pcor.test R Documentation

## Partial Correlation

### Description

Calculate the partial correlation coefficient of both of parametric ("Pearson") and non-parametric ("Spearman" and "Kendall") statistics.

### Usage

```pcor.test(x, y, z, use = c("mat","rec"), method = c("pearson","spearman","kendall"), na.rm = T)
```

### Arguments

 `x` a numeric vector. Missing values are allowed. `y` a numeric vector. Missing values are allowed. `z` a numeric vector, matrix or data frame. Missing values are allowed. `use` an optional character string giving a method for computing the partial correlation coefficients. This must be one of the strings "mat" (default) or "rec". `method` a character string indicating which partial correlation coefficient is to be computed. One of "pearson" (default), "kendall", or "spearman", can be abbreviated. `na.rm` logical. Should missing values be removed? Default is `True`

### Values

`estimate` gives the partial correlation coefficieint between `x` and `y` given `z`, `p.value` gives the p-value of the test, `statistic` gives the value of the test statistic, `n` gives the number of samples after deleting all the missing samples, `gn` gives the number of given variables, `Method` gives the correlation method used, and `Use` gives the computation method used.

### Details

Partial correlation is the correlation of two variables while controlling for a third or more other variables. There are two methods to compute the partial correlation coefficient in `pcor.test`. One is by using variance-covariance matrix ("`mat`") and the other recursive formula ("`rec`"). Both of "`mat`" and "`rec`" give the same result in case of `na.rm = T`. Otherwise, the `estimate` may be slightly different from each other due to the way dealing with the missing samples, if there are the missing samples.

### References

Kim, S-H. and Yi, S. (2007) Understanding relationship between sequence and functional evolution in yeast proteins . Genetica, In press.

Kim, S-H. and Yi, S. (2006) Correlated asymmetry between sequence and functional divergence of duplicate proteins in Saccharomyces cerevisiae . Molecular Biology and Evolution, 23: 1068–1075.

Johnson, Richard A. and Dean W. Wichern (2002) Applied multivariate statistical analysis. Prentice Hall.

Whittaker, Joe (1990) Graphical models in applied multivariate statistics. John Wiley & Sons.

`cor`, `cov2cor`, `eigen`, `cor.test`

### Example

```# load the R code "pcor.test"
source("pcor.R")

# data
y.data <- data.frame(
hl=c(7,15,19,15,21,22,57,15,20,18),
disp=c(0.000,0.964,0.000,0.000,0.921,0.000,0.000,1.006,0.000,1.011),
deg=c(9,2,3,4,1,3,1,3,6,1),
BC=c(1.78e-02,1.05e-06,1.37e-05,7.18e-03,0.00e+00,0.00e+00,0.00e+00,4.48e-03,2.10e-06,0.00e+00)
)

# partial correlation between "hl" and "disp" given "deg" and "BC"
pcor.test(y.data\$hl,y.data\$disp,y.data[,c("deg","BC")])
pcor.test(y.data[,1],y.data[,2],y.data[,c(3:4)])
pcor.test(y.data[,1],y.data[,2],y.data[,-c(1:2)])

```