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. Article type:research article

Evaluations of professor performance are based on the assumption that students learn more from highly qualified professors and the fact that students observe professor performance in the classroom. However, many studies question the methodologies used for such measurements, in general, because the averages of categorical responses make little statistical sense. In this paper, we propose Bayesian multi-faceted item response theory models to measure teaching performance. The basic model takes into account effects associated with the severity of the students responding to the survey, and the courses that are evaluated. The basic model proposed in this work is applied to a data set obtained from a survey of perception of professor performance conducted by Science Faculty of the Universidad Nacional de Colombia to its students. professor scores that are obtained as model outputs are real numerical values that can be used to calculate common statistics in professor evaluation. In this case, the statistics are mathematically consistent. Some of them are shown to illustrate the usefulness of the model.