Summary. Social data often contain missing information. The problem is inevitably severe when analysing historical data. Conventionally, researchers analyse complete records only. Listwise deletion not only reduces the effective sample size but also may result in biased estimation, depending on the missingness mechanism. We analyse household types by using population registers from ancient China (618–907 AD) by comparing a simple classification, a latent class model of the complete data and a latent class model of the complete and partially missing data assuming four types of ignorable and non-ignorable missingness mechanisms. The findings show that either a frequency classification or a latent class analysis using the complete records only yielded biased estimates and incorrect conclusions in the presence of partially missing data of a non-ignorable mechanism. Although simply assuming ignorable or non-ignorable missing data produced consistently similarly higher estimates of the proportion of complex households, a specification of the relationship between the latent variable and the degree of missingness by a row effect uniform association model helped to capture the missingness mechanism better and improved the model fit.