Latent growth curve models with spline functions are flexible and accessible
statistical tools for investigating nonlinear change patterns that exhibit
distinct phases of development in manifested variables. Among such models, the
bilinear spline growth model (BLSGM) is the most straightforward and intuitive
but useful. An existing study has demonstrated that the BLSGM allows the knot
(or change-point), at which two linear segments join together, to be an
additional growth factor other than the intercept and slopes so that
researchers can estimate the knot and its variability in the framework of
individual measurement occasions. However, developmental processes usually
unfold in a joint development where two or more outcomes and their change
patterns are correlated over time. As an extension of the existing BLSGM with
an unknown knot, this study considers a parallel BLSGM (PBLSGM) for
investigating multiple nonlinear growth processes and estimating the knot with
its variability of each process as well as the knot-knot association in the
framework of individual measurement occasions. We present the proposed model by
simulation studies and a real-world data analysis. Our simulation studies
demonstrate that the proposed PBLSGM generally estimate the parameters of
interest unbiasedly, precisely and exhibit appropriate confidence interval
coverage. An empirical example using longitudinal reading scores, mathematics
scores, and science scores shows that the model can estimate the knot with its
variance for each growth curve and the covariance between two knots. We also
provide the corresponding code for the proposed model.Comment: \c{opyright} 2020, American Psychological Association. This paper is
not the copy of record and may not exactly replicate the final, authoritative
version of the article. Please do not copy or cite without authors'
permission. The final article will be available, upon publication, via its
DOI: 10.1037/met000030