Package 'snha' reference manual

Title:	Creating Correlation Networks using St. Nicolas House Analysis
Description:	Create correlation networks using St. Nicolas House Analysis ('SNHA'). The package can be used for visualizing multivariate data similar to Principal Component Analysis or Multidimensional Scaling using a ranking approach. In contrast to 'MDS' and 'PCA', 'SNHA' uses a network approach to explore interacting variables. For details see 'Hermanussen et. al. 2021', <doi:10.3390/ijerph18041741>.
Authors:	Detlef Groth
Maintainer:	Detlef Groth <[email protected]>
License:	MIT + file LICENSE
Version:	0.2.1
Built:	2025-02-10 04:13:49 UTC
Source:	https://github.com/mittelmark/snha

snha package - association chain graphs from correlation networks

Description

The snha package can be used to construct association chain graphs based on the St. Nicolas House Analysis (SNHA) algorithm as described in Groth et. al. 2019. and Hermanussen et. al. 2021.

Details

The package provides the following functions: Function for graph generation from data:

snha(data): applys the SNHA method on the data and returns a new snha graph object

S3 methods for snha graphs:

plot.snha(x): plots a snha graph
as.list.snha(x): return a list representation of a snha graph object

Utility functions:

snha_get_chains(g): returns the chains found by the algorithm as matrix
snha_graph2data(A): create for the given adjacency matrix some data with the appropiate correlations
snha_layout(g): calculate layout coordinates for the given graph or adjacency matrix
snha_ll(g,chain): calculate log-likelihood for the given chain of the snha graph
snha_rsquare(data,g): for given data and graph or adjacency matrix calculate linear model r-square value

Value

No return value

Author(s)

Detlef Groth <[email protected]>

References

Groth, D., Scheffler, C., & Hermanussen, M. (2019). Body height in stunted Indonesian children depends directly on parental education and not via a nutrition mediated pathway - Evidence from tracing association chains by St. Nicolas House Analysis. Anthropologischer Anzeiger, 76 No. 5 (2019), p. 445 - 451. doi:10.1127/anthranz/2019/1027
Hermanussen, M., Assmann, & Groth, D. (2021). Chain Reversion for Detecting Associations in Interacting Variables - St. Nicolas House Analysis. International Journal of Environmental Research and Public Health. 18, 4 (2021). doi:10.3390/ijerph18041741.
Novine, M., Mattsson, C. C., & Groth, D. (2021). Network reconstruction based on synthetic data generated by a Monte Carlo approach. Human Biology and Public Health, 3:26. doi:10.52905/hbph2021.3.26

Examples

 
library(MASS) 
data(birthwt) 
as=snha(birthwt[,-1]) 
plot(as) 
as$theta 
ls(as) 
data(decathlon88) 
head(decathlon88) 
dec=snha(decathlon88,method="spearman",alpha=0.1) 
plot(dec,layout='sam') 
library(MASS) 
data(birthwt) 
as=snha(birthwt[,-1]) 
plot(as) 
as$theta 
ls(as) 
data(decathlon88) 
head(decathlon88) 
dec=snha(decathlon88,method="spearman",alpha=0.1) 
plot(dec,layout='sam')

return a list representation for an snha graph object

Description

The function 'as.list.snha' provides a S3 method to convert a snha graph object into a list object which can be for instance used to write a report into an XLSX file using the library openxlsx.

Usage

## S3 method for class 'snha'
as.list(x,...)## S3 method for class 'snha'
as.list(x,...)

Arguments

`x`	snha graph object created with the snha function
`...`	additional arguments, delegated to the list command

Value

list object with the components: 'chains' (the association chain), 'data' (original data), 'theta' (adjacency matrix, 'sigma' (correlations), 'p.value' (correlation p-values)

Examples

  
data(swiss) 
as=snha(swiss,method="spearman",alpha=0.1) 
result=as.list(as) 
ls(result) 
result$settings 
# can be writte as xlsx file for instance like: 
# library(openxlsx) 
# write.xlsx(result,file="some-result.xlsx") 
data(swiss) 
as=snha(swiss,method="spearman",alpha=0.1) 
result=as.list(as) 
ls(result) 
result$settings 
# can be writte as xlsx file for instance like: 
# library(openxlsx) 
# write.xlsx(result,file="some-result.xlsx")

Men Decathlon data from the 1988 Olympics

Description

A subset of data from the Decathlon from the 1988 Olympic games. Included are all athletes which finished with more than 7000 points.

Usage

decathlon88decathlon88

Format

A data frame with 33 rows and 10 columns:

disc: discus results in m
high: high jump results in m
jave: javelin through results in m
long: long jump results in m
pole: pole vault results in m
shot: shot put results in m
X100: running speed over 100m in km/h
X110: running speed over 110m hurdles in km/h
X1500: running speed over 1500m in km/h
X400: running speed over 400m in km/h

Source

<https://en.wikipedia.org/wiki/Athletics_at_the_1988_Summer_Olympics_-_Men's_decathlon>

Examples

data(decathlon88)
head(decathlon88)
A=snha(decathlon88,method="spearman",alpha=0.1)
cols=rep("salmon",10)
cols[names(A$data) %in% c("jave","shot","disc","pole")]="skyblue"
plot(A,layout="sam",vertex.color=cols,vertex.size=8,cex=1.2,edge.width=5)
snha_rsquare(A)

data(decathlon88)
head(decathlon88)
A=snha(decathlon88,method="spearman",alpha=0.1)
cols=rep("salmon",10)
cols[names(A$data) %in% c("jave","shot","disc","pole")]="skyblue"
plot(A,layout="sam",vertex.color=cols,vertex.size=8,cex=1.2,edge.width=5)
snha_rsquare(A)

create a mgraph object, an adjacency matrix of a specific type

Description

This is a function to create a few different graph types such as barabasi, random, cluster etc to test the snha algorithms.

