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# Compositional Data Analysis and Zeros in Micro Data

## Author

Listed:
• Jane M. Fry
• Tim R.L. Fry
• Keith R. McLaren

## Abstract

The application of compositional data analysis methods in economics has some attraction. In particular, this methodology ensures that the stochastic component of budget share models will satisfy the restriction of shares to the unit simplex. The methodology relies upon the use of log-ratios in the statistical analysis. Such an approach is not possible when the data to be analyzed includes observations where the observed budget share is zero. We therefore extend the methods of compositional data analysis to the situation where the data to be analyzed includes observations where the observed budget share is zero. The modified compositional data methods are discussed both in statistical terms and through potential economic interpretations of the method. Further, the modified methodology is applied to the 1988 Australian Household Expenditure Survey yielding estimates for a system of Engel curves.

## Suggested Citation

• Jane M. Fry & Tim R.L. Fry & Keith R. McLaren, 1996. "Compositional Data Analysis and Zeros in Micro Data," Centre of Policy Studies/IMPACT Centre Working Papers g-120, Victoria University, Centre of Policy Studies/IMPACT Centre.
• Handle: RePEc:cop:wpaper:g-120
as

File URL: http://www.copsmodels.com/ftp/workpapr/g-120.pdf
File Function: Initial version, 1996-03

File URL: http://www.copsmodels.com/elecpapr/g-120.htm

## References listed on IDEAS

as
1. Maureen T. Rimmer & Alan A. Powell, 1994. "Engel Flexibility in Household Budget Studies: Non-parametric Evidence versus Standard Functional Forms," Centre of Policy Studies/IMPACT Centre Working Papers op-79, Victoria University, Centre of Policy Studies/IMPACT Centre.
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## Citations

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Cited by:

1. Hikaru Hasegawa & Kazuhiro Ueda & Kunie Mori, 2008. "Estimation of Engel Curves from Survey Data with Zero Expenditures," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 70(4), pages 535-558, August.
2. Tsagris, Michail, 2014. "The k-NN algorithm for compositional data: a revised approach with and without zero values present," MPRA Paper 65866, University Library of Munich, Germany.
3. ARATA Yoshiyuki & ONOZAKI Tamotsu, 2017. "A Compositional Data Analysis of Market Share Dynamics," Discussion papers 17076, Research Institute of Economy, Trade and Industry (RIETI).
4. Johan Fourie & Dieter von Fintel, 2010. "The dynamics of inequality in a newly settled, pre-industrial society: the case of the Cape Colony," Cliometrica, Journal of Historical Economics and Econometric History, Association Française de Cliométrie (AFC), vol. 4(3), pages 229-267, October.
5. Andreas Chai & Christian Kiedaisch & Nicholas Rohde, 2017. "The saturation of spending diversity and the truth about Mr Brown and Mrs Jones," Discussion Papers in Economics economics:201701, Griffith University, Department of Accounting, Finance and Economics.
6. Andriansyah, Andriansyah & Messinis, George, 2016. "Intended use of IPO proceeds and firm performance: A quantile regression approach," Pacific-Basin Finance Journal, Elsevier, vol. 36(C), pages 14-30.
7. Jack Gregory & David I. Stern, 2012. "Fuel Choices in Rural Maharashtra," CCEP Working Papers 1207, Centre for Climate Economics & Policy, Crawford School of Public Policy, The Australian National University.
8. Snyder, Ralph D. & Ord, J. Keith & Koehler, Anne B. & McLaren, Keith R. & Beaumont, Adrian N., 2017. "Forecasting compositional time series: A state space approach," International Journal of Forecasting, Elsevier, vol. 33(2), pages 502-512.
9. J. Arauzo & M. ManjÃ³n & M. MartÃ­n & A. Segarra, 2007. "Regional and Sector-specific Determinants of Industry Dynamics and the Displacementâ€“replacement Effects," Empirica, Springer;Austrian Institute for Economic Research;Austrian Economic Association, vol. 34(2), pages 89-115, April.
10. Adam Butler & Chris Glasbey, 2008. "A latent Gaussian model for compositional data with zeros," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 57(5), pages 505-520.
11. Wang, Huiwen & Liu, Qiang & Mok, Henry M.K. & Fu, Linghui & Tse, Wai Man, 2007. "A hyperspherical transformation forecasting model for compositional data," European Journal of Operational Research, Elsevier, vol. 179(2), pages 459-468, June.
12. Tsagris, Michail & Preston, Simon & T.A. Wood, Andrew, 2016. "Nonparametric hypothesis testing for equality of means on the simplex," MPRA Paper 72771, University Library of Munich, Germany.
13. Tsagris, Michail & Preston, Simon & T.A. Wood, Andrew, 2016. "Improved classi cation for compositional data using the $\alpha$-transformation," MPRA Paper 67657, University Library of Munich, Germany.
14. Michail Tsagris & Simon Preston & Andrew T. A. Wood, 2016. "Improved Classification for Compositional Data Using the α-transformation," Journal of Classification, Springer;The Classification Society, vol. 33(2), pages 243-261, July.
15. Terence Mills, 2010. "Forecasting compositional time series," Quality & Quantity: International Journal of Methodology, Springer, vol. 44(4), pages 673-690, June.
16. Gordon Anderson & Maria Grazia Pittau & Roberto Zelli, 2016. "Assessing the convergence and mobility of nations without artificially specified class boundaries," Journal of Economic Growth, Springer, vol. 21(3), pages 283-304, September.

### Keywords

Engel Curves; Modified Almost Ideal Demand System; Composi- tional Data Analysis; Australian H E S data;

### JEL classification:

• C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
• D12 - Microeconomics - - Household Behavior - - - Consumer Economics: Empirical Analysis

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