This article investigates methodological problems of measuring family wealth among secondary school students with home possessions indicators. It employs multiple correspondence analysis (MCA) in order to explore (1) the dimensionality of home possessions items, (2) the nature of relationship between these items, and (3) the substantive meaning of the first and other relevant dimensions. It also employs regression analysis in order to study potential explanatory factors of the second dimension of the MCA solutions that may be related to measurement problems of the instrument. Two sources of data are used: (1) open access data from the National Survey of Student Achievement (NSSA) in Lithuania that provide a series of national educational studies conducted from 2002 to 2016, and (2) data from the Programme for International Student Assessment (PISA) study conducted in Lithuania in 2018 that is used to corroborate findings produced using the first data source. Results of the data analysis show that the first dimension of MCA solutions obtained from home possessions items in both NSSA and PISA data sets reflect high vs. low socio-economic status (SES) of the students. However, there is at least one more important dimension, and it reveals multi-dimensional nature of the measurement instrument. Analysis of potential explanatory factors of the second dimension of the MCA solutions revealed that reading abilities and school-related affect is related to this dimension. Thus, the second dimension of MCA solutions might also reflect methodological problems related to the measurement of home possessions in adolescent surveys.