Abstract
This paper suggests using a proportional hazard model to predict personal income, for the purpose of imputing missing income data in household travel surveys. The model has a hazard function that comprises two multiplicative components: (1) a non-parametric baseline hazard function that is dependent only on the income level and (2) a function that is dependent only on the other personal attributes of the survey respondents (excluding income). To estimate and validate the model, data is drawn from a travel characteristics survey conducted in Hong Kong in year 2001. The model is found to have a much higher accuracy when compared with a conventional ordered probit model based on the assumption that the logarithm of income is normally distributed.
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Notes
Although the likelihood function is in the form of an ordered logit model, it is a particular type of ordered logit model in which the logs of integrated baseline hazards (i.e., the δks) are assumed to be unknowns and treated as model parameters. The comparison model described in Sect. “An ordered probit model” is a standard ordered probit model because it is generally assumed that the logarithm of personal income follows a normal distribution.
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Acknowledgments
This study is supported by research grants HKU 7132/03E and No. 717306 from the Hong Kong Research Grant Council. The Transport Department of Hong Kong is gratefully acknowledged for providing survey data for model development. Two anonymous referees provided useful comments that resulted in improvements on an earlier draft of the paper.
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Tong, C.O., Lee, J.K.L. The use of a hazard-based duration model for imputation of missing personal income data. Transportation 36, 565–579 (2009). https://doi.org/10.1007/s11116-009-9213-0
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DOI: https://doi.org/10.1007/s11116-009-9213-0