View source: R/adjacency.polyReg.R

adjacency.polyReg | R Documentation |

adjacency.polyReg calculates a network adjacency matrix by fitting polynomial regression models to pairs of variables (i.e. pairs of columns from
`datExpr`

). Each polynomial fit results in a model fitting index R.squared.
Thus, the n columns of `datExpr`

result in an n x n dimensional matrix whose entries contain R.squared
measures. This matrix is typically non-symmetric. To arrive at a (symmetric) adjacency matrix, one can
specify different symmetrization methods with `symmetrizationMethod`

.

```
adjacency.polyReg(datExpr, degree=3, symmetrizationMethod = "mean")
```

`datExpr` |
data frame containing numeric variables. Example: Columns may correspond to genes and rows to observations (samples). |

`degree` |
the degree of the polynomial. Must be less than the number of unique points. |

`symmetrizationMethod` |
character string (eg "none", "min","max","mean") that specifies the method used to symmetrize the pairwise model fitting index matrix (see details). |

A network adjacency matrix is a symmetric matrix whose entries lie between 0 and 1. It is a special case of a similarity matrix.
Each variable (column of `datExpr`

) is regressed on every other variable, with each model fitting index recorded in a square matrix. Note that the model fitting index of regressing variable x and variable y is usually different from that of regressing y on x. From the polynomial regression model glm(y ~ poly(x,degree)) one can calculate the model fitting index R.squared(y,x).
R.squared(y,x) is a number between 0 and 1. The closer it is to 1, the better the polynomial describes the relationship between x and y and the more significant is the pairwise relationship between the 2 variables. One can also reverse the roles of x and y to arrive at a model fitting index R.squared(x,y). If `degree`

>1 then R.squared(x,y) is typically different from R.squared(y,x). Assume a set of n variables x1,...,xn (corresponding to the columns of `datExpr`

then one can define R.squared(xi,xj). The model fitting indices for the elements of an n x n dimensional matrix (R.squared(ij)).
`symmetrizationMethod`

implements the following symmetrization methods:
A.min(ij)=min(R.squared(ij),R.squared(ji)),
A.ave(ij)=(R.squared(ij)+R.squared(ji))/2,
A.max(ij)=max(R.squared(ij),R.squared(ji)).

An adjacency matrix of dimensions ncol(datExpr) times ncol(datExpr).

Lin Song, Steve Horvath

Song L, Langfelder P, Horvath S Avoiding mutual information based co-expression measures (to appear).

Horvath S (2011) Weighted Network Analysis. Applications in Genomics and Systems Biology. Springer Book. ISBN: 978-1-4419-8818-8

For more information about polynomial regression, please refer to functions
`poly`

and `glm`

```
#Simulate a data frame datE which contains 5 columns and 50 observations
m=50
x1=rnorm(m)
r=.5; x2=r*x1+sqrt(1-r^2)*rnorm(m)
r=.3; x3=r*(x1-.5)^2+sqrt(1-r^2)*rnorm(m)
x4=rnorm(m)
r=.3; x5=r*x4+sqrt(1-r^2)*rnorm(m)
datE=data.frame(x1,x2,x3,x4,x5)
#calculate adjacency by symmetrizing using max
A.max=adjacency.polyReg(datE, symmetrizationMethod="max")
A.max
#calculate adjacency by symmetrizing using max
A.mean=adjacency.polyReg(datE, symmetrizationMethod="mean")
A.mean
# output the unsymmetrized pairwise model fitting indices R.squared
R.squared=adjacency.polyReg(datE, symmetrizationMethod="none")
R.squared
```

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