National Cotton Variety Test (NCVT) was established in 1960 to standardize collection and analysis of field data for objectively evaluating new upland and Pima cotton varieties. The data from the NCVT is referred to as the multi-environment trials, which are essentially a series of field trials or experiments on different varieties across a range of geographic locations and over several years (or seasons). Missing data is one of the major challenges in statistical analyses because most of the varieties are only tested for one or two years. In addition, the underlying mechanism of missingness is complicated. First, both missing completely at random and missing not at random are present in NCVT. Secondly, the decision whether a variety is tested at a certain year after the entry depends on a set of traits, but these traits might not be the target trait which is of main interest. We analyze the NCVT data via joint modeling, and we consider the EM algorithm to estimate the parameters. The proposed method can accommodate different missing mechanisms. We also adapted the EM algorithm in which only the missing values under MNAR are sampled, and less computation is required.