Usage

mgraph( 
  x=NULL, 
  type="random", 
  mode="directed", 
  nodes=10, 
  edges=12, 
  m=1, 
  k=3, 
  p=NULL, 
  power=1) 
mgraph( 
  x=NULL, 
  type="random", 
  mode="directed", 
  nodes=10, 
  edges=12, 
  m=1, 
  k=3, 
  p=NULL, 
  power=1)

Arguments

`x`	either a adjacency matrix or an adjacency list, if given type is not used
`type`	graph type, one of 'angie', 'band', 'barabasi', 'circle', 'cluster', 'hubs', 'nicolas','random', 'regular' or 'werner', default: 'random'
`mode`	either 'undirected' or 'directed', default: 'directed'
`nodes`	number of nodes for a given type, default: 10
`edges`	number of edges for a given type, not used for type "barabasi", default: 12
`m`	number of edges added in each iteration of type is 'barabasi', can be values such as 1,2 or fractionla numbers such as 1.3 which means 70 percent single chain addition and 30 percent double chain additions, default: 1
`k`	the degree for a regular graph, or the number of clusters for a cluster graph or the number of hubs for a hubs graph, default: 2
`p`	the probabilty for edges if type is 'gnp',default=NULL
`power`	the power for preferential attachment if type is 'barabasi', 1 is linear preferential attachment, below one is sublinear, smaller hubs, 0 is no hubs, above 1 is super linear with super hubs, default: 1

Value

mgraph object, which contains an adjacency matrix and optional an attribute for a layout

Examples

 
M <- matrix(0,nrow=7,ncol=7) 
rownames(M)=colnames(M)=LETTERS[1:7] 
M[c('A','B'),'C']=1 
M['C','D']=1 
M['D',c('E','F')]=1 
M['E','F']=1 
G=mgraph(M) 
set.seed(125) 
R = mgraph(type="random",nodes=8,edges=9) 
summary(R) 
A = mgraph(type="angie",nodes=8,edges=9) 
A 
C = mgraph(type="circle",nodes=8) 
B = mgraph(type="band",nodes=8) 
W=mgraph(type='werner') 
W 
B=mgraph(type='barabasi') 
B 
D=mgraph(type='barabasi',m=1.3) 
D 
N=mgraph(type='nicolas') 
## Nicolas graph brings its own layout 
plot(N,layout=attr(N,'layout')) 
M <- matrix(0,nrow=7,ncol=7) 
rownames(M)=colnames(M)=LETTERS[1:7] 
M[c('A','B'),'C']=1 
M['C','D']=1 
M['D',c('E','F')]=1 
M['E','F']=1 
G=mgraph(M) 
set.seed(125) 
R = mgraph(type="random",nodes=8,edges=9) 
summary(R) 
A = mgraph(type="angie",nodes=8,edges=9) 
A 
C = mgraph(type="circle",nodes=8) 
B = mgraph(type="band",nodes=8) 
W=mgraph(type='werner') 
W 
B=mgraph(type='barabasi') 
B 
D=mgraph(type='barabasi',m=1.3) 
D 
N=mgraph(type='nicolas') 
## Nicolas graph brings its own layout 
plot(N,layout=attr(N,'layout'))

quality measures for a predicted graph

Description

The function 'mgraph_accuracy' measures the prediction quality of a predicted graph in comparison to a known true one. The graph comparisons are done on the basis of undirected graphs only. Directed graphs are converted to undirected internally.

The most used accuracy measure to balance the different measures is the F-score where:

the F0.5 measure (beta=0.5) gives more weight on precision, less weight on sensitivity/recall.
the F1 measure (beta=1.0) balances the weight on precision and sensitivity/recall.
the F2 measure (beta=2.0) gives less weight on precision, more weight on sensitivity/recall

Usage

mgraph_accuracy(g.true,g.pred)mgraph_accuracy(g.true,g.pred)

Arguments

`g.true`	snha, mgraph or or adjacency matrix of a the true graph
`g.pred`	snha, mgraph or or adjacency matrix of a the predicted graph

Value

returns list object with various accuracy measures, such as Sens(itivity), Spec(ificity), Prec(ision), Acc(uracy), Non-information-rate (NIR), balanced classification rate (BCR), F1 measure and Mathhews correlation coefficient (MCC)

Examples

 
ang=mgraph(type="angie",nodes=12,edges=18) 
data=snha_graph2data(ang) 
pred=snha(t(data))$theta 
round(unlist(mgraph_accuracy(ang,pred)),2) 
#  using vectors 
tvec=c(1,1,1,0,0,0) 
pvec=c(1,1,0,1,0,0) 
table(tvec,pvec) 
mgraph_accuracy(tvec,pvec) 
ang=mgraph(type="angie",nodes=12,edges=18) 
data=snha_graph2data(ang) 
pred=snha(t(data))$theta 
round(unlist(mgraph_accuracy(ang,pred)),2) 
#  using vectors 
tvec=c(1,1,1,0,0,0) 
pvec=c(1,1,0,1,0,0) 
table(tvec,pvec) 
mgraph_accuracy(tvec,pvec)

create names for nodes and other data structures

Description

This function aids in creating standard node labels for graphs.

