Hi Viridiana,
The terms 'expected' and 'predicted' as presented on the lecture
slides
refer to the value of the outcome variable y, so we are interested in the
difference between expected values and predicted values.
In this case, an expected value is a probability, so we can use the terms
expected probability and expected value interchangeably. Notice that if we
average over a lot of outcome variables, we're averaging a lot of 1's and
0's, which means we're dividing the total number of 1's by the total
number
of 1's and 0's, which means we get a probability of o-ring failure. (hence,
the last step in simulating an expected value returns a probability).
You rightly point out that the dependent variable in this case is
dichotomous- either o-rings fail or they do not; y can only be a zero or a
one. To estimate one expected value, you draw one set of betas (a B0 and a
B1), fix your x's, and calculate a probability using the function you
mentioned (1/(1+e^(-Bxi)) ). That function will return n probabilities,
where n is the number of observations. Plug those n probabilities in to the
stochastic component to get n y's, average those n y's, and you have one
expected value/expected probability. (note that these last two steps are
superfluous in the case of a logit model).
Hope this helps,
Jenn
On Sat, Mar 15, 2008 at 3:33 PM, Viridiana Rios <vrios at fas.harvard.edu>
wrote:
Hi all,
Can anybody please, explain to me the difference between expected values
and expected probability in the context of a dichotomic dependent variable?
Here is my confusion: We have a probit model (y=B0+B1x1). We draw 1000
Betas from a normal distribution. We calculate y=B0+B1x1 using all the Betas
of the draw. So, now we have 1000 different values of y (one for each draw
of Betas). Then, we transform y to a probability using the function
1/(1+e^(-Bxi)). Now we have 1000 different probabilites. Are these
probabilities the expected probability or the expected value? If these are
the expected probabilities, howe can I get the expected values? Are the
expected values the 1000 values of y?
Best,
Viridiana R?os
617-997-2471