Langmuir adsortion isotherm with regular and irregular autoregressive error structures

The Langmuir isotherm is a nonlinear regression model, being one of the most applied in adsorption studies. In this type of study, the data are collected over time, which can provide correlated errors; in addition, the collection is not always done in an equidistant way, which may influence the estimation of model parameters. One way of modelling the dependent errors in a regression model is to use an autoregressive process that assumes that the observations are performed at equidistant intervals. However, the definition of the independent variable is often performed at irregular intervals, causing a reduction of information obtained from the dataset. One possible improvement in the adjustment quality of these models is the use of the irregular autoregressive process. The objective of this work was to compare the estimates of isotherm parameters with different irregular and regular autoregressive error structures, considering the positive autocorrelation in different sample sizes, error autocorrelation values and positioning of non-equidistant observations. It was found that there is a need to respect the assumptions of the model. The irregular autoregressive model is more appropriate because it is mostly more precise and accurate, especially when non-equidistance occurs in the initial third.