Usage

mgraph_autonames( 
  n, 
  prefix=NULL) 
mgraph_autonames( 
  n, 
  prefix=NULL)

Arguments

`n`	how many labels
`prefix`	the node prefix, per defaultif not given LETTERS with numbers will be used, default: NULL

Examples

 
mgraph_autonames(12) 
mgraph_autonames(12,LETTERS[1:4]) 
mgraph_autonames(12,"R") 
mgraph_autonames(12) 
mgraph_autonames(12,LETTERS[1:4]) 
mgraph_autonames(12,"R")

create an undirected graph out of a directed graph

Description

This function gets an directed graph and convertes all edges from directed ones to undirected ones. The number of edges should stay the same, the edge sign (+ or -) stays the same.

Usage

mgraph_d2u(g)mgraph_d2u(g)

Arguments

`g`	a mgraph object or an adjacency matrix

Examples

 
A=mgraph(type="angie",nodes=4,edges=4) 
A 
U=mgraph_d2u(A) 
U 
A=mgraph(type="angie",nodes=4,edges=4) 
A 
U=mgraph_d2u(A) 
U

return the number of edges for each node

Description

This function returns the number of edges adjacent to every node, for directed graphs it will as well return the in and out going edges.

Usage

mgraph_degree( 
  g, 
  mode='undirected') 
mgraph_degree( 
  g, 
  mode='undirected')

Arguments

`g`	a mgraph object
`mode`	how should the graph been analyzed, either 'undirected', 'out' or 'in', default: 'undirected'

Examples

 
A=mgraph(type="regular",nodes=8,k=3) 
mgraph_degree(A) 
mgraph_degree(A,mode="out") 
mgraph_degree(A,mode="in") 
A=mgraph(type="regular",nodes=8,k=3) 
mgraph_degree(A) 
mgraph_degree(A,mode="out") 
mgraph_degree(A,mode="in")

using linear models to check the create snha graph

Description

This function checks a given snha graph against its own data using linear models. Edges are removed if they do not add more than 2 percent of the adjusted R-square value. The function might be only called directly if the user would like to change the default values for del and add. The function snha uses defaults of 0.02 for del(eting) and 0.05 for add(ing) values.

Usage

mgraph_lmc(x,del=0.02,add=NULL,method='pearson')mgraph_lmc(x,del=0.02,add=NULL,method='pearson')

Arguments

`x`	snha graph object
`del`	r-square threshold to delete edges, edges not adding more than this value to the linear model to the target node will be deleted, default: 0.02
`add`	r-square threshold to add edges, if NULL no edges will be added, recommended value is 0.05, default: NULL
`method`	The method which was used to generate a graph, if spearman or mutual information were given data are rank transformed, default: 'pearson'

Value

returns adjacency matrix where edges migh be removed if they are not adding explanation to the model

Examples

 
set.seed(123) 
B=mgraph(type="barabasi",m=2,nodes=6) 
data=t(snha_graph2data(B)) 
aa=snha(data) 
aa$theta 
unlist(mgraph_accuracy(B,aa$theta)) 
ab=mgraph_lmc(aa) 
unlist(mgraph_accuracy(B,ab)) 
ab 
aa$theta-ab 
ac=mgraph_lmc(aa,add=0.02) 
unlist(mgraph_accuracy(B,ac)) 
set.seed(123) 
B=mgraph(type="barabasi",m=2,nodes=6) 
data=t(snha_graph2data(B)) 
aa=snha(data) 
aa$theta 
unlist(mgraph_accuracy(B,aa$theta)) 
ab=mgraph_lmc(aa) 
unlist(mgraph_accuracy(B,ab)) 
ab 
aa$theta-ab 
ac=mgraph_lmc(aa,add=0.02) 
unlist(mgraph_accuracy(B,ac))

linear model backward variable selection

Description

This function is a simple version of linear model building using backward variable selection. At each step the variable with the lowest decrease value in the adjusted R-square value is removed from the model and the r-square value is stored in the return matrix.

Usage

mgraph_lms(x)mgraph_lms(x)

Arguments

`x`	a data matrix or data frame

Value

returns matrix with the adjusted r-square values attributed by the variables

Examples

 
data(swiss) 
round(mgraph_lms(swiss)*100,2) 
W = mgraph(type='werner') 
data=t(snha_graph2data(W)) 
round(mgraph_lms(data)*100,2) 
data(swiss) 
round(mgraph_lms(swiss)*100,2) 
W = mgraph(type='werner') 
data=t(snha_graph2data(W)) 
round(mgraph_lms(data)*100,2)

network deconvolved data matrix using the algorithm of Feizi et. al. 2013

Description

This function is a R implementation for "A General Method to Distinguish Direct Dependencies over Networks" by Feizi et. al (2013). For the Matlab code look here: http://compbio.mit.edu/nd/code/ND.m

Usage

mgraph_nd(x,beta=0.99,alpha=1,control=FALSE)mgraph_nd(x,beta=0.99,alpha=1,control=FALSE)

Arguments

`x`	symmetric relevance matrix, where high similarity between nodes is expressed with high values such as in an correlation matrix
`beta`	scaling paramater, the largest absolute eigenvalue is mapped to beta, values should be between 0 and 1, default: 0.99
`alpha`	fraction of edges of the observed dependency matrix to be kept, should be between 0 (none) and 1 (all), default: 1
`control`	if FALSE only direct weights are displayed, if TRUE also non-observed interactions are displayed, default: FALSE

