A Proof-of-Concept Simulation of the Accelerated Longitudinal Planned Missing Design for Latent Panel Modeling

Longitudinal planned missing, represented in the literature by the time-lag model (McArdle & Woodcock, 1997) and the cohort sequential design (Nesselroade & Baltes, 1979), has been thus far restricted to growth modeling and often does not fully utilize the benefits of the planned missingness by estimating a full-longitudinal model. The accelerated longitudinal design may serve as a more flexible and powerful alternative. This study presents a test of the accelerated longitudinal design in a simulated latent panel modeling framework to examine the method’s appropriateness for contexts untestable using traditional longitudinal planned missing designs. Three-, four-, and five-cohort models are tested, using a continuum of sample sizes and cohort effect sizes. Results indicate that factor loadings, factor variances, and stabilities across time are replicated well, while characteristics and relationships of the means (i.e., manifest intercepts, latent means, and especially cohort differences) show low efficiency relative to the full sample case. In general, the technique is recommended when no cohort effects are expected, though more expansive research into other possible modeling situations should follow. iii List of Figures 1 Representation of accelerated longitudinal collection scheme . . . . . . . . . . . . 4 2 Population model for a Single Cohort . . . . . . . . . . . . . . . . . . . . . . . . 10 3 Accelerated longitudinal data structures . . . . . . . . . . . . . . . . . . . . . . . 13 4 Estimation model for four-cohort condition . . . . . . . . . . . . . . . . . . . . . 14 5 Manifest Intercept MSE across Both Cohort Effects for Three Cohort Condition with Full-Sample Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 6 Latent Mean MSE across Cohort Effects for Cohorts 2 and 4 for Five Cohort Condition with Full-Sample Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 7 Manifest Intercept MSE across Both Cohort Effects for Three Cohort Condition with Accelerated Longitudinal Data . . . . . . . . . . . . . . . . . . . . . . . . . 20 8 Latent Mean MSE across Cohort Effects for Cohorts 2 and 4 for Five Cohort Condition with Full-Sample Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 9 Actual vs. Imputed Values for the First Variable in a Four Cohort Replication . . . 22 10 Actual vs. Imputed Values for the First Variable in a Four Cohort Replication with No Cohort Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 11 Relative Efficiency of Factor Loadings across Sample Size for Four Cohort Condition 26 12 Relative Efficiency of Factor Loadings across Cohort 1 Effect Size for Four Cohort Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 iv List of Tables 1 Relative Bias and MSE Across Conditions . . . . . . . . . . . . . . . . . . . . . . 17 2 Relative Difference in Bias and Relative Efficiency Between Designs . . . . . . . . 25