Tobit with Varied Censor Bounds

[atm4jg]

For my project, my dependent variable Yi is (# of Suicides)/(Population of county/100000). However the CDC censors data from Counties with less than 9 suicides. Thus I have a tobit model with a bound that varies based on the population.
My first solution was to have a new dependent variable Zi where Z=Yi-ci and ci=100000*9/Population. Then the model would be tobit Zi=XiB-aci+ui with a lowerbound on Zi of 0. The problem is that I cannot constrain the coefficient a to be -1 because tobit does not have the constraint option.

I have been researching all day and don't know what other solution there is to my problem. There is an offset option for tobit but I don't know if that is the correct solution for this issue. Some
say that for rate regression models like Poisson, they add the ln(Population/100000) to the right side and log transform the dependent variable but I am not able to understand if this applies to tobit.

Any help would be much appreciated.

[Clyde Schechter]

I think you can get what you want with the -intreg- command.

[Clyde Schechter]

I don't know. I've never used -cnreg-, and according to the help, it's an unsupported command.

To use -intreg- for your problem it would look something like this. I'm assuming that you have, or can create, a variable, censor, which identifies which observations in your data are censored.

gen lower_dv = Z if !censor
replace lower_dv = . if censor
gen upper_dv = Z if !censor
replace upper_dv =  9*100000/Population if censor
intreg lower_dv upper_dv [whatever...]

[Kieran McCaul]

Your suicide data has:
count - the number of suicides in a given time period (1 year, say);
pop - the size of the population in which these suicides occurred.
This should be the population size in the middle of the time period. If the suicides are counted over a calendar year, the population would be the mid-year population. The mid-year population size is an estimate of the total person-years accumulated over the period of time that the suicides were observed.

You could model this with:

poisson count, exp(pop)

However, your counts are left-censored, so you need a Poisson model that will handle this.

Have a look at Joe Hilbe's cpoissone program, this will fit left-censored poisson models.

[Nick Cox]

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