Theory construction in cognitive psychology relies on choosing a suitable statistical model for data analyses. I hypothesized that the general linear model (GLM), which is currently used for analyzing data in the field of mental arithmetic by most researchers, is not suitable for analyzing data that is typical in this field. In particular, mental arithmetic data have three features that make them unsuitable for GLM analyses: repeated measurements from individual participants, a mixture of categorical and continuous predictors, and unevenly distributed observations across levels of predictors. I proposed an alternative approach using linear mixed models (LMM), as a better candidate. I tested the hypothesis by applying GLM and LMM to three archival datasets typical in the field of mental arithmetic. Across the re-analyses, LMM consistently showed advantages over GLM. LMM was used successfully on unbalanced designs (Chapter 5) and better preserved the continuous nature of independent variables (Chapters 3, 4, and 5). I discussed the findings and provided advice for researchers who want to adopt LMM in their studies.