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st: parameter estimation doubts


From   "Narasimhan Sowmyanarayanan" <narasimhan.sowmyanarayanan@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: parameter estimation doubts
Date   Wed, 23 Aug 2006 10:44:24 -0400

Hi All,

I have a question on parameter estimation. I would be grateful if
someone can give me opinion or some thoughts on this. I have a
situation where certain events are happening and I am classifying them
as successes or failures. Lets say my data looks like this

Total population - 300
period 1: 100 success and 10 failures
period 2:  50 success and 20 failures
period 3:  40 success  and 15 failures
period 4: 20 S and              45 F

I have tried to fit some alternative hazard functions to this kind of
data. My question is the following. Please excuse if some of it is
naive.

1. When I get values of expected success the sum of expected success
does not equal the sum of actual success for some of my functions. Is
this normal ? and what do you make out of it. When I do my Chi-Square
tests it gives me a message in stata that the numbers dont match (I am
using a downloaded script "chitest")

2. My overall mean absolute deviation is greater For the model (say
model a) where the sum of expected successes matches the sum of actual
successes as compared to the model where it does not match (say model
b). To add, the difference in the actual total success and the total
success for model B is not extremely large (2-3% point difference on
the total observations)

3. Just looking at the deviation every period between expected and
actual (eyeballing) tells me that the "model b" performs better than
"model a" even though the sum of actual values is different from the
sum of expected values.

The LR test typically rejects both models but I am not going to go by
it because I think eyeballing gives me a very good evidence of fit in
both cases.

I know I am not making any mistake in my likelihood functions. I have
seen that time and again. Model b for me gives better theoretical
motivation as compared to model a of the phenomenon though.

Could someone suggest which one I should choose. I can intuitively
understand why expected and actual need not match when I look at my
distibutions.

I hope I have provided all the information. I have been bugged by this
thought for a few days and I wanted some alternative opinions on this.

Thanks.
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