https://kimcourage.github.io/Yonggi KimMethodology & Psychometrics 2026-09-28T16:48:54+09:00 Yonggi Kim https://kimcourage.github.io/ Jekyll © 2026 Yonggi Kim /assets/img/favicons/favicon.ico /assets/img/favicons/favicon-96x96.png Singular Value Decomposition2026-09-27T10:00:00+09:00 2026-09-27T10:00:00+09:00 https://kimcourage.github.io/mathematics/2026/09/27/singular-value-decomposition.html Yonggi Kim A square matrix with $n$ linearly independent eigenvectors factors into a product that separates directions from scalings. That factorization requires the matrix to be square and to have a full set of eigenvectors. For a rectangular matrix, eigenvalues are not defined, because the input space and the output space have different dimensions. Singular value decomposition provides a factorization o... Comparing Self-Esteem Across Ages with Moderated Nonlinear Factor Analysis2026-09-21T10:00:00+09:00 2026-09-21T10:00:00+09:00 https://kimcourage.github.io/research%20methods/2026/09/21/comparing-self-esteem-across-ages-with-moderated-nonlinear-factor-analysis.html Yonggi Kim Introduction A researcher plans to compare self-esteem between children aged 8 to 14. The 900 children come from a research panel of families, one child per family, with ages spread evenly. Age is computed from the date of birth. Each child completes a 10-item self-esteem questionnaire with five positively worded and five negatively worded items. Items are rated from 1, strongly disagree, to 5... Marginal Maximum Likelihood2026-09-21T10:00:00+09:00 2026-09-21T10:00:00+09:00 https://kimcourage.github.io/mathematics/2026/09/21/marginal-maximum-likelihood.html Yonggi Kim The maximum likelihood estimate is the parameter value under which the observed data is most probable. Finding it is direct when every variable in the model is recorded. Many models include variables that are never recorded. Examples include a random effect attached to each group, a latent ability attached to each examinee, and an unobserved class label attached to each measurement. One option ... Ordering Students by a Test Score with Mokken Scale Analysis2026-09-20T10:00:00+09:00 2026-09-20T10:00:00+09:00 https://kimcourage.github.io/research%20methods/2026/09/20/ordering-students-by-a-test-score-with-mokken-scale-analysis.html Yonggi Kim Introduction A researcher has written a 10-item fraction test for fifth grade, with items from basic to advanced tasks. Each item is scored 1 if correct and 0 if incorrect. The 500 fifth-grade students in the district schools that agreed to take part complete the test during a regular lesson. The researcher plans to rank students by total score and assign the lowest scorers to small-group inst... Profile Likelihood2026-09-17T10:00:00+09:00 2026-09-17T10:00:00+09:00 https://kimcourage.github.io/mathematics/2026/09/17/profile-likelihood.html Yonggi Kim A model might need several parameters to describe the data, but you might only care about one of them. The others are necessary parts of the model, and they have to take some value, but they are not the target of the investigation. The likelihood function is defined over all of these dimensions at once, and reading it for information about one parameter while the rest vary freely is hard. Profi...