Latent growth curve modeling and latent class growth analysis: An application of prospective subjective well-being

In this study, a person-centered longitudinal measurement method that can be used to define intra-individual and inter-individual growth trajectories, to determine the predictor variables that can be used to explain these trajectories, and if there are categorical differences in these trajectories to test whether these differences are latent classes or not was studied. Latent Growth Curve Modeling and Latent Class Growth Analysis are introduced and the measurement method using these statistical analyses is designed as a three-step approach. This approach conducted repeated measurements of subjective well-being data and discussed in terms of contribution to findings. Example data came from as a part of a larger longitudinal study following 154 university students were used to illustrate the suggested approach. The data were collected at four-equally spaced time points from participants who volunteered to participate in research. For the first and second step of the approach, the analysis was carried out using Latent Growth Curve Modeling which contains continuous latent variables. In the first step, a series of unconditional growth models (e.g., linear-Model 0, quadratic-Model I) was fitted to the data to find the best representation of growth trajectories. It was found that linear growth specification was sufficient, a single average growth trajectory for the entire sample tended to decrease over time and the variances of growth factors (intercept and slope) were significant. In the second step, conditional growth models were fitted to the data in an attempt to explain the variation of growth factors. The conditional growth models included predictor variables as time-varying covariates that can explain a large proportion of the variances of growth factors. Three conditional growth models were tested in the second step: 1) model including sleep quality (Model II), 2) model including sleep quality and resilience (Model III), and 3) model including stress with the addition of the two other predictor variables (Model IV) and the effects of all predictor variables were controlled at all time points. Judging from the current model fit indices and statistics, Model IV fitted the data better than previous ones after controlling for sleep quality, resilience, and stress as time-varying covariates. Model IV results showed that model fit indices were improved, standard errors of parameter estimation and unexplained variance of the model were decreased compared to the unconditional growth model. In the third step, specifying the Latent Class Growth model with no within-class variance was used to explore distinct latent growth classes following the same pattern of change over time. Several latent class model alternatives, ranging from 1-class to 3-class models, were tested to define latent growth classes. Then, it was seen that fit indices of the models suggested that the 2-class model was the best fitting model and the results showed that the first latent class with a smaller starting point and decrease of subjective well-being, and the second latent class with a higher starting point and increase of subjective well-being over time. In summary, Model 0 results showed that the rate of subjective well-being change tended to decrease over time. After predictor variables were included as time-varying covariates to Model IV, the results showed that the decrease of the rate of change was more steeply. Then, when categorical latent classes were added to the model, it was found that the decrease in Model IV was observed only in the first latent class. The results of this study show that the change of subjective well-being, the rate of change, and its predictors are not constant for the entire sample. Therefore, the results of this study support that the use of longitudinal measurement models to examine intra-individual and inter-individual differences over time. In general, the focus of the current study to provide an overview of latent growth curve and latent class growth analyses and to highlight the strengths of these statistical models using application data. This study illustrated the potential utility and importance of these statistical approaches to identifying developmental patterns and quantifying intra-individual and inter-individual differences in these patterns.