Multidimensional Profiles of Critical Thinking in Physics Labs: Latent Structure, Instructional Change, and Connections to Physics Identity

The Physics Lab Inventory of Critical Thinking (PLIC) measures three components of students' critical thinking in physics labs: evaluating data, evaluating methods, and proposing next steps. Prior work has analyzed these components in isolation or as a composite score. In this study, we apply latent profile analysis (LPA) to the three PLIC scales using a large, multi-institutional dataset of 5,513 matched pre/post student records to identify characteristic response patterns across the three components simultaneously. At both pre- and post-instruction, a two-profile solution best fit the data. Profile composition shifted substantially over instruction, with 48.4\% of students in the lower-performing profile at pre-test transitioning to the higher-performing profile at post-test, while 43.6\% of students moved in the opposite direction. Course type was statistically associated with profile membership at both timepoints, though the effect was small (Cram\'er's $V \approx 0.10$). To examine the relationship between profile transitions and students' affective development, we estimated cross-lagged panel models (CLPMs) linking profile membership to belonging, recognition, self-efficacy, and agency. Belonging emerged as the principal upstream predictor, prospectively predicting recognition, self-efficacy, agency, and higher-knowledge profile membership. Agency and self-efficacy formed a reciprocal but asymmetric loop, with the path from agency to later self-efficacy being stronger. Recognition functioned primarily as a downstream construct over this timescale. These results provide the first person-centered, multidimensional characterization of PLIC performance and demonstrate that epistemic and identity-related constructs are interlinked in physics lab learning.