×

Testing the difference between two independent regression models. (English) Zbl 1349.62049

Summary: In some situations, for example, in biology or psychology studies, we wish to determine whether the linear relationship between response variable and predictor variables differs in two populations. The analysis of the covariance (ANCOVA) or, equivalently, the partial \(F\)-test approaches are the commonly used methods. In this study, the asymptotic distribution for the difference between two independent regression coefficients was established. The proposed method was used to derive the asymptotic confidence set for the difference between coefficients and hypothesis testing for the equality of the two regression models. Then a simulation study was conducted to compare the proposed method with the partial \(F\) method. The performance of the new method was comparable with that of the partial \(F\) method.

MSC:

62F03 Parametric hypothesis testing
62F05 Asymptotic properties of parametric tests
62F12 Asymptotic properties of parametric estimators
62J05 Linear regression; mixed models
62J10 Analysis of variance and covariance (ANOVA)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] DOI: 10.1007/978-1-4899-4549-5 · doi:10.1007/978-1-4899-4549-5
[2] Green P.J., Nonparametric Regression and Generalized Linear Models: A roughness penalty approach (1993)
[3] DOI: 10.1016/j.jspi.2006.02.004 · Zbl 1107.62050 · doi:10.1016/j.jspi.2006.02.004
[4] DOI: 10.1016/j.csda.2007.01.015 · Zbl 1445.62166 · doi:10.1016/j.csda.2007.01.015
[5] DOI: 10.1016/j.csda.2010.01.022 · Zbl 1284.62418 · doi:10.1016/j.csda.2010.01.022
[6] DOI: 10.1002/bimj.200610322 · doi:10.1002/bimj.200610322
[7] DOI: 10.1198/016214504000000395 · Zbl 1117.62391 · doi:10.1198/016214504000000395
[8] DOI: 10.1002/sim.2756 · doi:10.1002/sim.2756
[9] DOI: 10.1016/j.jspi.2005.09.007 · Zbl 1098.62087 · doi:10.1016/j.jspi.2005.09.007
[10] DOI: 10.1016/0022-4405(88)90032-5 · doi:10.1016/0022-4405(88)90032-5
[11] Potthoff R.F., Statistical Aspects of the Problem of Biases in Psychological Tests (1966)
[12] DOI: 10.3758/BF03200751 · doi:10.3758/BF03200751
[13] DOI: 10.3758/s13428-012-0289-7 · doi:10.3758/s13428-012-0289-7
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.