TESTING THE PRODUCT OF SLOPES IN RELATED REGRESSIONS

被引:0
|
作者
Morrell, Christopher H. [1 ,2 ]
Shetty, Veena [3 ]
Phillips, Terry [4 ]
Arumugam, Thiruma V. [5 ]
Mattson, Mark P. [6 ]
Wan, Ruiqian [6 ]
机构
[1] Loyola Univ Maryland, Math & Stat Dept, 4501 North Charles St, Baltimore, MD 21210 USA
[2] NIA, Biomed Res Ctr, Lab Cardiovasc Sci, Baltimore, MD 21224 USA
[3] MedStar Res Inst, Hyattsville, MD USA
[4] Natl Inst Biomed Imaging & Bioengn, Lab Bioengn & Phys Sci, Bethesda, MD 20892 USA
[5] Univ Queensland, Sch Biomed Sci, Brisbane, Qld, Australia
[6] NIA, Lab Neurosci, Baltimore, MD 21224 USA
关键词
multivariate multiple regression; linear mixed-effects model; non-linear mixed-effects model; repeated measures; delta method;
D O I
暂无
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
A study was conducted of the relationships among neuroprotective factors and cytokines in brain tissue of mice at different ages that were examined on the effect of dietary restriction on protection after experimentally induced brain stroke. It was of interest to assess whether the cross-product of the slopes of pairs of variables vs. age was positive or negative. To accomplish this, the product of the slopes was estimated and tested to determine if it is significantly different from zero. Since the measurements are taken on the same animals, the models used must account for the non-independence of the measurements within animals. A number of approaches are illustrated. First a multivariate multiple regression model is employed. Since we are interested in a non-linear function of the parameters (the product) the delta method is used to obtain the standard error of the estimate of the product. Second, a linear mixed-effects model is fit that allows for the specification of an appropriate correlation structure among repeated measurements. The delta method is again used to obtain the standard error. Finally, a non-linear mixed-effects approach is taken to fit the linear mixed-effects model and conduct the test. A simulation study investigates the properties of the procedure.
引用
收藏
页码:29 / 46
页数:18
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