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Unformatted text preview: mizes the probability of obtaining the
data
from the known distribution. Combining
and
as follows, we can consider the
two classes at the same time: Assuming the data P(Y = 0  X = x) is drawn independently, the likelihood function is Since it is more convenient to work with the log likelihood function, take the log of both sides, we get So, wikicour senote.com/w/index.php?title= Stat841&pr intable= yes 28/74 10/09/2013 Stat841  Wiki Cour se Notes To maximize the log likelihood, set its derivative to 0. There are n+1 nonlinear equations in / β. The first column is vector 1, then i.e. the expected number of class ones matches the observed number. To solve this equation, the Newton Raphson algorithm (http://numericalmethods.eng.usf.edu/topics/newton_raphson.html) is used which requires the second derivative in
addition to the first derivative. This is demonstrated in the next section.
Advantage s and Dis advantage s
Logistic regression has several advantages over discriminant analysis:
it is more robust: the independent variables don't have to be normally distributed, or have equal variance in each group
It does not assume a linear relationship between the IV and DV
It may handle nonlinear effects
You can add explicit interaction and power terms
The DV need not be normally distributed.
There is no homogeneity of variance assumption.
Normally distributed error terms are not assumed.
It does not require that the independents be interval.
It does not require that the independents be unbounded.
With all this flexibility, you might wonder why anyone would ever use discriminant analysis or any other method of analysis. Unfortunately, the advantages of logistic
regression come at a cost: it requires much more data to achieve stable, meaningful results. With standard regression, and DA, typically 20 data points per predictor is
considered the lower bound. For logistic regression, at least 50 data points per predictor is necessary to achieve stable results.
some resources: [15] (http://www...
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 Winter '13

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