Langmuir adsortion isotherm with regular and irregular autoregressive error structures

Cristiane Costa Da Fonseca Cintra,Denismar Alves Nogueira,Luiz Alberto Beijo

doi:10.4025/actascitechnol.v40i1.37792

Cristiane Costa Da Fonseca Cintra, Denismar Alves Nogueira + Show 1 more

Open Access

https://doi.org/10.4025/actascitechnol.v40i1.37792

Copy DOI

Abstract

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.

Highlights

By adjusting a nonlinear regression model, it is assumed that the model errors are uncorrelated, that is, they are independent of each other
In almost all sample sizes, the IS-AR(1) model was more accurate than the AR(1) model and it can be stated that the lack of data in the initial third decreases the precision of the estimates more than when the loss occurs in the other thirds
By adjusting the model with autoregressive error structures, considering the positive autocorrelation and non-equidistance in the independent variable, it is concluded that the estimates of parameter K of the irregular model (IS-AR(1)) are more precise and more accurate than estimates of the regular model (AR(1)) in practically all scenarios studied, regardless of the factors under study

Summary

Introduction

By adjusting a nonlinear regression model, it is assumed that the model errors are uncorrelated, that is, they are independent of each other. When working with statistical modelling, the idea is that, when performing the adjustment of the usual model, it is verified whether it meets the assumptions of the regression methodology, which can be verified by graphical analysis of errors and confirmed analytically by tests of independence, normality and homogeneity of variances. In some studies, the definition of the independent variable is often performed at different or non-equidistant intervals. By ignoring this irregularity in the measurements, you can have, for example, the reduction of information obtained from the dataset with possible problems of super or underestimation of model parameters. An alternative to improve the quality of the adjustment is to consider the irregularity in the data collection by applying the irregular autoregressive process

Objectives

Results

Conclusion