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  • ​Ordinal probit model with ordinal endogenous regressor

    We are researching the determinants of stress. We are motivated in our study to determine if commute to work contributes to stress, in addition to other triggers.

    Our dependent variable is an ordinal variable for self-reported levels of stress. We have used ordered probit model to regress self- reported levels of stress on controls (explanatory variables).

    One of our key variables is self-reported (dis) satisfaction with commuting. We have been advised that commute satisfaction (COMSAT) may be endogenous. Also, stress may contribute to COMSAT as much as COMSAT may contribute to stress. We do have other proxies for the commuting effort: mode of travel, commute duration, frequency of exposure to traffic congestion.

    We need help in answering the following questions:
    1. Unknown heterogeneity may be influencing both commute time satisfaction and stress. Unobserved traits, such as optimism versus pessimism may be behind both.
      1. Also, we do not have information on job satisfaction and other related factors.
    2. Two-way causation. Commute time dis/satisfaction may be causing stress, or stress may be responsible for commute time dis/satisfaction.
    We believe some variation of the instrumental variable approach is needed. Given that both the dependent variable and the endogenous variable are ordinal, we are hoping to land on an ordinal probit model with ordinal endogenous regressor.

    We have come across gsem for ordinal probit model with endogenous regressors (http://blog.stata.com/2013/11/07/fit...-gsem-command/) and cmp (http://www.stata-journal.com/article...article=st0224). Some colleagues are suggesting path analysis (SEM, http://www.stata.com/stata12/structu...tion-modeling/).

    We are requesting colleagues to help us determine if we are heading in the right direction (the IV approach) and to recommend more apt routines/approaches.

    We remain grateful for any help the Stata community is able to offer.

    Best regards,
    Murtaza Haider
    [email protected]

    PS. We have cross-sectional data set. Explanatory variables used from the data set included the following:

    Demographics:
    - Education
    - Income. categorical
    - Gender (male/female)
    - Age, categorical
    - Children at home (yes/no)
    - Province of residence in Canada
    Transport-related variables:
    - Mode of travel to work: transit, car, etc.
    - Commute time satisfaction. Satisfied, not satisfied, etc.
    - Exposure to traffic congestion: Never, sometimes, every day, etc.
    - Commute duration: categorical in minutes, 0 to 10 minutes, 11 to 20 minutes, etc.
    Work-life balance
    - Flexible work hours allowed (yes/no)
    - Enough time for familial responsibilities (categorical)
    - Hours worked in a week, categorical
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