I am having some problems deciding which type of regression to use, OLS or RMA. I find support for each one with my dataset and goals. I am regressing nitricline depth against C:Chl ratios. The thoughts for using RMA are that there is error in both measurements and the objective is to possibly define a mutual and codependent underlying the interaction between X and Y (Sprent, 1966). However, the thoughts for using OLS are X (NC) is being used to predict Y (C:Chl) (Smith, 1994), the purpose of the regression is to understand the range of Y values at a given X, and the error in X is
If your aim is to use the regression to predict C:Chl values from NC then OLS is appropriate. Model II regression is used to assess the correlation between two independent variables with independent error in both measurements. However, when using a linear regression in a predictive mode you assume dependency of Y on X and you use a Model I regression.
Thanks Ricardo! I was leaning towards OLS for that reason. My advisor suggested just putting both regressions in, but I think I'll stick with simply OLS...unless the reviewers thing differently. But I think I can strongly defend OLS.
If the error in x is indeed tiny, the two should give you the same answer. Another issue is whether you want to use robust regression (e.g. minimizing absolute differences, having point with large uncertainty weigh less than those with little etc'). Classical type-I minimize square of differences and assume all points are equal in the weight.
Andrew, I thought I'd chime in late with another good reference on the matter. One thing to consider if you went with RMA or other Type II is that you can regress both y on X and x on Y in order to establish bounds on your model.
McArdle, B.H. Lines, models, and errors: Regression in the field. Limonology and Oceanography 48, 1363-1366 (2003).
A good reference on the topic is by Smith 'Use and misuse of the reduced major axis for line-fitting 2009 Am J Phys Anthropol p v 140 (3) 476-86
In my opinion, one of the best treatments on the use of linear regression applied to an ecological problem is presented by Ricker in: Ricker, W. E. 1973, Linear regressions in fishery research. J. Fish. Res. Board Can. 30: 409-434. see: http://www.nrcresearchpress.com/doi/pdf/10.1139/f73-072
Just in case, attached is a matlab routine wrote 20+ years ago to estimate linear relationship using different regression models. The routine generates the following outputs: correlation r, t, and critical value, as well as slope and intercept for model I, model II geometric mean, and model II major axis regressions with confidence intervals at 95 or 99%. The math is derived from:
Ricker (1973). Linear regressions in Fishery Research. J. Fish. Res. Board Can.30: 409-434.
Jolicoeur (1975). Linear Regressions in Fishery Research: Some Comments. J. Fish. Res. Board Can. 32: 1491-1494.
Ricker (1975). A Note Concerning Professor Jolicoeur’s Comments. J. Fish. Res. Board Can. 32: 1494-1498.
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