Nonignorable missingness in the outcome variable complicates the longitudinal data analysis, as it is necessary to incorporate the missing data model into the observed data likelihood function. We investigate two approximate likelihood methods, bivariate pseudo-likelihood (BPL) of Sinha et al. (2011) and independent pseudo-likelihood (IPL) of Troxel et al. (1998), along with the exact likelihood, for analyzing longitudinal data with nonignorable and nonmonotone missing responses. Our numerical study shows that the BPL is more efficient than the IPL method in terms of both smaller biases and MSEs, especially when the within-subject correlation is high. Investigating the standard errors of estimators in an application with real world data, we also get similar findings. Overall, similarly to Sinha et al. (2011), our study confirms better performance of the BPL method over the IPL method when the number of longitudinal outcomes from a given subject is small.