Financial capital measure with item response theory: A didactic approximation - Henry Sebastián Rangel Qui\~nonez; Alvaro Mauricio Montenegro Díaz; Luisa Fernanda Arenas Estevez (Entrepreneurial Business and Economics Review (EBER), 2022)
Objective: The objective of the article is to present in a didactic and concise way the fundamental concepts of item response theory (IRT) and its possible application in the economic sciences and show the bias problem that occurred when estimating a latent variable such as financial capital in microentrepreneurs through IRT, assuming normal distribution in an unfounded a priori way. Research Design & Methods: We introduce a Bayesian hierarchical IRT model for graded responses where the latent traits have a skew normal distribution. Financial capital was measured by a survey applied to 384 microentrepreneurs from the metropolitan area of Bucaramanga (Colombia). The preliminary statistical analysis of data hints that the latent trait is not symmetric. Models that include a normal and a skew normal distribution were tested. Findings: We detected that assuming the distribution of the normal trait may overestimate the calculation of financial capital in microentrepreneurs, which would cause loans to be assigned without support. Implications & Recommendations: When applying IRT to economic matters such as in the measurement of financial capital, it is recommended to review the assumptions that this technique handles, especially the normality of the latent trait, since if assumed without verification or theoretical support can cause bias in parameters. Contribution & Value Added: An improvement is presented to the graded response model with normal distribution in IRT for the measurement of financial capital, paying special interest in providing a pedagogical explanation for a public related to economics.
Keywords: G21; C11; C52; 330; IRT in economics; Skew model; Latent trait; Graded Model; Bayesian method; Financial Capital