Incomplete data poses formidable difficulties in the application of statistical techniques and requires special procedures to handle. The most common ways to solve this problem are by ignoring, truncating, censoring or collapsing those data, but these may lead to inappropriate conclusions because those data might contain important information. Most of the research for estimating cell probabilities involving incomplete categorical data is based on the EM algorithm. A likelihood approach is employed for estimating cell probabilities for missing values and makes comparisons between maximum likelihood estimation (MLE) and the EM algorithm. The MLE can provide almost the same estimates as that of the EM algorithm without any loss of properties. Results are compared for different distributional assumptions. Using clinical trial results from a group of 59 epileptics, results from the application of MLE and EM algorithm are compared and the advantages of MLE are highlighted.