The Using of Latent Growth Models for Educational Researches

The concept of education is explained with some concepts such as development, change, and growth. Because of it, educational measurements used to determine learners' achievement growth and cognitive development, or learners' status of achievement. Linear or nonlinear traditional statistical models used for status of analysis. To determine the change commonly used paired t test statistics, constructed on the pre-test and post- test experimental design, and variance of analysis based on repeated measurements. However, these methods include some limitations and not enough to define the growth. On the other side, the latent growth modelling has been increasingly used to analyze longitudinal data, especially for educational researches. In this article, the latent growth modelling was dealt with for educational purposes and discussed. Also to determine the achievement growth (cognitive development), the all of latent growth models have been applied on a simulated data set. SUMMARY Purpose and Significance: The educational purposes are commonly explained in terms of the change because learning implies change. In traditional approaching, classical statistical modelling yielded a lot of correlated errors in developmental researches. The other experimental design, commonly used, consists of pre-test and post-test based on two occasional data and the model not enough for explain the growth. Latent growth modelling has been used for analyzing of longitudinal data gathered from more occasional data. Latent growth models analyze longitudinal changes in means, variances, and covariances of variables. Latent growth curve methodology also provides a means of modelling a developmental function as a factor repeated observations over time in educational researches. The developmental trajectories in educational studies are generally monotonic increasing functions based on longitudinal data include cognitive measures based on achievement data. So the graphical representation of longitudinal data shows cognitive developmental trajectories. We renamed the intercept parameter in LGM as priori achievement parameter and the slope parameter as ratio of cognitive development. In this article, using the univariate and multivariate LGM for educational aims were introduced and the models were applied to repeated data in Turkish, mathematics, and sciences. Method: The achievement growth in learning domains of Turkish, mathematics, and sciences separately tested with unconditional LGM and conditional LGM respect to gender. Also to determine relations among latent growth factor patterns used the associative LGM in terms of multivariate LGM. We used the second order LGM to test whether higher order learning construct describes the relations among lower order developmental factors. Results and Discussion: In this study, we analyzed the different six latent growth models sequentially for three learning domain and each learning domain consist with three measurement occasions. Each data set fits linear growth with satisfied data-fit index values. The findings in each model were discussed according to educational approaching. It was declared in this study, it is important to use the multivariate LGM in educational researches, because latent growth factors have relations such as the growth achievement (slope) in mathematics and priori achievement (intercept) in reading (in Turkish).