# Re: st: RE: Generating skewed distributions on closed intervals

 From Reza C Daniels <[email protected]> To [email protected] Subject Re: st: RE: Generating skewed distributions on closed intervals Date Thu, 29 Sep 2005 13:28:39 +0200

Hi Maarten,

My problem is exactly one of data coarsening, as explained by Heitjan and Rubin (JASA, 1991). The exception is that they applied this to heights and I'm wanting to apply it to age.

I am also aware of the need to multiply impute. However, I wanted the uniform, normal and skewed distributions first before imputing, so that once I obtained the multiply imputed estimates, I would have something to compare them to.

Reza

Maarten Buis wrote:

Hi Reza,

Will you be using this new age variable as a
dependent/explained/y-variable or as an
independent/explanatory/x-variable?

If you are using age as an explained variable you will probably end
up in survival analysis, and they have good techniques of dealing
with discrete time, so I see no need to invent something new there.
See: "An Introduction to Survival Analysis Using Stata" by Mario
Cleves, William W. Gould, and Roberto Gutierrez available from Stata
Press.

If you will be using age as an explanatory variable than it is good
to know that even very coarsely categorized variables often produce
good estimates. If you still want to do something about the
categorisation, than you would probably want to do some form of
multiple imputation. The way to think about it is that there is one
age distribution, which was chopped up in bits. You don't want to use
different distributions for each age band, since than you would
assume a very bumpy overall age distribution. So you would first
estimate the parameters of this age distribution. Than if you wanted
to draw an age for a person in category 20-30, you would draw from a
value this distribution truncated between 20 and 30. You would create
multiple datasets this way, estimate the regression or whatever other
parameter of interest for each of these datasets, and the mean of
these effects would be your estimate controlling for the
categorisation of age. However, I repeat that this is probably more
trouble that its worth.

I'd like to be sure that this is what you want, before I spent an
afternoon writing Stata code for you.

Maarten

-----Original Message----- From: [email protected]
[mailto:[email protected]]On Behalf Of Reza C
Daniels Sent: donderdag 29 september 2005 12:34 To:
[email protected] Subject: Re: st: RE: Generating skewed
distributions on closed intervals

Hi Maarten,

I tried this in the following way:

set obs 100 -gen z1=invnorm(uniform())- where z>0 -gen z2=ln(z1)- for
positively skewed -gen z3=exp(z1)- for negatively skewed

As I'm sure you know, this gives me the correct shape of the distributions I'm looking for, but the incorrect range.

So, I still can't solve it.

Thanks anyway, Reza

Maarten Buis wrote:

It reminds me of an ordered probit problem: you have one unobserved
distribution, which is being carved up. Only now you also have
information about where the cuts are made. This should be solvable.
You might want to look at the log normal instead of the normal
though, since no one can get, or has ever been, -2 (even with
plastic surgery).

-----Original Message----- From:
[email protected]
[mailto:[email protected]]On Behalf Of Nick Cox Sent: donderdag 29 september 2005 11:09 To:
[email protected] Subject: RE: st: RE: Generating
skewed distributions on closed intervals

Well, I guess wildly the literature you are unaware of holds better
solutions, but that's an empty comment as I don't know what it is.
The idea that an age distribution is a bunch of little truncated Gaussians sitting next to each other on a line sounds at best
strange to me, but as I said I don't understand what your problem
is.

Nick [email protected]

Reza C Daniels

```There is a literature on this problem that I am aware of. I'm
just having trouble with the code in Stata to generate my
required results.
```
```
```
```Whatever your problem is, it is difficult to believe that there
is not a literature on it, e.g. in demography, actuarial
science, population ecology.
```
```

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