where is the product operator. Note that we can write the joint probability density function as a product of individual density functions because each Yi is drawn independently and each Yi has the same (logistic) density function. The joint probability given in Eq. (4) is known as the likelihood function (LF).
Equation (4) is a little awkward to manipulate. But if we take its natural logarithm, we obtain what is called the log likelihood function (LLF):
n ln f (Y1, Y2,..., Yn) = ^ [Yi ln Pi + (1 - Yi)ln(1 - Pi)]
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