alternating conditional expectation (ace) algorithm for robust regression analysis ofsimulated dataset in the presence of homoscedastic and heteroscedastic noise

Regression analysis, aimed at efficiently predicting outcomes by examining the relationships betweenvariables, is acknowledged as a crucial research area in the field of chemometrics. the relationship amongvariables and the nature of noise are two important components of information in regression modeling.when these parts are known, the regression is carried out easily. but what about the unknown data? thismeans data without any prior information about the relationships between variables and patterns of noise.the aim of this study is to answer this challenging question. actually, classical regression procedures mayencounter problems in this situation because these methods are based solely on constant and normallydistributed residuals [1, 2]. therefore, an alternative solution must be provided.this solution utilizes robust methods. in this work, the performance of several regression methodsincluding simple least squares (sls) as a classical regression technique, weighted least squares (wls)method, and alternating conditional expectation (ace) as a robust method were evaluated for univariateregression analysis of a simulated dataset with 100 data points. these data points were mathematicallysimulated according to a nonlinear equation: y = 2.1 + 0.4 x2. the study was conducted in four steps. in thefirst step, the data produced without noise were analyzed using regression approaches. then, homoscedastic(constant) noise with values of 0.1 and 10 were added to raw data, and these noisy datasets were utilizedas inputs for regression models in second and third steps, respectively. in the last step, heteroscedastic (nonconstant) noise was added to raw data for further analysis.the statistical parameters such as r2 of 1.000, r2adj of 1.000, sum of squares of residuals (sse) of 3.65e-05, the variance inflation factor (vif) of 2714149.979, and the bayes information criterion (bic) of -1473.126508 were the results of ace for heteroscedastic data. the results demonstrate that ace has themost efficient performance compared to other methods. this superiority stems from transformation-basednature of this approach. ace suggests the best transformation function with the highest correlation betweenresponse and descriptor variables. variable transformation makes the error variance stable and normalizesits distribution. therefore, highly satisfying outputs are obtained without needing to consider therelationship among the variables and the noise pattern [3, 4].