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Comparisons of Tobit, Linear, and Poisson-Gamma Regression Models

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  • Judith E. Brown
  • Peter K. Dunn

Abstract

Time use data (TUD) are distinctive, being episodic in nature and consisting of both continuous and discrete (exact zeros) values. TUD is non-negative and generally right skewed. To analyze such data, the Tobit, and to a lesser extent, linear regression models are often used. Tobit models assume the zeros represent censored values of an underlying normally distributed latent variable that theoretically includes negative values. Both the linear regression and Tobit models have normality as a key assumption. The Poisson-gamma distribution is a distribution with both a point mass at zero (corresponding to zero time spent on a given activity) and a continuous component. Using generalized linear models, TUD can be modeled utilizing the Poisson-gamma distribution. Using TUD, Tobit and linear regression models are compared to the Poisson-gamma with respect to the interpretation of the model, the model fit (analysis of residuals), and model performance through the use of a simulated data experiment. The Poisson-gamma is found to be theoretically and empirically more sound in many circumstances.

Suggested Citation

  • Judith E. Brown & Peter K. Dunn, 2011. "Comparisons of Tobit, Linear, and Poisson-Gamma Regression Models," Sociological Methods & Research, , vol. 40(3), pages 511-535, August.
    • Handle: RePEc:sae:somere:v:40:y:2011:i:3:p:511-535
    DOI: 10.1177/0049124111415370
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    References listed on IDEAS

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    1. Cragg, John G, 1971. "Some Statistical Models for Limited Dependent Variables with Application to the Demand for Durable Goods," Econometrica, Econometric Society, vol. 39(5), pages 829-844, September.
    2. Hurd, Michael, 1979. "Estimation in truncated samples when there is heteroscedasticity," Journal of Econometrics, Elsevier, vol. 11(2-3), pages 247-258.
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    1. Priyanka Anand & Yonatan Ben-Shalom, 2014. "How Do Working-Age People With Disabilities Spend Their Time? New Evidence From the American Time Use Survey," Demography, Springer;Population Association of America (PAA), vol. 51(6), pages 1977-1998, December.
    2. Jones, Benjamin A., 2016. "Work more and play less? Time use impacts of changing ecosystem services: The case of the invasive emerald ash borer," Ecological Economics, Elsevier, vol. 124(C), pages 49-58.
    3. Spitzer, Sonja & Hammer, Bernhard, 2016. "The Division of Labour Within Households: Fractional Logit Estimates based on the Austrian Time Use Survey," MPRA Paper 81791, University Library of Munich, Germany.
    4. Lyn Craig & Janeen Baxter, 2016. "Domestic Outsourcing, Housework Shares and Subjective Time Pressure: Gender Differences in the Correlates of Hiring Help," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 125(1), pages 271-288, January.

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