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My situation is as follows: Respondents in my questionnaire had the option to take money (anything from 0-10). In the end, they were advised to take that money out of an envelope. This process was not controlled, so they were able to take a different amout of money and "steal", so to say. I want to analyze this stealing (in a tobit modell or linear regression).

My problem is that not everyone had the same chance to steal. Someone who took all the money officially cannot deviate positively from this amount. Some people actually took out less than what they noted in the questionnaire, so they have a negative amount of stealing.

I thought about only analyzing positive amounts of stealing and work with a tobit modell. Alternatively, I could analyzie all deviations and work with a linear regression. Nevertheless, one problem stays: People are not really comparable. People with a stealing amount of zero are either honest or have taken all the money in the first place and there wasn't anything left to steal. Is there a statistical method to solve this dependency (I work with Stata in case that matters)?

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    $\begingroup$ So there were 0-10 (dollars, euros, whatever) in an envelope, & each person was told they were allowed take some amount, $a$, but they actually took some amount, $t$, & subsequently reported taking some amount, $r$. Is that right? Do you have the $a, t, r$ values for each person? Do you want the model to help you test a hypothesis, or to predict something? What? $\endgroup$
    – gung - Reinstate Monica
    Jul 18, 2015 at 20:26
  • $\begingroup$ They were allowed to take the amount reported beforehand, $r$ and took some amount $t$. I do have $r$ and $t$ values for each person, yes. I'm trying to test a hypothesis. For example how, let's say hair colour affects how much a person reported to take ($r$) and how much she steals ($t-r$). Calculating a model with $r$ as dependent variable is straight forward, but I'm confused how to include the stealing-value since the people are not really comparable (like I explained before). Understandable? $\endgroup$
    – user3804488
    Jul 18, 2015 at 20:39
  • $\begingroup$ It sounds like $t-r$ is your real dependent variable, & you need the tobit to somehow address the fact that $10-r$ is sometimes $0$. Is that right? $\endgroup$
    – gung - Reinstate Monica
    Jul 18, 2015 at 20:51
  • $\begingroup$ Basically, yes. But my problem is that $t-r$ can be $0$ because people were honest, reported to take $r$ and did take $r$ ($r=t$) or because people reported to take all the money and did not have the chance to behave dishonestly ($r=10$). $\endgroup$
    – user3804488
    Jul 18, 2015 at 21:09
  • $\begingroup$ Additionally: I would only use the tobit modell if I ignored the people where $t<r$ and only address people who actually stole something, since only then my data is censored at $0$. $\endgroup$
    – user3804488
    Jul 18, 2015 at 21:13

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