The Latent Time-to-Criterion Model: Research Design Considerations for Optimizing Parameter Estimate Accuracy and Precision

Abstract

The latent time-to-criterion (T2C) model is arguably a more policy action-oriented approach to modeling longitudinal data than the traditional intercept-slope growth model. However, despite their mathematical equivalence (in terms of model parameters), the traditional intercept-slope latent growth model and the latent time-to-criterion (T2C) latent models were hypothesized to differ in their parameter estimation performance due in part to typical attrition-type missingness in longitudinal studies that would uniquely affect the time-to-criterion (tau) parameter stability. To investigate this phenomenon, this dissertation used a Monte Carlo simulation that systematically varied attrition-type missingness, along with sample size, number of time points data is collected, pre-defined criterion levels, measure reliability, and growth rate variability. Simulation results showed that, in smaller sample sizes of N = 100, estimates of the time-to criterion (tau) factor and its predictor effect can be biased and suffer from lower power when missingness and growth rate variability are high. Further, these effects were exacerbated by poor scale reliability (i.e., α ≤ .4). Not surprisingly, sample size was also found to be the key predictor of bias in both parameters of interest: a sample size of at least N = 250 yielded parameter estimates with minimal to no relative bias or standard error bias as well as power close to or at 100%. In the real data analysis, which used a subsample of publicly available data from the NCES Early Childhood Longitudinal Study 2010-2011 kindergarten cohort, both the traditional latent growth model and the latent T2C model were demonstrated as a concrete example of a scenario with a large sample size and modest attrition – a scenario in which the parameter estimates would not be expected to be biased. Concrete research design recommendations for applied researchers wishing to use the T2C model, as well as future research directions, are discussed.