Value

returns matrix with deconvoluted relevance matrix

Author(s)

@2013 KELLIS-LAB, Soheil Feizi, Matlab code
@2021 Detlef Groth, University of Potsdam, R code

References

Feizi, S., Marbach, D., Medard, M., & Kellis, M. (2013). Network deconvolution as a general method to distinguish direct dependencies in networks. Nature biotechnology, 31(8), 726-733. DOI 10.1038/nbt.2635

Examples

 
W=mgraph(type="werner") 
W 
data=snha_graph2data(W) 
C=cor(t(data)) 
round(C,2) 
round(mgraph_nd(C,beta=0.9,alpha=0.3),2) 
# manually prepare the deconvoluted matrix 
D=mgraph_nd(C,beta=0.9,alpha=0.3) 
diag(D)=1 
par(mfrow=c(2,2)) 
plot(W) 
plot(snha(t(data))) 
plot(snha(t(data),nd=TRUE)) 
plot(snha(D)) 
W=mgraph(type="werner") 
W 
data=snha_graph2data(W) 
C=cor(t(data)) 
round(C,2) 
round(mgraph_nd(C,beta=0.9,alpha=0.3),2) 
# manually prepare the deconvoluted matrix 
D=mgraph_nd(C,beta=0.9,alpha=0.3) 
diag(D)=1 
par(mfrow=c(2,2)) 
plot(W) 
plot(snha(t(data))) 
plot(snha(t(data),nd=TRUE)) 
plot(snha(D))

create node colors for directed graphs

Description

This function simplifies automatic color coding of nodes for directed graphs. Nodes will be colored based on their degree properties, based on their incoming and outcoming edges.

Usage

mgraph_nodeColors(g, 
    col=c("skyblue","grey80","salmon") 
)mgraph_nodeColors(g, 
    col=c("skyblue","grey80","salmon") 
)

Arguments

`g`	a mgraph object or an adjacency matrix or an adjacency list
`col`	default colors for nodes with only incoming, in- and outgoing and only outgoing edges, default: c("skyblue","grey80","salmon")

Examples

 
par(mfrow=c(1,2),mai=rep(0.1,4)) 
A=mgraph(type="random",nodes=6,edges=8) 
cols=mgraph_nodeColors(A) 
mgraph_degree(A,mode="in") 
mgraph_degree(A,mode="out") 
cols 
plot(A, layout="star") 
plot(A, layout="star",vertex.color=cols)  
par(mfrow=c(1,2),mai=rep(0.1,4)) 
A=mgraph(type="random",nodes=6,edges=8) 
cols=mgraph_nodeColors(A) 
mgraph_degree(A,mode="in") 
mgraph_degree(A,mode="out") 
cols 
plot(A, layout="star") 
plot(A, layout="star",vertex.color=cols)

checking possible chains with 3 nodes for triad structures

Description

Experimental:

This function checks a given snha graph for possible triad structures which were not recognized by the original algorithm. The method checks all nodes within path length 2 for a possible edge by comparing the ratio of the correlation coefficients. The function snha uses defaults of 0.02 for del(eting) and 0.05 for add(ing) values.

Usage

mgraph_trf(x,frac=1.2)mgraph_trf(x,frac=1.2)

Arguments

`x`	snha graph object
`frac`	amount which the absolute correlation exceeds in compariuson of the product of the other two correlations in the possible triad, value should be larger than 1, default: 1.2

Value

returns snha graph object with added triads to chains and to the adjacency matrix

Examples

 
set.seed(124) 
W=mgraph(type="werner") 
data=t(snha_graph2data(W)) 
aa=snha(data) 
aa$theta 
unlist(mgraph_accuracy(W,aa$theta)) 
# remove false positive by linear model 
ab=mgraph_lmc(aa) 
aa$theta=ab 
aa=mgraph_trf(aa) 
unlist(mgraph_accuracy(W,aa$theta)) 
set.seed(124) 
W=mgraph(type="werner") 
data=t(snha_graph2data(W)) 
aa=snha(data) 
aa$theta 
unlist(mgraph_accuracy(W,aa$theta)) 
# remove false positive by linear model 
ab=mgraph_lmc(aa) 
aa$theta=ab 
aa=mgraph_trf(aa) 
unlist(mgraph_accuracy(W,aa$theta))

reate a directed graph out of an undirected graph

Description

This function creates a directed graph from an undirected one by the given input nodes. Input nodes can be chosen by names or a number for random selection of input nodes will be given. Input nodes will have at least shortest path distance to other input nodes of pathlength two. Selected input nodes will draw in each iteration outgoing edges to other nodes in the nth iteration neighborhood. The input nodes will alternatively select the next edges on the path to not visited nodes. All edges will be only visited onces.

