returns the log of the likelihood of theta, given a vector of item responses, item parameters. Note that this is the simple ll - it is the continuing product of the response probabilities. It includes a hack, that will nudge the raw response to the first item to adjust for zeros and perfects. This should be updated to work with adjusted raw scores instead...
theta_ll(theta, responses, itemParams)
Arguments
theta: a scalar value of theta.
responses: a vector of item responses (used in a call to pX).
itemParams: a list of item designs (each used in a call to simplef). Must be of same length as responses.