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# Generating ordinal data

## Author

Listed:
• Pier Alda FERRARI
• Alessandro BARBIERO

## Abstract

Due to the increasing use of ordinal variables in different fields, new statistical methods for their analysis have been introduced, whose performances need to be investigated under different experimental conditions. Proper procedures to simulate from ordinal variables are then requested. The present paper deals with the simulation from multivariate ordinal random variables. A new proposal for generating samples from ordinal random variables with pre-specified correlation matrix and marginal distributions is presented. Its features are examined and a comparison to its main competitors is discussed. A software implementation by the R package is provided. Examples of application are also supplied.

## Suggested Citation

• Pier Alda FERRARI & Alessandro BARBIERO, 2011. "Generating ordinal data," Departmental Working Papers 2011-38, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
• Handle: RePEc:mil:wpdepa:2011-38
as

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File URL: http://wp.demm.unimi.it/files/wp/2011/DEMM-2011_038wp.pdf
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## References listed on IDEAS

as
1. Biswas, Atanu, 2004. "Generating correlated ordinal categorical random samples," Statistics & Probability Letters, Elsevier, vol. 70(1), pages 25-35, October.
2. Philip M. Lurie & Matthew S. Goldberg, 1998. "An Approximate Method for Sampling Correlated Random Variables from Partially-Specified Distributions," Management Science, INFORMS, vol. 44(2), pages 203-218, February.
3. Stanhope, Stephen, 2005. "Case studies in multivariate-to-anything transforms for partially specified random vector generation," Insurance: Mathematics and Economics, Elsevier, vol. 37(1), pages 68-79, August.
4. Ferrari, Pier Alda & Annoni, Paola & Barbiero, Alessandro & Manzi, Giancarlo, 2011. "An imputation method for categorical variables with application to nonlinear principal component analysis," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2410-2420, July.
Full references (including those not matched with items on IDEAS)

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## More about this item

### Keywords

Likert scale; marginal distribution; Monte Carlo simulation; multivariate discrete random variable; non-linear principal component analysis; Pearson correlation coefficient;
All these keywords.

### JEL classification:

• C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
• C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
• C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

### Statistics

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