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Compute Correlation Type Analysis with Statistical Significance

Source: R/corr_fun.R
corr_fun.Rd

Performs correlation type analysis on two mixed-class columns of a given dataframe. The dataframe can contain columns of four types: integer, numeric, factor, and character. The character column is considered as a categorical variable.

Usage

corr_fun(
  df,
  nx,
  ny,
  p.value = 0.05,
  verbose = TRUE,
  num.s = 250,
  rk = FALSE,
  comp = c("greater", "less"),
  alternative = c("greater", "less", "two.sided"),
  cor.nn = c("pearson", "mic", "dcor", "pps"),
  cor.nc = c("lm", "pps"),
  cor.cc = c("cramersV", "uncoef", "pps"),
  lm.args = list(),
  pearson.args = list(),
  dcor.args = list(),
  mic.args = list(),
  pps.args = list(ptest = FALSE),
  cramersV.args = list(),
  uncoef.args = list()
)

Arguments

df

[data.frame]
input data frame.

nx

[character(1)]
first variable column name: independent/predictor variable.

ny

[character(1)]
second variable column name: dependent/target variable.

p.value

[logical(1)]
P-value probability of obtaining the observed results of a test, assuming that the null hypothesis is correct. By default p.value=0.05 (Cutoff value for p-value.).

verbose

[logical(1)]
Activate verbose mode.

num.s

[numeric(1)]
Used in permutation test. The number of samples with replacement created with y numeric vector.

rk

[logical(1)]
Used in permutation test. if its TRUE transform x, y numeric vectors with samples ranks.

comp

[character(1)]
The parameter p.value must be greater or less than those estimated in tests and correlations.

alternative

[character(1)]
a character string specifying the alternative hypothesis for the correlation inference. It must be one of "two.sided" (default), "greater" or "less". You can specify just the initial letter.

cor.nn

[character(1)]
Choose correlation type to be used in integer/numeric pair inference. The options are pearson: Pearson Correlation,mic: Maximal Information Coefficient, dcor: Distance Correlation,pps: Predictive Power Score.Default is Pearson Correlation.

cor.nc

[character(1)]
Choose correlation type to be used in integer/numeric - factor/categorical pair inference. The option are lm: Linear Model,pps: Predictive Power Score. Default is Linear Model.

cor.cc

[character(1)]
Choose correlation type to be used in factor/categorical pair inference. The option are cramersV: Cramer's V,uncoef: Uncertainty coefficient, pps: Predictive Power Score. Default is Cramer's V.

lm.args

[list]
additional parameters for linear model to be passed to lm.

pearson.args

[list]
additional parameters for Pearson correlation to be passed to cor.test.

dcor.args

[list]
additional parameters for the distance correlation to be passed to dcor_t_test.

mic.args

[list]
additional parameters for the maximal information coefficient to be passed to mine.

pps.args

[list]
additional parameters for the predictive power score to be passed to score.

cramersV.args

[list]
additional parameters for the Cramer's V to be passed to cramersV.

uncoef.args

[list]
additional parameters for the uncertainty coefficient to be passed to UncertCoef.

Value

[list]
A list containing statistical and basic information with 8 elements:

  • infer: The method or metric used to assess the relationship between the variables (e.g., Maximal Information Coefficient or Predictive Power Score).

  • infer.value: The value or score obtained from the specified inference method, representing the strength or quality of the relationship between the variables.

  • stat: The statistical test or measure associated with the inference method (e.g., P-value or F1_weighted).

  • stat.value: The numerical value corresponding to the statistical test or measure, providing additional context about the inference (e.g., significance or performance score).

  • isig: A logical value indicating whether the statistical result is significant (TRUE) or not, based on predefined criteria (e.g., threshold for P-value).

  • msg: A message or error related to the inference process.

  • varx: The name of the first variable in the analysis (independent variable or feature).

  • vary: The name of the second variable in the analysis (dependent/target variable).

All statistical tests are controlled by the confidence interval of p.value parameter. If the statistical tests do not obtain a significance greater/less than p.value the value of variable isig will be FALSE.
If any errors occur during operations the association measure (infer.value) will be NA.
The result data and index will have \(N^2\) rows, where N is the number of variables of the input data. By default there is no statistical significance test for the PPS algorithm. In this case isig is NA, you can enable it by setting ptest = TRUE in pps.args.
All the *.args can modify the parameters (p.value, comp, alternative, num.s, rk, ptest) for the respective method on it's prefix.

Pair Types

Numeric pairs (integer/numeric):

  • Pearson Correlation Coefficient: A widely used measure of the strength and direction of linear relationships. Implemented using cor. For more details, see https://doi.org/10.1098/rspl.1895.0041. The value lies between -1 and 1.

  • Distance Correlation: Based on the idea of expanding covariance to distances, it measures both linear and nonlinear associations between variables. Implemented using dcorT.test. For more details, see https://doi.org/10.1214/009053607000000505. The value lies between 0 and 1.

  • Maximal Information Coefficient (MIC): An information-based nonparametric method that can detect both linear and non-linear relationships between variables. Implemented using mine. For more details, see https://doi.org/10.1126/science.1205438. The value lies between 0 and 1.

  • Predictive Power Score (PPS): A metric used to assess predictive relations between variables. Implemented using score. For more details, see https://zenodo.org/record/4091345. The value lies between 0 and 1.

Numeric and categorical pairs (integer/numeric - factor/categorical):

  • Square Root of R² Coefficient: From linear regression of the numeric variable over the categorical variable. Implemented using lm. For more details, see https://doi.org/10.4324/9780203774441. The value lies between 0 and 1.

  • Predictive Power Score (PPS): A metric used to assess predictive relations between numeric and categorical variables. Implemented using score. For more details, see https://zenodo.org/record/4091345. The value lies between 0 and 1.

Categorical pairs (factor/categorical):

References

KS Srikanth, sidekicks, cor2, 2020. URL https://github.com/talegari/sidekicks/.

Paul van der Laken, ppsr, 2021. URL https://github.com/paulvanderlaken/ppsr.

Author

Igor D.S. Siciliani, Paulo H. dos Santos

Examples


# since both `nx` and `ny` columns are numerical the method type is defined by `cor.nn`
corr_fun(iris, nx = "Sepal.Length", ny = "Sepal.Width", cor.nn = "dcor")
#> Sepal.Width vs. Sepal.Length. Alternative hypothesis: true Distance Correlation is not equal to 0. P-value: 0.
#> $infer
#> [1] "Distance Correlation"
#> 
#> $infer.value
#> [1] 0.08006887
#> 
#> $stat
#> [1] "P-value"
#> 
#> $stat.value
#> [1] 0
#> 
#> $isig
#> [1] TRUE
#> 
#> $msg
#> [1] "Sepal.Width vs. Sepal.Length. Alternative hypothesis: true Distance Correlation is not equal to 0. P-value: 0."
#> 
#> $varx
#> [1] "Sepal.Length"
#> 
#> $vary
#> [1] "Sepal.Width"
#>