Lord's bias function and the weighted likelihood estimation method are effective in reducing the bias of the maximum likelihood estimate of an examinee's ability under the assumption that the true item parameters are known. This paper presents simulation studies to determine the effectiveness of these two methods in reducing the bias when the item parameters are unknown. The simulation results show that Lord's bias function and the weighted likelihood estimation method might not be as effective in bias reduction in the 3PL cases when item parameters are unknown as they are when the true item parameters are given. Algorithms and methods for obtaining the global maximum value of a likelihood function or a weighted likelihood function are discussed in this paper.