Historical documents in social and emographic research inevitably contain partially missing data. Conventionally, researchers analyze complete records only. Listwise deletion not only reduces effective sample size, but also may result in biased estimation, depending on the missing mechanism. This paper begins with a simple classification of the household structure in Tang China (618-907 AD). A latent class model is then used to estimate the latent complex household with the complete data. The model further includes partially missing data via the EM algorithm, assuming MCAR and NMAR in two separate analyses. The findings show that either a frequency classification or a latent class analysis using the complete records only will yield biased estimates and incorrect conclusion in the presence of partially missing data of nonignorable mechanism.