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Tobit Models

  • Reference work entry
Encyclopedia of Quality of Life and Well-Being Research

Synonyms

Heckit, sample selection models (type II Tobit); Normal censored data, regression model

Definition

Family of statistical regression models that describe the relationship between censored or truncated continuous dependent variables and some independent variables.

Description

The Tobit models are a family of statistical regression models that describe the relationship between a censored (or truncated, in an even broader sense of this family) continuous dependent variable yi and a vector of independent variables xi. The model was originally proposed by James Tobin (1958) to model nonnegative continuous variables with several observations taking value 0 (household expenditure).

Generally, the Tobit models assume there is a latent continuous variable \( y_i^{*} \), which has not been observed over its entire range. It can happen due to truncation or censoring.

When truncation occurs, individuals on certain range of the variable \( y_i^{*} \)are not included in the dataset. In the...

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References

  • Amemiya, T. (1973). Regression analysis when the dependent variable is truncated normal. Econometrica, 41(6), 997.

    Google Scholar 

  • Amemiya, T. (1984). Tobit models: A survey. Journal of Econometrics, 24, 3–61.

    Google Scholar 

  • Arabmazar, A., & Schmidt, P. (1981). Further evidence on the robustness of the Tobit estimator to heteroskedasticity. Journal of econometrics, 17(2), 253–258.

    Google Scholar 

  • Bharmal, M., & Thomas, J. (2006). Comparing the EQ-5D and the SF-6D descriptive systems to assess their ceiling effects in the US general population. Value in Health, 9(4), 262–271.

    Google Scholar 

  • Clarke, P., Gray, A., & Holman, R. (2002). Estimating utility values for health states of type 2 diabetic patients using the EQ-5D (UKPDS 62). Medical Decision Making, 22(4), 340–349.

    Google Scholar 

  • Greene, W. (1997). Econometric analysis (3rd ed.). Saddle River: Prentice Hall.

    Google Scholar 

  • Greene, W. (1999). Marginal effects in the censored regression model. Economic Letters, 64(1), 13–49.

    Google Scholar 

  • Guo, N., Marra, C. A., Marra, F., Moadebi, S., & Elwood, R. K. (2008). Health state utilities in latent and active tuberculosis. Value in Health, 11(7), 1154–1161.

    Google Scholar 

  • Hasan, S. A., Subhani, M. I., & Osman, A. (2011). Marketing is all about taking money from customers (an application of Tobit model). International Research Journal of Finance and Economics, 81, 30–37.

    Google Scholar 

  • Hurd, M. (1979). Estimation in truncated samples when there is heteroscedasticity. Journal of Econometrics, 11, 247–258.

    Google Scholar 

  • Iwata, S. (1993). A note on multiple roots of the Tobit log likelihood. Journal of Econometrics, 56, 441–445.

    Google Scholar 

  • Johnson, J. A., & Pickard, A. S. (2000). Comparison of the EQ-5D and SF-12 health surveys in a general population survey in Alberta, Canada. Medical Care, 38(1), 115–121.

    Google Scholar 

  • Luo, N., Johnson, J. A., Shaw, J. W., & Coons, S. J. (2009). Relative efficiency of the EQ-5D, HUI2, and HUI3 index scores in measuring health burden of chronic medical conditions in a population health survey in the United States. Medical Care, 47(1), 53–60.

    Google Scholar 

  • Maddala, G.S., Nelson, F.D. (1975). Specification errors in limited dependent variable models. NBER Working Paper Series, Vol. w0096.

    Google Scholar 

  • McDonald, J. F., & Moffitt, R. A. (1980). The uses of Tobit analysis. The Review of Economics and Statistics, 62(2), 318–321.

    Google Scholar 

  • McDowell, I. (2006). Measuring health: A guide to rating scales and questionnaires (3rd ed.). New York: Oxford University Press.

    Google Scholar 

  • Moock, J., & Kohlmann, T. (2008). Comparing preference-based quality-of-life measures: Results from rehabilitation patients with musculoskeletal, cardiovascular, or psychosomatic disorders. Quality of Life Research, 17(3), 485–495.

    Google Scholar 

  • Olsen, R. J. (1978). Note on the uniqueness of the maximum likelihood estimator for the Tobit model. Econometrica, 46, 1211–1215.

    Google Scholar 

  • Payakachat, N., Summers, K., Pleil, A., Murawski, M., Thomas, J., Jennings, K., & Anderson, J. (2009). Predicting EQ-5D utility scores from the 25-item National Eye Institute Vision Function Questionnaire (NEI-VFQ 25) in patients with age-related macular degeneration. Quality of Life Research, 18(7), 801–813.

    Google Scholar 

  • Petrou, S., & Hockley, C. (2005). An investigation into the empirical validity of the EQ-5D and SF-6D based on hypothetical preferences in a general population. Health Economics, 14(11), 1169–1189.

    Google Scholar 

  • Petrou, S., & Kupek, E. (2009). Estimating preference-based health utilities index mark 3 utility scores for childhood conditions in England and Scotland. Medical Decision Making, 29(3), 291–303.

    Google Scholar 

  • Pullenayegum, E. M., Tarride, J. E., Xie, F., Goeree, R., Gerstein, H. C., & O'Reilly, D. (2010). Analysis of health utility data when some subjects attain the upper bound of 1: Are Tobit and CLAD models appropriate? Value in Health, 13(4), 487–494.

    Google Scholar 

  • Saarni, S. I., Härkänen T., Sintonen, H., Suvisaari, J., Koskinen, S., Aromaa, A., & Lönnqvist, J. (2006). The impact of 29 chronic conditions on health-related quality of life: A general population survey in finland using 15D and EQ-5D. Quality of Life Research, 15(8), 1403–1414.

    Google Scholar 

  • Schnedler, W. (2005). Likelihood estimation for censored random vectors. Econometric Reviews, 24(2), 195–217.

    Google Scholar 

  • Sullivan, P. W., & Ghushchyan, V. (2005). A national catalog of preference-based scores for chronic conditions in the United States. Medical Care, 43(7), 736–749.

    Google Scholar 

  • Sullivan, P. W., & Ghushchyan, V. (2006). Preference-based EQ-5D index scores for chronic conditions in the United States. Medical Decision Making, 26(4), 410–420.

    Google Scholar 

  • Tobin, J. (1958). Estimation of relationships for limited dependent variables. Econometrica, 26(1), 24–36.

    Google Scholar 

  • Vainiola, T., Pettilä, V., Roine, R. P., Räsänen, P., Rissanen, A. M., & Sintonen, H. (2010). Comparison of two utility instruments, the EQ-5D and the 15D, in the critical care setting. Intensive Care Medicine, 36(12), 2090–2093.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Health Services Research Unit, IMIM-Hospital del Mar, Carrer del Doctor Aiguader, 88, Barcelona, Spain

    Oriol Cunillera

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  1. Oriol Cunillera
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Correspondence to Oriol Cunillera .

Editor information

Editors and Affiliations

  1. University of Northern British Columbia, Prince George, BC, Canada

    Alex C. Michalos

  2. (residence), Brandon, MB, Canada

    Alex C. Michalos

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Cunillera, O. (2014). Tobit Models. In: Michalos, A.C. (eds) Encyclopedia of Quality of Life and Well-Being Research. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0753-5_3025

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  • DOI: https://doi.org/10.1007/978-94-007-0753-5_3025

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-007-0752-8

  • Online ISBN: 978-94-007-0753-5

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