Re: MLE
- From: vontressms@xxxxxx
- Date: Wed, 28 May 2008 05:59:04 -0700 (PDT)
On May 21, 12:09 am, sagar <ariji...@xxxxxxxxx> wrote:
Hi,
I want to know what are the properties that made MLE a better
regression model than OLS. I also want to know what are the properties
of MLE.
Arijit
In my opinion, MLE is generally a better way to go when you have a
linear model embeded in the mean of a random variable. In the case
where the random variable is normal (with a constant variance), OLS
and MLE give the same answer. But suppose our mean from a poisson is
exp(b0+b1*x), we would want to maximize the likelihood function with
respect to b0 and b1 to make our best inference about the poisson
response variables. The large sample properties of the MLE estimates
help with inference about the regression parameters. You can find more
discussion about this in the subject called genearlized linear
models.
OLS is okay if you just want to draw a line of best fit through the
data and don't really care about the distribution of the residuals.
You can make some inference about the parameters using the large
sample normality of the parameter estimates, much in the same way we
use the central limit theorem to make inference about a population
mean from the large sample properties of the sample mean. However,
inference or prediction about the response variables may not be very
good when using OLS for non-normal data. You usually have to use
transformations for this to work well. You can connect generalized
linear models to these transformations - called "links" and then
weighted least squares is used to estimate the parameters, rather than
OLS.
Mark
.
- References:
- MLE
- From: sagar
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