Evaluates whether the relationship between two vectors is linear or nonlinear. Performs a test to determine how well a linear model fits the data compared to higher order polynomial models. Jhang et al. (2004)
R package for polynomial evaluation of linearity.
lin.eval
is a R package for performing polynomial evaluation of linearity.
lin.eval
can be installed via Github:
if (!require(devtools)) { install.packages('devtools') } devtools::install_github('vishesh-shrivastav/lin.eval')
Polynomial evaluation of linearity is a technique of assessing if the best way to describe the relationship between two vectors.
Fit three models - linear, second-order polynomial and third-order polynomial
Find out best-fitting model among the three by comparing their p-values. Model with the lowest p-value out of the three is the best-fitting one.
If the best-fitting model is linear, linearity is established and no further steps need to be carried out. This is called Linear 1 type.
Else, best-fitting model is either second or third order polynomoal model. In this case, calculate average deviation from linearity (adl). This is given by:
where, l
is the vector of predictions from linear model and p
is the vector of predictions from best-fitting polynomial model.
If adl
is greater than or equal to the threshold value for deviation from linearity, conclude that the relationship is non-linear.
Else if adl
is less than the threshold value for deviation from linearity, conclude that although the best-fitting model is not linear, deviation from linearity is not significant and hence, it is still a linear relationship. This is called a Linear 2 type.
Call the poly_eval()
function with the following parameters:
y
: vector of response values
x
: vector of predictor values
threshold
: threshold value for average deviation from linearity as percentage. Defaults to 5.
> foo <- c(165.3929, 165.3929, 1119.5714, 1119.5714, 2073.7500, 2073.7500, 3027.9286, 3027.9286, 3982.1071, 3982.1071, 4936.2857, 4936.2857, 5890.4643, 5890.4643)> bar <- c(386.2143, 386.2143, 840.6548, 840.6548, 1829.6905, 1829.6905, 3074.4048, 3074.4048, 4295.8810, 4295.8810, 5215.2024, 5215.2024, 5553.4524, 5553.4524)> derp <- poly_eval(bar, foo, 30)Best fitting model is third-order polynomial.Computing average deviation from linearity:Average Deviation from Linearity: 27.28 %Although the best fitting model is nonlinear, since average deviation from linearity is 27.28; which is less than or equal to 30; linearity is established. We call this linearity type as Linear 2
You can check the values stored in the result variable:
> derp$p1[1] 8.851095e-12> derp$p2[1] 2.514044e-10> derp$p3[1] 1.930392e-78> derp$adl[1] 27.28302
Usage without passing in optional argument for adl:
> xx <- c(0, 1, 2, 4, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 29, 30)> yy <- c(126.6, 101.8, 71.6, 101.6, 68.1, 62.9, 45.5, 41.9, 46.3, 34.1, 38.2, 41.7, 24.7, 41.5, 36.6, 19.6, 22.8, 29.6, 23.5, 15.3, 13.4, 26.8, 9.8, 18.8, 25.9, 19.3)> poly_eval(yy, xx)Best fitting model is second-order polynomial.Computing average deviation from linearity...Average Deviation from Linearity: 70.42 %Since, average deviation from linearity is greater than 5, nonlinearity is established.The relationship between the two input vectors is best described by a second order polynomial