The Effect of Sampling-Time Variation on Latent Growth Curve Models

Abstract

Longitudinal data are often collected in waves in which a participant’s data can be collected at different times within each wave, resulting in sampling-time variation that is unaccounted for when waves are treated as single time points. Little research has been reported on the effects of this temporal imprecision on longitudinal growth-curve modeling. This article describes the results of a simulation study into the effect of sampling-time variation on parameter estimation, model fit, and model comparison with an empirical validation of the model fit and comparison results.

Keywords:

• fit indexes
• longitudinal growth curve model
• parameter bias
• sampling

ACKNOWLEDGMENTS

The authors would like to thank Dr. Joseph E. Gonzales for providing inspiration and advice on this research.

Notes

¹ Because perfect synchronicity in data collection times is not usually possible, some might argue that all longitudinal data are collected in waves; it is not our intention to nitpick small variations in data collection intervals.

² In some cases, even when data are collected with reasonable synchrony, individuals’ actual change over time might not be perfectly synchronous, resulting in similar effects on data collection.

³ Note that Hu and Bentler (1999) suggested researchers not rely solely on the thresholds they recommended.

⁴ In this case, groups of students within the same schools will share the same time binning variations, but cases in which each individual has an idiosyncratic pattern of time binning can be imagined.

⁵ The distance between the initial times of measurement for different individuals is subsumed under this question as part of the overall effect of sampling-time variation.

⁶ The first Monday was scored as Day 0 for the linear and quadratic models, and as Day 7 for the logarithmic model to avoid taking the log of 0; further, the linear term was omitted from the quadratic model because we were simply determining if the empirical data matched the stylized functional form.

⁷ The algorithm provided in Yuan et al. (2016) to estimate the noncentrality parameter does not work properly when chi-square gets close to degrees of freedom, and degrades in performance even before it fails entirely (see Venables, 1975). Because many models in our research fit the data very well, we modified the algorithm as described in the technical note in Appendix C.

⁸ Note that for goodness-of-fit tests, cases with a passing fit index for a model that did not fit the data-generating model were coded as successes; that is, these cases were incorrect successes. For fit-comparison tests, there were no incorrect successes, because success in this case only referred to correct model selection. Because only 100 replications were conducted for each condition, there were some conditions in which 0 or 100 successes were recorded; these conditions were assigned dummy logistic values of −5.3 and 5.3, respectively (corresponding to success rates of .005 and .995) to allow those conditions to be entered into the regression. Because these tests were used only to provide guidance on display of the results and are not part of our substantive conclusions, we believe this interpolation was reasonable.