Although previous studies on structural equation modeling (SEM) have indicated that the second-order latent growth model (SOLGM) is a more appropriate approach to longitudinal intervention effects, its application still requires researchers to collect at least three-wave data (e.g. randomized pretest, posttest, and follow-up design). However, in some circumstances, researchers can only collect two-wave data for resource limitations. With only two-wave data, the SOLGM can not be identified and researchers often choose alternative SEM models to fit two-wave data. Recent studies show that the two-wave longitudinal common factor model (2W-LCFM) and latent change score model (2W-LCSM) can perform well for comparing latent change between groups. However, there still lacks empirical evidence about how accurately these two-wave models can estimate the group effects of latent change obtained by three-wave SOLGM (3W-SOLGM). The main purpose of this dissertation, therefore, is trying to examine to what extent the fixed effects of the tree-wave SOLGM can be recovered from the parameter estimates of the two-wave LCFM and LCSM given different simulation conditions. Fundamentally, the supplementary study (study 2) using three-wave LCFM was established to help justify the logistics of different model comparisons in our main study (study 1). The data generating model in both studies is 3W-SOLGM and there are in total 5 simulation factors (sample size, group differences in intercept and slope, the covariance between the slope and intercept, size of time-specific residual, change the pattern of time-specific residual). Three main types of evaluation indices were used to assess the quality of estimation (bias/relative bias, standard error, and power/type I error rate). The results in the supplementary study show that the performance of 3W-LCFM and 3W-LCSM are equivalent, which further justifies the different models' comparison in the main study. The point estimates for the fixed effect parameters obtained from the two-wave models are unbiased or identical to the ones from the three-wave model. However, using two-wave models could reduce the estimation precision and statistical power when the time-specific residual variance is large and changing pattern is heteroscedastic (non-constant). Finally, two real datasets were used to illustrate the simulation results. / Doctor of Philosophy / To collect and analyze the longitudinal data is a very important approach to understand the phenomenon of development in the real world. Ideally, researchers who are interested in using a longitudinal framework would prefer collecting data at more than two points in time because it can provide a deeper understanding of the developmental processes. However, in real scenarios, data may only be collected at two-time points. With only two-wave data, the second-order latent growth model (SOLGM) could not be used. The current dissertation compared the performance of two-wave models (longitudinal common factor model and latent change score model) with the three-wave SOLGM in order to better understand how the estimation quality of two-wave models could be comparable to the tree-wave model. The results show that on average, the estimation from two-wave models is identical to the ones from the three-wave model. So in real data analysis with only one sample, the point estimate by two-wave models should be very closed to that of the three-wave model. But this estimation may not be as accurate as it is obtained by the three-wave model when the latent variable has large variability in the first or last time point. This latent variable is more likely to exist as a statelike construct in the real world. Therefore, the current study could provide a reference framework for substantial researchers who could only have access to two-wave data but are still interested in estimating the growth effect that supposed to obtain by three-wave SOLGM.