Which one of the following are valid link functions? Recall that a link function g is required to be monotone increasing and differentiable. (Choose all that apply.)

Note: The link function, in general, can be monotone increasing or monotone decreasing. In this class, we have chosen as convention to require it be monotone increasing.

g(\mu ) = \mu , \mu \in \mathbb {R}

g(\mu ) = -\frac{1}{\mu }, \mu > 0

g(\mu ) = \mu ^2, \mu \in \mathbb {R}

\ln \left(\frac{\mu ^3}{1-\mu ^3}\right),\, 0<\mu < 1

-\ln \left[-\ln \left(\frac{\mu }{n}\right)\right], 0 < \mu < n and n > 0 known

1 answer

The valid link functions are:

g(\mu ) = \mu , \mu \in \mathbb {R}

g(\mu ) = \mu ^2, \mu \in \mathbb {R}

\ln \left(\frac{\mu ^3}{1-\mu ^3}\right),\, 0<\mu < 1