Performance of second-order latent growth model under partial longitudinal measurement invariance: A comparison of two scaling approaches
Professor Su-Young Kim’s recent publication, “Performance of second-order latent growth model under partial longitudinal measurement invariance: A comparison of two scaling approaches,” investigates some new scaling approaches in the context of analyzing longitudinal data in the social sciences.
The temporal change of humans is of fundamental interest in the social and behavioral sciences. Latent growth models (LGMs) have been a preferred form of longitudinal data analysis for decades. This univariate approach is easily implemented but limited in that it treats the construct as if it was free from measurement errors. As a potential solution to this limitation, second-order latent growth models (SLGMs) have received increasing attention from methodologists and substantive researchers in recent years. As an extension of traditional LGM, SLGM allows multiple items at each measurement occasions in the model by substituting a complete measurement model for a single indicator in the traditional LGM. This multivariate approach has been mentioned as advantageous in modeling the change of a theoretically error-free latent factor (Hancock et al., 2001).
Although there is little room for doubt about the known theoretical strengths of SLGMs, applying them in real life is not as straightforward as suggested. In SLGM, the first-order measurement model requires scale assignment on latent factors (i.e., scaling) for model identification. From among several scaling methods for common measurement models, two in particular – marker variable and effects coding – assign meaningful metrics to latent factors in their longitudinal context. Because the effects coding method was introduced in relatively recent years (Little et al., 2006), the marker variable method has been dominant among real applications so far.
The marker variable method, however, runs the risk of model misspecification in case of a mischosen scaling item. In contrast to the item-level invariance of the marker variable method, the effects coding method presupposes scale-level invariance for an item set across time. While the marker variable method would yield a model misspecification with only a non-invariant scaling item, the effects coding method might not produce a model misspecification even with a non-invariant scaling item as long as the scale-level invariance holds across time.
The investigation of a less-risky scaling method for the estimation of SLGM under possible partial measurement invariance (MI) situations is therefore a critical issue for real applications. The purpose of the study was to investigate and compare the performance of two scaling methods, the marker variable method and the effects coding method, in the estimations of an SLGM under partial longitudinal MI. To achieve this aim, a series of Monte Carlo simulations was conducted under various partial MI conditions. The results are as follows. Using the marker variable method for scaling SLGMs seems to be reasonable as long as researchers can select an invariant scaling item. In a practical point of view, however, applying the marker variable method should pose a risk as it is hard to determine one truly invariant item among multiple items in real-world data (Jung & Yoon, 2017). Compared with the marker variable method, the effects coding method is a relatively undemanding approach as it does not require that we select an item for scaling. The robustness to the non-invariant scaling item may also suggest the effects coding method’s appeal when the selection of an invariant scaling item is ambiguous.
Although the simulation conditions somewhat limit the generalizability of the findings, the results should be useful in understanding the two scaling methods, the marker variable and effects coding approaches, for SLGM-based studies. The present study provides a first thorough investigation of the impact of these two different scaling methods and their relative performance for an SLGM. The study, with all its findings and discussions, suggests that researchers who are willing to apply an SLGM should be aware of the possible risk of scaling-related misspecification unless data fully satisfy longitudinal MI, and that the effects coding method could be a practical and beneficial mode of scaling in SLGM.
Hancock, G. R., Kuo, W. L., & Lawrence, F. R. (2001). An illustration of second-order latent growth models. Structural Equation Modeling, 8(3), 470-489.
Jung, E., & Yoon, M. (2016). Comparisons of three empirical methods for partial factorial invariance: forward, backward, and factor-ratio tests. Structural Equation Modeling, 23(4), 567-584.
Little, T. D., Slegers, D. W., & Card, N. A. (2006). A non-arbitrary method of identifying and scaling latent variables in SEM and MACS models. Structural Equation Modeling, 13(1), 59-72.
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Min-Jeong Jeon, Su-Young Kim, Performance of Second-Order Latent Growth Model Under Partial Longitudinal Measurement Invariance: A Comparison of Two Scaling Approaches, Structural Equation Modeling: A Multidisciplinary Journal, Volume 28, 2021 - Issue 2