Effect of sample size and number of measurement on latent growth models

Longitudinal data has been in the forefront of the last 40-50 years because of the fact that they carry more information than cross-sectional data, because it contains causality and is dynamic, and also because of the large amount of data accumulated over many years. There are many types of models that can be formulated with this kind of data, and there are many analytical methods (as Hierarchical Linear Modeling, Autocorrelated Models etc.) where these data can be tested. However, the most prominent method in the last 30 - 40 years is structural equation modeling. The reason why structural equation modeling has attracted so much interest is that it can melt the regression and confirmatory factor analysis in the same pot and thus offer a wide range of modeling oppurtunities to the user. Another important feature of structural equation modeling is that it can model the underlying processes that cannot be measured directly but with indicators, structures are shown to be the underlying effect. These structures are called latent structures. When a measure of indicators of the same latent structure is measured in different time periods, the change across time in this latent structure can be measured by conventional methods (such as t-test, ANOVA), but the unexplained variance is accepted as error. At this point, structural equation modeling with latent variables both allows the underlying structure to be measured at more than two time points, and can also explain the variance that traditional methods accept as errors thanks to time-varying and time-invariant predictor variables that can be added to the model. Like most multivariate methods, latent growth models have limitations and assumptions are of great importance in order to give accurate results. At the same time, important details such as how long and how many times a sample should be measured are still being studied. The aim of this study is to provide an idea about the sample size and the number of measurements required for a latent growth modeling research with real data.