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Latent curve models (LCMs) have been used extensively to analyse longitudinal data. However, little is known about the power of LCMs to detect nonlinear trends when they are present in the data. This study utilized simulated data to investigate the power of LCMs to detect the mean of the quadratic slope, Type I error rates, and rates of nonconvergence during the estimation of quadratic LCM. Five factors were examined: number of time points, growth magnitude and inter-individual variability, sample size, and the R² of the measured variables. The results showed that the empirical Type I error rates are close to the nominal value of 5%. The empirical power to detect the mean of the quadratic slope was affected by the simulation factors. Finally, a substantial proportion of samples failed to converge under the conditions of no to small variation in the quadratic factor, small sample sizes and small R² of the repeated measures. In general, we recommended that quadratic LCMs be based on samples of: (a) at least 250 but ideally 400 when 4 measurement points are available; (b) at least 100 but ideally 150 when 6 measurement points are available; (c) at least 50 but ideally 100 when 10 measurement points are available.


Institute for Positive Psychology and Education

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Open Access Journal Article

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Open Access


Authors accepted manuscript. The final publication is available at Springer via

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