Analysis of repeated measures data with clumping at zero

Abstract

Longitudinal or repeated measures data with clumping at zero occur in many applications in biometrics, including health policy research, epidemiology, nutrition, and meteorology. These data exhibit correlation because they are measured on the same subject over time or because subjects may be considered repeated measures within a larger unit such as a family. They present special challenges because of the extreme non-normality of the distributions involved. A model for repeated measures data with clumping at zero, using a mixed-effects mixed-distribution model with correlated random effects, is presented. The model contains components to model the probability of a nonzero value and the mean of nonzero values, allowing for repeated measurements using random effects and allowing for correlation between the two components. Methods for describing the effect of predictor variables on the probability of nonzero values, on the mean of nonzero values, and on the overall mean amount are given. This interpretation also applies to the mixed-distribution model for cross-sectional data. The proposed methods are illustrated with analyses of effects of several covariates on medical expenditures in 1996 for subjects clustered within households using data from the Medical Expenditure Panel Survey.

Get full access to this article

View all access options for this article.

References

Lachenbruch P. Analysis of data with clumping at zero . Biometrische Zeitschrift 1976; 18: 351-356 .

Lachenbruch P. Utility of regression analysis in epidemiologic studies of the elderly. In: Wallace R , Woolson R , eds. The epidemiologic study of the elderly. Oxford University Press , 1992.

Duan N , Manning WG , Morris CN , Newhouse JP. A comparison of alternative models for the demand for medical care. Santa Monica, California: The RAND Corporation , 1982. R-2754-HHS.

Amemiya T. Advanced econometrics. Cambridge, Massachusetts: Harvard University Press , 1985.

Grunwald GK , Jones RH. Markov models for time series with mixed distribution . Environmetrics 2000; 11: 327-339 .

Manning W , Duan N , Rogers W. Monte Carlo evidence on the choice between sample selection and two-part models . Journal of Econometrics 1987; 35: 59-82 .

Diggle PJ , Liang K-Y , Zeger SL. Analysis of longitudinal data. Oxford: Oxford University Press , 1994.

Heckman JJ. The common structure of statistical models of truncation, sample selection, and limited dependent variables and a simple estimator of such models . Annals of Economic and Social Measurement 1976; 5: 475-492 .

Robertson JS , Bolinger K , Glasser LM , Sloane NJ , Gross R. Chapter 1. In: Zwillinger D , ed. CRC standard mathematical tables and formulae. Boca Raton: CRC Press , 1996: 71-71.

10.

Aitchinson J. On the distribution of a positive random variable having a discrete probability mass at the origin . Journal of the American Statistical Association 1955; 50: 901-908 .

11.

Wolfinger R , O’Connell M. Generalized linear models . Journal of Statistical Computer Simulation 1993; 48: 233-243 .

12.

Breslow N , Clayton D. Approximate inference in generalized linear models . Journal of the American Statistical Association 1993; 88: 9-25 .

13.

Pinheiro JC , Bates DM. Approximations to the log-likelihood function in the nonlinear mixed-effects model . Journal of Computational and Graphical Statistics 1995; 4: 12-35 .

14.

McCullagh P , Nelder J. Generalized linear models (2nd ed). London: Chapman & Hall , 1989.

15.

Zeger SL , Karim MR. Generalized linear models with random effects . Journal of the American Statistical Association 1991; 86: 79-86 .

16.

Hyndman RJ , Grunwald GK. Generalized additive modeling of mixed distribution markov models with application to Melbourne’s rainfall . Australian and New Zealand Journal of Statistics 2000; 42: 145-158 .

17.

Silverman BW. Density estimation for statistics and data analysis. London: Chapman and Hall , 1986.

18.

Lambert D. Zero-inflated Poisson regression, with an application to defects in manufacturing . Technometrics 1992; 34: 1-14 .

19.

Dunson D and Haseman J. Modeling tumor onset and multiplicity using transition models with latent variables . Biometrics 1999; 55: 965-970 .

20.

Hall D. Zero-inflated Poisson and binomial regression with random effects: A case study . Biometrics 2000; 56: 1030-1039 .

21.

Maddala G. Limited dependent variable models using panel data . Journal of Human Resources 1987; 22: 307-338 .

22.

Vella F. Estimating models with sample selection bias . Journal of Human Resources 1998; 33: 127-169 .