This paper illustrates two psychometric methods, latent class analysis (LCA) and taxometric analysis (TA) using empirical data from research probing children's mental representation in science learning. LCA is used to obtain a typology based on observed variables and to further investigate how the encountered classes might be related to external variables, where the effectiveness of classification process and the unbiased estimations of parameters become the main concern. In the step-wise LCA, the class membership is assigned and subsequently its relationship with covariates is established. This leading-edge modeling approach suffers from severe downward-biased estimations. The illustration of LCA is focused on alternative bias correction approaches and demonstrates the effect of modal and proportional class-membership assignment along with BCH and ML correction procedures. The illustration of LCA is presented with three covariates, which are psychometric variables operationalizing formal reasoning, divergent thinking and field dependence-independence, respectively. Moreover, taxometric analysis, a method designed to detect the type of the latent structural model, categorical or dimensional, is introduced, along with the relevant basic concepts and tools. TA was applied complementarily in the same data sets to answer the fundamental hypothesis about children's naïve knowledge on the matters under study and it comprises an additional asset in building theory which is fundamental for educational practices. Taxometric analysis provided results that were ambiguous as far as the type of the latent structure. This finding initiates further discussion and sets a problematization within this framework rethinking fundamental assumptions and epistemological issues.
Keywords: BCH and ML corrections; L-Mode; MAXEIG; comparison curve fit index; latent class analysis; mental models; taxometrics MAMBAC; taxon.