*! version 1.0: 22-July-2022

help bivpoissongithub.com/zhangyl334/bivpoisson

version 1.0

bivpoisson -- Seemingly unrelated count regression

Syntax

bivpoisson ( depvar = indepvars1 )
( depvar2 = indepvars2 ) [if statement]

options Description

Option
if statement select a subsample

depvar1 and depvar2 are count-valued independent variables for the first and second equations respectively.
They cannot be zero inflated; model warns and exits on zero inflated data.

indepvars1 and indepvars2 are the independent variables for the first and second equations respectively.
Model automatically includes a constant; the constant cannot be omitted.

Description

bivpoisson is a user-written command that fits a seemingly unrelated count regression model using maximum likelihood estimation. It is
implemented as an lf0 ml evaluator. The model involves one equation with
the count valued dependent variable depvar1 and a second equation with count valued dependent
variable depvar2. Both dependent variables depvar1 and depvar2 have to be both integer valued.

bivpoisson allows the independent variables in indepvars1 and indepvars2 to be different or identical.
bivpoisson is limited to a model with two equations.

Example

Setup

. use "https://github.com/zhangyl334/bivpoisson/raw/main/Health_Data.dta", clear

Seemingly unrelated count regression

. bivpoisson (ofp = privins black numchron) (ofnp = privins black numchron age)

Seemingly unrelated count regression with if statement

. bivpoisson (ofp = privins black numchron) (ofnp = privins black numchron age) if emr <= 1

Stored results

bivpoisson stores the following in e():

Scalars

e(N) number of observations

e(ic) number of iterations

e(k) number of parameters

e(k_eq) number of equations in e(b)

e(k_dv) number of dependent variables

e(converged) 1 if converged, 0 otherwise

e(rc) return code

Macros

e(cmdline) command as typed

e(indep2) names of first equation independent variables

e(depvar2) names of first equation dependent variable

e(indep1) names of second equation independent variables

e(depvar1) names of second equation dependent variable

e(title) title in estimation output

e(cmd) bivpoisson

e(opt) type of optimization

e(predict) program used to implement predict

e(user) name of likelihood-evaluator program: BivPoissNormLF()

e(ml_method) type of ml method

e(technique) maximization technique

e(which) max or min; whether optimizer is to perform
maximization or minimization

e(depvar) names of two dependent variables as Y1 and Y2

e(properties) b V

Matrices

e(b) coefficient vector

e(V) variance-covariance matrix of the estimators

e(ilog) iteration log (up to 20 iterations)

e(gradient) gradient vector

References

Aitchison, J., & Ho, C. H. (1989). The multivariate Poisson-log normal distribution. Biometrika, 76(4), 643–653. DOI: https://doi.org/10.1093/biomet/76.4.643

Chib, S., & Winkelmann, R. (2001). Markov Chain Monte Carlo Analysis of Correlated Count Data. Journal of Business & Economic Statistics, 19(4), 428–435. DOI: https://doi.org/10.1198/07350010152596673

Mander, A. (2018). INTEGRATE_AQ: Stata Module to do Adaptive Quadrature for Integrals. Statistical Software Components, Boston College. URL: https://econpapers.repec.org/software/bocbocode/s458502.htm

Zhang, Y. (2021). Exploring the Importance of Accounting for Nonlinearity in Correlated Count Regression Systems from the Perspective of Causal Estimation and Inference. DOI: https://doi.org/10.7912/C2/2873

Author

Abbie Zhang

email: zhangyl334@gmail.com

github: github.com/zhangyl334

webpage: https://yileizhang.com

Coauthors

James Fisher

email: jamescdf@gmail.com

Joseph Terza

email: jvterza@iupui.edu