Usage

mgraph_u2d( 
    g,input=2,negative=0.0,shuffle=FALSE 
)mgraph_u2d( 
    g,input=2,negative=0.0,shuffle=FALSE 
)

Arguments

`g`	mgraph object created with mgraph
`input`	number or names of input nodes in the graph, if number of input nodes is smaller than number of components, for each component one input node is automatically created
`negative`	proportion of inhibitive associations in the network value between 0 and 1 are acceptable, Default 0.0
`shuffle`	should just the edge directions beeing shuffled, if TRUE the graph will be very random without a real structure or chains of associations, default: FALSE

Examples

 
par(mfrow=c(2,2),mai=rep(0.1,4)) 
G=mgraph(type="angie",nodes=7,edges=9) 
mgraph_degree(G,mode='in') 
U=mgraph_d2u(G) 
H=mgraph_u2d(U,input=c("G","E")) 
identical(G,H) 
I=mgraph_u2d(U,shuffle=TRUE) 
identical(G,I) 
lay=snha_layout(G) 
plot(G,layout=lay,vertex.color=mgraph_nodeColors(G)) 
plot(U,layout=lay) 
plot(H,layout=lay,vertex.color=mgraph_nodeColors(H)) 
plot(I,layout=lay,vertex.color=mgraph_nodeColors(I)) 
par(mfrow=c(2,2),mai=rep(0.1,4)) 
G=mgraph(type="angie",nodes=7,edges=9) 
mgraph_degree(G,mode='in') 
U=mgraph_d2u(G) 
H=mgraph_u2d(U,input=c("G","E")) 
identical(G,H) 
I=mgraph_u2d(U,shuffle=TRUE) 
identical(G,I) 
lay=snha_layout(G) 
plot(G,layout=lay,vertex.color=mgraph_nodeColors(G)) 
plot(U,layout=lay) 
plot(H,layout=lay,vertex.color=mgraph_nodeColors(H)) 
plot(I,layout=lay,vertex.color=mgraph_nodeColors(I))

display network or correlation matrices of snha graphs

Description

The function 'plot.snha' provides a simple display of network graphs or correlation matrices using filled circles (vertices) to represent variables and edges which connect the vertices with high absolute. correlation values. Positive correlations are shown in black, negative correlations are shown in red. For more information see the details section.

Usage

 
## S3 method for class 'snha'
plot( 
 x, 
 type = "network", 
 layout = "circle", 
 vertex.color = "salmon", 
 cex = 1, 
 vertex.size = 5, 
 edge.width = 2, 
 edge.color = c("grey70", "red"), 
 edge.text = NULL, 
 edge.cex = 0.8, 
 edge.pch = 0, 
 noise = FALSE, 
 hilight.chain = NULL, 
 chain.color = c("black", "red"), 
 star.center = NULL, 
 plot.labels = TRUE, 
 lty = 1, 
 threshold = c(0.25, 0.5, 0.75), 
 interactive = FALSE, 
 ... 
) 
## S3 method for class 'snha'
plot( 
 x, 
 type = "network", 
 layout = "circle", 
 vertex.color = "salmon", 
 cex = 1, 
 vertex.size = 5, 
 edge.width = 2, 
 edge.color = c("grey70", "red"), 
 edge.text = NULL, 
 edge.cex = 0.8, 
 edge.pch = 0, 
 noise = FALSE, 
 hilight.chain = NULL, 
 chain.color = c("black", "red"), 
 star.center = NULL, 
 plot.labels = TRUE, 
 lty = 1, 
 threshold = c(0.25, 0.5, 0.75), 
 interactive = FALSE, 
 ... 
)

Arguments

`x`	snha graph object usually created with the 'snha' function or an adjacency matrix
`type`	character string specifying the plot type either 'network' or ' cor', default: 'network'
`layout`	graph layout for plotting one of 'circle', 'sam', 'samd', 'grid', 'mds', 'mdsd', 'star', default: 'circle'
`vertex.color`	default color for the vertices, either a single value, all vertices have hen this color or a vector of values, for different colors for the nodes, default: 'salmon'
`cex`	size of the vertex labels which are plotted on the vertices, default: 1
`vertex.size`	number how large the vertices should be plotted, default: 5
`edge.width`	number on how strong the edges should be plotted, if edge.width=0, then the number is based on the correlation values, default: 2
`edge.color`	color to be plotted for edges. Usually vector of length two. First color for positive correlations, second color for negative correlations. Default: c('grey','red')
`edge.text`	optional matrix to give edge labels, default: NULL
`edge.cex`	character expansion for edge labels, default: 0.8
`edge.pch`	plotting character which should be placed below the edge.text, default: 0
`noise`	should be noise added to the layout. Sometimes useful if nodes are too close. Default: FALSE
`hilight.chain`	which chain should be highlighted, default: NULL (no chain highlight)
`chain.color`	which color for chain edges, default: black
`star.center`	the centered node if layout is 'start', must be a character string for the node name, default: NULL
`plot.labels`	should node labels plotted, default: TRUE
`lty`	line type for standard edges in the graph, default: 1
`threshold`	cutoff values for bootstrap probabilities for drawing edges as dotted, broken lines and solid lines, default: c(0.25,0.5,0.75)
`interactive`	switch into interactive mode where you can click in the graph and move nodes with two clicks, first selecting the node, second click gives the new coordinates for the node, default: FALSE
`...`	currently not used

Details

This is a plot function to display networks or correlation matrices of 'snha' graph objects. In case of bootstrapping the graph by using the 'snha' function with the 'prob=TRUE' option lines in style full, broken and dotted lines are drawn if they are found in more than 75, 50 or 25 percent of all re-samplings. You can change these limits by using the 'threshold' argument.

