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In longitudinal study, researchers are mostly interested in estimating growth parameters, which capture the intra- and inter-individual difference in the growth of a construct over time. In psychology research, many constructs are latent that are measured using multiple items. Researchers have advocated the use of curve-of-factors models to analyze longitudinal data. This paper focuses on the identification methods for latent factors in the curve-of-factors model. We show that under strict longitudinal measurement invariance, estimates of growth parameters depend on how the latent factors are assigned a scale. Applied researchers need to be cautious when interpreting estimates of growth parameters when the curve-of-factors model is applied.