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We consider a linear mixed-effects model in which the response panel vector has missing components and the missing data mechanism depends on observed data as well as missing responses through unobserved random effects. Using a transformation of the data that eliminates the random effects, we derive asymptotically unbiased and normally distributed estimators of certain model parameters. Estimators of model parameters that cannot be estimated using the transformed data are also constructed, and their asymptotic unbiasedness and normality are established. Simulation results are presented to examine the finite sample performance of the proposed estimators and a real data example is discussed.