| The fit of Quasi-Simplex (QS), Linear Growth Curve (LGC), and Latent Difference Score (LDS) longitudinal models to known data structures was evaluated in a simulation study. Multiple data samples were generated across a range of parameters (e.g., autoregressive coefficient, factor variance), sample sizes and numbers of measurement occasions. Nine global conditions resulted: three models fitted to three data structures, one congruent model and two non-congruent models for each type of data. Fitted models were evaluated on four criteria: (a) parameter recovery, (b) model convergence, (c) inadmissible parameter estimates (e.g., variance less than 0), and (d) goodness of fit criteria. Goodness of fit was evaluated by the chi2 statistic and other commonly-reported indices (e.g., RMSEA, TLI). Parameter recovery was excellent: within the limits of measurement error, parameter estimates were their expected value for each model fitted to its own data structures. Only the QS model failed to converge on a number of data samples, and this was true for data of all three models. All three models fitted to all three data structures resulted in inadmissible parameter estimates in certain percentages of the data samples. The QS model resulted in the highest percentages of samples with an inadmissible parameter estimate, with most inadmissibility in LDS data, followed by LGC data, and then QS data. Substantial inadmissibility also occurred for the LGC model fitted to LDS data. Except for the QS model with a small autoregression coefficient and small sample size, all three models fitted to congruent data structures generally resulted in acceptable fit. For models fitted to non-congruent data (e.g., QS model fitted to LGC data), (a) large residual variance, (b) small sample size, (c) few measurement occasions, and (d) small values of model-specific parameters (e.g., Slope factor variance in LGC and LDS data) in the simulated data improved the chances of acceptable model fit, leading to an incorrect decision. Within-model characteristics that indicated an incorrect model had been fitted included (a) large autoregressive coefficient estimates in the QS model, (b) negative Level-Slope correlation estimates in LGC and LDS models, and (c) large residual variance estimates for all models. Such information provides guidelines for alerting researchers to potential incorrect model choice, dependent upon the empirical data structure. |
