I am using a package in R called BSL (Bare soil line), package is at https://rdrr.io/cran/landsat/man/BSL.html. I've used it successfully to run regression line for my soil study area but it is Model II regression (specifically the lmodel2 package in R) and I don't understand why it's Model II regression and not a simple linear regression using the lm() function in R. Can someone explain why it would be using Model II regression instead of Simple Linear Regression?
A bit more info: the soil line is a linear relationship between reflectance values between Red and Near-infrared wavelengths and is defined by the equation:
NIR = αRed + β where NIR and Red correspond to the near-infrared and red bands of the satellite sensor, alpha is the slope, and beta the y intercept.
For my research, I'm discovering that more fertile soil may have lower y-intercept value and smaller slope values, but this seems to be based on the Model 2 regression values.
For my soil study area, I run the BSL command in R and I get this output:
> result.bsl$BSL Intercept Slope 1323.007184 0.640505 > result.bsl$summary Model II regression Call: lmodel2(formula = bsl.joint[ratio43 < quantile(ratio43, llimit), 2]~ bsl.joint[ratio43 < quantile(ratio43, llimit), 1]) n = 3 r = 0.9878535 r-square = 0.9758546 Parametric P-values: 2-tailed = 0.09932547 1-tailed = 0.04966273 Angle between the two OLS regression lines = 0.6373716 degrees Regression results Method Intercept Slope Angle (degrees) P-perm (1-tailed) 1 OLS 1350.359 0.6359507 32.45435 NA 2 MA 1323.007 0.6405050 32.63976 NA 3 SMA 1303.397 0.6437702 32.77223 NA Confidence intervals Method 2.5%-Intercept 97.5%-Intercept 2.5%-Slope 97.5%-Slope 1 OLS -6286.498 8987.216 -0.6351029 1.907004 2 MA 48805.536 9004.094 -0.6384682 -7.265783 3 SMA -11020.651 4246.396 0.1537332 2.695840 Eigenvalues: 66506.64 336.0233 H statistic used for computing C.I. of MA: 0.8240161
If I run lm(nir~red, mydata), I get a different slope and intercepts for the same data:
Call: lm(formula = mydata$X1.5 ~ mydata$X1.3, data = mydata) Residuals: Min 1Q Median 3Q Max -713.28 -100.97 9.46 118.72 505.87 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 454.07689 240.22340 1.89 0.0594 mydata$X1.3 0.89429 0.03846 23.25 <2e-16 Signif. codes: 0 0.001 0.01 0.05 . 0.1 1 Residual standard error: 185.8 on 439 degrees of freedom Multiple R-squared: 0.5518, Adjusted R-squared: 0.5508 F-statistic: 540.6 on 1 and 439 DF, p-value: < 2.2e-16
In the model 2 regression, my y intercept and slope are 1323 and 0.64 respectively. But in the lm model, my y intercept and slope are 454.08 and 0.89 respectively. I've studied statistics at the first year college level, so I seek any explanations about why model 2 Regression is used here.