[R] test regression against given slope for reduced major axis regression (RMA)

[david bird]

Patrick Drechsler wrote on 11 Jul 2006 02:10:21 MET: 

[...] 
> I am now confronted with the problem that I have data which 
> requires a modelII regression (also called reduced major axes 
> regression (RMA) or geometric mean regression). For this I use 
> the function "modelII" (see below). 
> 
> What would be a good way of adapting 
> "test_regression_against_slope" for use with RMA regression? 
> 
> The question I am trying to answer is: "Does the slope acquired 
> from experimental data differ significantly from theoretical 
> predictions?" 

JFTR: David Warton's "smatr" package solves the problem. 


DFB: Note that there are conflicting solutions to this question. The
confidence limits based on Pitman, EJG (1939) "A note on normal
correlation".  Biometrika 31: 9-12, as implemented in the smatr package, are 
liberal (i.e. narrow), compared to the alternative limits found in Tan, CY
and B. Iglewicz (1999) Measurement-methods comparisons and linear
statistical relationship, Technometrics 41: 192-201.

Note also that "equation error", if present, invalidates any confidence
limits calculations. That is, in using the RMA, you are looking for the
perfect underlying relationship between two variables. If the underlying
relationship is not perfect, because missing variables are also important,
the RMA is the wrong approach.
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