A design framework for longitudinal individual difference research: Conceptual, methodological, and analytical considerations

Individual growth curve modeling for applied linguistics research

“…Need frustration, a hypothesized antecedent of disengagement, represents the frustration of basic psychological needs in three subdimensions and was measured in a similar way. Before conducting IGCM, CFA and longitudinal measurement invariance tests (i.e., configural, metric, and scalar) were performed for the disengagement and need frustration constructs, confirming that equivalence of measurement for all constructs was established across time (see also Nagle, 2022). Gender was treated as a dummy variable with 0 for female and 1 for male.…”

“…This is essential because different individuals may exhibit a different trajectory for a certain outcome: some trajectories may change in a linear way, some may include curves (i.e., quadratic change), some may exhibit rising and falling trajectories (i.e., cubic change), and some may demonstrate floor or ceiling effects (i.e., nonlinear change). The strength of IGCM to investigate developmental trajectories of outcome variables in such a flexible way is especially crucial in language learning research (Nagle, 2022), which increasingly considers language learning as a complex dynamic process with nonlinear features such as discontinuities and fluctuations in variability. Investigating individuals' change using IGCM also resonates with calls from theorists and methodologists alike (e.g., Larsen-Freeman, 2009;Verspoor & de Bot, 2022;Han et al, 2022) who argue that individual variability is the core of researching intraindividual phenomena such as language learners' development.…”

Measuring the development of general language skills in English as a foreign language—Longitudinal invariance of the C-test

“…In applied linguistics, there is a high demand to ensure test scores' comparability over time to recommend certain instruments for usage in longitudinal research designs (Nagle, 2022). CFA proved to be the method of choice for longitudinal measurement modeling to investigate their longitudinal MI.…”

“…CFA is a widely used method for modeling theoretical constructs in educational measurement (Brown, 2015), especially in longitudinal designs (Little, 2013). However, in applied linguistics, there is a high demand for implementing this method to ensure the comparability of language test scores over time to recommend their usage in longitudinal research designs (Nagle, 2022).…”

“…One challenge in measuring language development arises from the fact that tests used for cross-sectional measurements are not necessarily applicable to longitudinal designs. In settings with repeated measurements of theoretical constructs, such as language proficiency, tests must meet both: (1) standards of test quality such as validity, reliability, and objectivity (American Educational Research Association [AERA], 2014) and (2) longitudinal measurement invariance (MI) which allows for valid interpretations of the development in test scores over time (Barkaoui, 2014; Nagle, 2022). Development is defined as a change over time (Little, 2013).…”