Testing the product of slopes in related regressions

Morrell, Christopher H., Shetty, Veena, Phillips, Terry, Arumugam, Thiruma V., Mattson, Mark P. and Wan, Ruiqian (2010). Testing the product of slopes in related regressions. In: Elizabeth Hill, 2010 JSM proceedings. 2010 Joint Statistical Meetings, Vancouver, BC, Canada, (1243-1253). 31 July - August 5 2010.

Author Morrell, Christopher H.
Shetty, Veena
Phillips, Terry
Arumugam, Thiruma V.
Mattson, Mark P.
Wan, Ruiqian
Title of paper Testing the product of slopes in related regressions
Conference name 2010 Joint Statistical Meetings
Conference location Vancouver, BC, Canada
Conference dates 31 July - August 5 2010
Proceedings title 2010 JSM proceedings
Place of Publication Alexandria, VA, United States
Publisher American Statistical Association
Publication Year 2010
Sub-type Fully published paper
ISBN 9780979174797
Editor Elizabeth Hill
Start page 1243
End page 1253
Total pages 11
Collection year 2010
Language eng
Abstract/Summary A study was conducted of the relationships among neuroprotective factors and proinflammatory cytokines in brain tissue samples from laboratory mice at different ages that were examined on the effect of dietary energy restriction on the protection of experimentally induced brain stroke. It was of interest to assess whether the cross-product of the slopes of concentrations of pairs of variables vs. age was positive or negative. To accomplish this, the product of the slopes was estimated and further tested to determine if it is significantly different from 0. Since the measurements are taken on the same animals, the models used to fit the data must account for the non-independence of the measurements within animals. A number of approaches to fitting the model, obtaining estimates of the product and its standard error, and conducting the test are illustrated. First a multivariate multiple regression model is employed. Since we are interested in a nonlinear 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 of the product. Finally, a non-linear mixed-effects approach is taken to fit the linear-mixed-effects model and conduct the test of the product of the slopes. A simulation study investigates the properties of the testing procedure. The analytical outcomes revealed the intrinsic relationships among the products, and were consistent with the biological outcomes from the present study.
Keyword Multivariate multiple regression
Linear mixed-effects model
Non-linear mixed effects model
Q-Index Code E1
Q-Index Status Provisional Code
Institutional Status UQ
Additional Notes Biometrics Section. Proceedings: 1 CD-ROM : col. ; 4 3/4 in.

Document type: Conference Paper
Collection: School of Biomedical Sciences Publications
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