Value

returns the layout of the plotted network or NULL if type is 'corrplot' (invisible)

Examples

  
data(swiss) 
sw.g=snha(swiss,method='spearman') 
sw.g$theta 
round(sw.g$sigma,2) 
plot(sw.g,type='network',layout='circle') 
plot(sw.g,type='network',layout='sam') 
plot(sw.g,type='corplot') 
# adding correlation values 
plot(sw.g,edge.text=round(sw.g$sigma,2),edge.cex=1.2,edge.pch=15) 
sw.g=snha(swiss,method='spearman',prob=TRUE) 
sw.g$theta 
sw.g$probabilities 
plot(sw.g,type='network',layout='sam') 
sw.g$chains 
# plot chains for a node 
plot(sw.g,layout="sam",lty=2,hilight.chain="Infant.Mortality", 
 edge.width=3,edge.color=c("black","red")) 
# an example for an adjacency matrix 
M=matrix(rbinom(100,1, 0.2),nrow=10,ncol=10) 
diag(M)=0 
colnames(M)=rownames(M)=LETTERS[1:10] 
plot.snha(M) 
data(swiss) 
sw.g=snha(swiss,method='spearman') 
sw.g$theta 
round(sw.g$sigma,2) 
plot(sw.g,type='network',layout='circle') 
plot(sw.g,type='network',layout='sam') 
plot(sw.g,type='corplot') 
# adding correlation values 
plot(sw.g,edge.text=round(sw.g$sigma,2),edge.cex=1.2,edge.pch=15) 
sw.g=snha(swiss,method='spearman',prob=TRUE) 
sw.g$theta 
sw.g$probabilities 
plot(sw.g,type='network',layout='sam') 
sw.g$chains 
# plot chains for a node 
plot(sw.g,layout="sam",lty=2,hilight.chain="Infant.Mortality", 
 edge.width=3,edge.color=c("black","red")) 
# an example for an adjacency matrix 
M=matrix(rbinom(100,1, 0.2),nrow=10,ncol=10) 
diag(M)=0 
colnames(M)=rownames(M)=LETTERS[1:10] 
plot.snha(M)

Initialize a snha object with data.

Description

The main entry function to initialize a snha object with data where variables are in columns and items are in rows. If you like to use the network deconvolution method of Feizi et al. instead of the data submit the deconvoluted matrix. As methods either correlation methods such as pearson, spearman or kendall or mutual information (mi) can be used. The latter method as well covers non-linear linear relationships.

Usage

snha( 
  data, 
  alpha=0.05, 
  method='pearson', 
  threshold=0.01, 
  check.singles=FALSE, 
  prob=FALSE, 
  prob.threshold=0.2, 
  prob.n=25, 
  nd=FALSE, 
  lmc=FALSE, 
  lma=FALSE) 
snha( 
  data, 
  alpha=0.05, 
  method='pearson', 
  threshold=0.01, 
  check.singles=FALSE, 
  prob=FALSE, 
  prob.threshold=0.2, 
  prob.n=25, 
  nd=FALSE, 
  lmc=FALSE, 
  lma=FALSE)

Arguments

`data`	a data frame where network nodes are the row names and data variables are in the columns.
`alpha`	confidence threshold for p-value edge cutting after all chains were generated, default: 0.05.
`method`	method to calculate correlation/association values, can be 'pearson', 'spearman' or 'kendall', 'mi', default: 'pearson'.
`threshold`	R-squared correlation coefficient threshold for which r-square values should be used for chain generation, r=0.1 is r-square of 0.01, default: 0.01.
`check.singles`	should isolated nodes connected with sufficient high R^2 and significance, default: FALSE.
`prob`	should be probabilities computed for each edge using bootstrapping. Only in this case the parameters starting with prob are used, default: FALSE
`prob.threshold`	threshold to set an edge, a value of 0.5 means, that the edge must be found in 50% of all samplings, default: 0.2
`prob.n`	number of bootstrap samples to be taken, default: 25
`nd`	perfom network deconvolution due to the method of Feizi et. al. 2013, default: FALSE
`lmc`	perfom a linear model check, edges which does not improve the node model by adjacent edges more than 0.02 are removed, default: FALSE
`lma`	perfom a linear model check, edges which does improve the node model by adjacent edges with more than 0.02 R-square are added, works only if lmc is TRUE,default: FALSE

Value

A snha graph data object with the folling components:

chains: association chains building the graph
data: representing the original input data
p.values: matrix with p-values for the pairwise correlations
probabilities: in case of re-samplings, the proportion how often the chain was found
sigma: correlation matrix used for the algorithm
theta: adjacency matrix found by the SNHA method

Examples

 
data(swiss) 
sw.g=snha(swiss,method='spearman') 
# what objects are there? 
ls(sw.g) 
sw.g$theta 
round(sw.g$sigma,2) 
sw.g=snha(swiss,method='spearman',check.singles=TRUE,prob=TRUE) 
sw.g$theta 
sw.g$probabilities 
sw.m=snha(swiss,method="mi") 
sw.m$theta 
par(mfrow=c(1,2)) 
plot(sw.g) 
plot(sw.m) 
data(swiss) 
sw.g=snha(swiss,method='spearman') 
# what objects are there? 
ls(sw.g) 
sw.g$theta 
round(sw.g$sigma,2) 
sw.g=snha(swiss,method='spearman',check.singles=TRUE,prob=TRUE) 
sw.g$theta 
sw.g$probabilities 
sw.m=snha(swiss,method="mi") 
sw.m$theta 
par(mfrow=c(1,2)) 
plot(sw.g) 
plot(sw.m)

visualize a matrix of pairwise correlations

Description

This function returns xy coordinates for a given input adjacency matrix or snha graph. It is useful if you like to plot the same set of nodes with different edge connections in the same layout.

