOTCHR 0.203 0.0249 0.197 0.0278

PRIVATE 0.139 0.0610 0.108 0.0454

Intercept −6.337 3.961 −8.799 3.290

π 1 0.878 0.0860 0.405 0.099

lnα 1 −1.186 0.307

lnα 2 −0.828 0.0811

log-like − 12148 − 9311 − 8711