I have data sets with strong non linearity and want to find correlations between them for my research paper calculations. I know that Pearson correlation coefficient is used only for linear relationships. I have found some methods for non linear relations but not satisfied since not sure whether they are appropriate.
#Correlation coefficient # Non linear
Any suggestions?
I recommend you use non-parametric correlation coefficients Spearman’s D and rs, . Spearman’s (non-parametric) rank-order correlation coefficient is the linear correlation coefficient (Pearson’s r) of the ranks. Following Press et al. (1992). Kendall’s tau This non-parametric correlation coefficient is not in very common use. It is computed according to Press et al. (1992). All possible N(N-1)/2 pairs of bivariate data points are considered.
The Mantel test is another good option to determine correlation in data that do not meet a normal distribution. The Mantel test (Mantel 1967, Mantel & Valand 1970) is a permutation test for correlation between two distance or similarity matrices.
Performing these analyzes in PAST 3.18 is very good because it performs complementary robustness analyzes to your statistical processing. Example: Permutation tests Monte Carlo permutation tests (N=9999) are available for all the correlation coefficients.
Other analyzes you can do for multilevel analysis: Principal coordinates analysis (PCO) is another ordination method, also known as Metric Multidimensional Scaling. Non-metric MDS.
You can use some non-linear model to establish the determination coefficient depending on the nature of your variables. Example: Linear, Quadratic, Power, Exponential etc.
I enclose the PAST 3.18 manual and determine which analysis best fits your variables and study design.
Hi, Malsha,
This article may be useful: https://odajournal.com/2019/01/19/when-to-evaluate-a-nonlinear-model
I recommend you use non-parametric correlation coefficients Spearman’s D and rs, . Spearman’s (non-parametric) rank-order correlation coefficient is the linear correlation coefficient (Pearson’s r) of the ranks. Following Press et al. (1992). Kendall’s tau This non-parametric correlation coefficient is not in very common use. It is computed according to Press et al. (1992). All possible N(N-1)/2 pairs of bivariate data points are considered.
The Mantel test is another good option to determine correlation in data that do not meet a normal distribution. The Mantel test (Mantel 1967, Mantel & Valand 1970) is a permutation test for correlation between two distance or similarity matrices.
Performing these analyzes in PAST 3.18 is very good because it performs complementary robustness analyzes to your statistical processing. Example: Permutation tests Monte Carlo permutation tests (N=9999) are available for all the correlation coefficients.
Other analyzes you can do for multilevel analysis: Principal coordinates analysis (PCO) is another ordination method, also known as Metric Multidimensional Scaling. Non-metric MDS.
You can use some non-linear model to establish the determination coefficient depending on the nature of your variables. Example: Linear, Quadratic, Power, Exponential etc.
I enclose the PAST 3.18 manual and determine which analysis best fits your variables and study design.
Hi, Malsha,
As Enrigue suggests, there are alternatives to correlation/regression.
For example, there is a modern non-parametric statistical paradigm which always finds the most accurate model(s) for the sample, and that has no distributional requirements.
- https://odajournal.com/2013/09/20/maximizing-the-accuracy-of-multiple-regression-models-using-unioda-regression-away-from-the-mean
Only this non-parametric method may be used to identify the model which maximizes predictive accuracy for a sample--in training and cross-generalizability analysis:
- https://odajournal.com/2016/09/19/novometric-analysis-with-ordered-class-variables-the-optimal-alternative-to-linear-regression-analysis
This modern method also resists overfitting--it is less likely to find relationships when none exist, compared to historical algorithms:
- https://odajournal.com/2019/03/21/some-machine-learning-algorithms-find-relationships-between-variables-when-none-exist-cta-doesnt
Dr. Paul Yarnold and Enrique Reynaldo de la Cruz Thank you very much for your answers. I'll go through with these resources and I thought to use Spearman’s (non-parametric) rank-order correlation coefficient , but will also check other coefficients.
Hi, Malsha,
- Distance correlation measures both linear and nonlinear association between two random variables or random vectors. For more detail, see https://en.wikipedia.org/wiki/Distance_correlation
- R package is available, see https://www.rdocumentation.org/packages/energy/versions/1.7-5/topics/distance%20correlation
- Python package is available, see https://docs.scipy.org/doc/scipy0.14.0/reference/generated/scipy.spatial.distance.correlation.html.
Yongjin Li Hi Yongjin Li, Thank you very much for your answer, I'll go through it .
If you want to make a regression analsysis, you should be apply a nonparametric techniques. Then, I suggest you use any non-parametric correlation coefficients in the statistical literature
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