Usage

snha_corrplot( 
   x, 
   text.lower=FALSE, 
   text.upper=FALSE, 
   pch.minus=19, 
   pch.plus=19, 
   xtext=NULL, 
   cex=1.0, 
   ...) 
snha_corrplot( 
   x, 
   text.lower=FALSE, 
   text.upper=FALSE, 
   pch.minus=19, 
   pch.plus=19, 
   xtext=NULL, 
   cex=1.0, 
   ...)

Arguments

`x`	matrix with pairwise correlations
`text.lower`	should in the lower diagonal the correlation coefficient be shown, default: TRUE
`text.upper`	should in the upper diagonal the correlation coefficient be shown, default: FALSE
`pch.minus`	the plotting symbol for negative correlations, default: 19
`pch.plus`	the plotting symbol for positive correlations, default: 19
`xtext`	labels which should be placed at the bottom of the plot, default: NULL
`cex`	character expansion for text and correlation symbols, default: 1
`...`	arguments delegated to the plot function

Examples

 
data(swiss) 
sw=swiss 
colnames(sw)=abbreviate(colnames(swiss),6) 
options(warn=-1) # avoid spearman warnings 
snha_corrplot(cor(sw,method="spearman"),cex.sym=8,text.lower=TRUE) 
options(warn=0) 
data(swiss) 
sw=swiss 
colnames(sw)=abbreviate(colnames(swiss),6) 
options(warn=-1) # avoid spearman warnings 
snha_corrplot(cor(sw,method="spearman"),cex.sym=8,text.lower=TRUE) 
options(warn=0)

Return the chains of a snha graph as data frame

Description

This is a utility function to return the chains which constructs the graph as a matrix.

Usage

snha_get_chains(graph)snha_get_chains(graph)

Arguments

graph

a snha graph object

Value

matrix with one chain per row, shorter chains are filled up with empty strings

Examples

 
data(swiss) 
sw.g=snha(swiss) 
snha_get_chains(sw.g) 
data(swiss) 
sw.g=snha(swiss) 
snha_get_chains(sw.g)

create correlated data for the given adjacency matrix representing a directed graph or an undirected graph

Description

This function is a short implementation of the Monte Carlo algorithm described in Novine et. al. 2022.

Usage

snha_graph2data( 
  A, 
  n=100, 
  iter=50, 
  val=100, 
  sd=2, 
  prop=0.025, 
  noise=1, 
  method="mc" 
  ) 
snha_graph2data( 
  A, 
  n=100, 
  iter=50, 
  val=100, 
  sd=2, 
  prop=0.025, 
  noise=1, 
  method="mc" 
  )

Arguments

`A`	an adjacency matrix
`n`	number of values, measurements per node, default: 100
`iter`	number of iterations, default: 50
`sd`	initial standard deviation, default: 2
`val`	initial node value, default: 100
`prop`	proportion of the target node value take from the source node, default: 0.025
`noise`	sd for the noise value added after each iteration using rnorm function with mean 0, default: 1
`method`	method for data generation, either 'mc' for using Monte Carlo simulation or 'pc' for using a precision matrix, default: 'mc'

Value

matrix with the node names as rows and samplings in the columns

References

Novine, M., Mattsson, C. C., & Groth, D. (2021). Network reconstruction based on synthetic data generated by a Monte Carlo approach. Human Biology and Public Health, 3:26. doi:10.52905/hbph2021.3.26

Examples

 
opar=par(mfrow=c(1,2),mai=rep(0.2,4)) 
A=matrix(0,nrow=6,ncol=6) 
rownames(A)=colnames(A)=LETTERS[1:6] 
A[1:2,3]=1 
A[3,4]=1 
A[4,5:6]=1 
A[5,6]=1 
plot.snha(A,layout="circle");  
data=snha_graph2data(A) 
round(cor(t(data)),2) 
P=snha(t(data)) 
plot(P,layout="circle") 
par(opar) 
opar=par(mfrow=c(1,2),mai=rep(0.2,4)) 
A=matrix(0,nrow=6,ncol=6) 
rownames(A)=colnames(A)=LETTERS[1:6] 
A[1:2,3]=1 
A[3,4]=1 
A[4,5:6]=1 
A[5,6]=1 
plot.snha(A,layout="circle");  
data=snha_graph2data(A) 
round(cor(t(data)),2) 
P=snha(t(data)) 
plot(P,layout="circle") 
par(opar)

Determine graph layouts

Description

This function returns xy coordinates for a given input adjacency matrix or snha graph. It is useful if you like to plot the same set of nodes with different edge connections in the same layout.

Usage

snha_layout( 
   A, 
   mode='sam', 
   method='pearson',  
   noise=FALSE,  
   star.center=NULL, 
   interactive=FALSE) 
snha_layout( 
   A, 
   mode='sam', 
   method='pearson',  
   noise=FALSE,  
   star.center=NULL, 
   interactive=FALSE)

Arguments

`A`	an adjacency matrix or an snha graph object
`mode`	character string for the layout type, can be either 'mds' (mds on graph using shortest paths), 'mdsd' (mds on data) 'sam' (sammon on graph), 'samd' (sammon on data), 'circle', 'grid' or 'star', default: 'sam'
`method`	method for calculating correlation distance if mode is either 'mdsd' or 'samd', default: 'pearson'
`noise`	should some noise be added, default: FALSE
`star.center`	the centered node if layout is 'star', must be a character string for the node name, default: NULL
`interactive`	switch into interactive mode where you can click in the graph and move nodes with two clicks, first selecting the node, second click gives the new coordinates for the node, default: FALSE

