A Modified Two-Stage Method for Parameter Estimation in Sinusoidal Models of Correlated Gene Expression Profiles
Keywords:Non-linear regression, correlated responses, two-stage method, generalized least squares
A two-stage method by Seber and Wild (2003) used to fit nonlinear regression models with correlated errors by using residuals obtained from the ordinary least square estimation has been shown by Pukdee et al. (2018) to underestimate the standard errors of parameter estimates in sinusoidal models, leading to poor coverage probabilities. In order to improve inferential statistics, a modified two-stage method is developed using residuals from the one-way ANOVA model to estimate variance components in the iterative estimation procedure and compared with the two-stage, conditional least squares and generalized least squares methods. A simulation study shows that the proposed method has similar successful convergence rates as the two-stage and conditional least squares methods but produces more reliable point and interval estimates. Although very little difference is seen between estimates produced by generalized least squares and the proposed method, the latter has a consistently higher successful convergence rate, and consequently is more likely to produce a result than the former, and this difference in rates becomes substantial when the model complexity increases.