Comparison of Methodologies for Analysis of Longitudinal Data Using MATLAB

In several areas of scientific knowledge there is a need for studying the behavior of one or more variables using data generated by repeated measurements of the same unit of observations along time or spatial region. Due to this, many experiments are constructed in which various treatments are applied on the same plot at different times, or only one treatment is applied to an experimental unit and it is made a measurement of a characteristic or a set of features in more than one occasion [Khattree & Naik, 2000]. Castro and Riboldi [Castro & Riboldi, 2005] define data collected under these kinds of experimental setups as repeated measures. More specifically, he asserts that “repeated measures is understood as the data generated by repeatedly observing a number of investigation units under different conditions of evaluation, assuming that the units of investigation are a random sample of a population of interest”. In order to analyze repeated measures data it is necessary to take a care about not independency between observations. This is so because it is expected a high degree of correlation between data collected on the same observation unit over time, and there is usually more variability in the measurements between the subjects than within a given subject. A very common type of repeated measures is longitudinal data, i.e., repeated measures where the observations within units of investigation were not or can not have been randomly assigned to different conditions of evaluation, usually time or position in space. There are basically two paths to be taken in the analysis of longitudinal data; univariate analysis, which requires as a precondition a rigid structure of covariances, or multivariate analysis, which, despite being more flexible, is less efficient in detecting significant differences than the univariate methodology. In Advances in Longitudinal Data Analysis [Fitzmaurice et al., 2009], Fitzmaurice comments that despite the advances made in statistical methodology in the last 30 years there has been a lag between recent developments and their widespread application to substantive problems, and adds that part of the problem why the advances have been somewhat slow to move into the mainstream is due to their limited implementation in widely available standard computer software. In this context this work proposes to develop a single and easy computational implementation to solve a great number of practical problems of analysis of longitudinal