Value

matrix with x and y columns for the layout

Examples

 
data(swiss) 
sw.s=snha(swiss,method='spearman') 
sw.p=snha(swiss,method='pearson') 
lay=snha_layout(sw.s,mode='sam') 
plot(sw.s,layout=lay) 
plot(sw.p,layout=lay) 
plot(sw.s,layout='star',star.center='Education') 
rn1=rnorm(nrow(swiss)) 
nswiss=cbind(swiss,Rn1=rn1) 
plot(snha(nswiss,method='spearman'),layout='sam') 
plot(snha(nswiss,method='spearman'),layout='samd', 
  vertex.size=2,vertex.color='beige') 
data(swiss) 
sw.s=snha(swiss,method='spearman') 
sw.p=snha(swiss,method='pearson') 
lay=snha_layout(sw.s,mode='sam') 
plot(sw.s,layout=lay) 
plot(sw.p,layout=lay) 
plot(sw.s,layout='star',star.center='Education') 
rn1=rnorm(nrow(swiss)) 
nswiss=cbind(swiss,Rn1=rn1) 
plot(snha(nswiss,method='spearman'),layout='sam') 
plot(snha(nswiss,method='spearman'),layout='samd', 
  vertex.size=2,vertex.color='beige')

log-likelihood for the given snha graph and the given chain

Description

This function returns the log-likelihood for the given snha graph and the given chain. If the 'block.p.value' is lower than 0.05 than that the chain is not sufficient to capture the variable dependencies, p-values above 0.05 indicate a good coverage of the chain for the linear dependencies between the nodes.

Usage

snha_ll(graph,chain=NULL)snha_ll(graph,chain=NULL)

Arguments

`graph`	a snha graph object
`chain`	a chain object of a snha graph, if not given a data frame with the values is returned for all chains, default: NULL

Value

list with the following components: 'll.total', 'll.chain', 'll.rest', 'll.block', data frame 'df' with the columns 'chisq', 'p.value', 'block.df', 'block.ch', 'block.p.value'. If chain is not given an overall summary is made for all chains an returned as data frame.

Examples

 
data(swiss) 
sw.g=snha(swiss) 
snha_ll(sw.g,sw.g$chain$Catholic) 
head(snha_ll(sw.g)) 
data(swiss) 
sw.g=snha(swiss) 
snha_ll(sw.g,sw.g$chain$Catholic) 
head(snha_ll(sw.g))

mutual information for two vectors or a matrix

Description

This function computes the mutual information between two numerical variables or for all pairs of variables if a matrix is given. The normalization is actual value divided by the the geometric mean: I'(X,Y) = I(X,Y)/sqrt(I(X)*I(Y))

Usage

snha_mi(x,y=NULL,breaks=4,coc=FALSE,gnorm=FALSE,norm=FALSE)snha_mi(x,y=NULL,breaks=4,coc=FALSE,gnorm=FALSE,norm=FALSE)

Arguments

`x`	either a binned table, a matrix or data.frame or a numerical vector
`y`	numerical vector, required if x is a vector, otherwise ignored,default:NULL
`breaks`	number of breaks to create a binned table, default: 4
`coc`	Coefficient of constrains, Cxy=Ixy/Hy and Cyx=Ixy/Hx, this measure is asymetric,default:FALSE
`gnorm`	mutual information should be normalized by using the geometric mean Ixy=Ixy/sqrt(Ix*Iy),default:FALSE
`norm`	divide every MI value by the MI value for the variable, this measure is as well asymetric,default:FALSE

Value

mutual information value as scalar if input is table or two vectors or as matrix if input is matrix or data.frame

Examples

 
rn1=rnorm(100,mean=10,sd=1); 
rn2=rn1+0.5*rnorm(100) 
cor(rn1,rn2) # high 
cor(rn1,sample(rn2)) #random  
snha_mi(rn1,rn2) # high  
snha_mi(rn1,sample(rn2)) #random 
snha_mi(rn1,rn2,breaks=4) 
snha_mi(rn1,rn2,breaks=7) 
data(swiss) 
round(snha_mi(swiss),2) 
round(snha_mi(swiss,gnorm=TRUE),2) 
as=snha(snha_mi(swiss,gnorm=TRUE)) 
plot(as) 
rn1=rnorm(100,mean=10,sd=1); 
rn2=rn1+0.5*rnorm(100) 
cor(rn1,rn2) # high 
cor(rn1,sample(rn2)) #random  
snha_mi(rn1,rn2) # high  
snha_mi(rn1,sample(rn2)) #random 
snha_mi(rn1,rn2,breaks=4) 
snha_mi(rn1,rn2,breaks=7) 
data(swiss) 
round(snha_mi(swiss),2) 
round(snha_mi(swiss,gnorm=TRUE),2) 
as=snha(snha_mi(swiss,gnorm=TRUE)) 
plot(as)

linear model based r-square values for given data and graph

Description

The function 'snha_rsquare' calculates for given data and a graph the covered r-squared values by a linear model for each node. The linear model predicts each node by an additive mode using it's neighbor nodes in the graph.

Usage

snha_rsquare(data,graph=NULL)snha_rsquare(data,graph=NULL)

Arguments

`data`	data matrix or data frame where variables are in columns and samples in rows or a snha graph
`graph`	graph object or adjacency matrix of an (un)directed graph, not needed if data is a snha graph, default: NULL.

Value

vector of rsquare values for each node of the graph

Examples

  
# random adjacency matrix 
A=matrix(rbinom(100,1, 0.2),nrow=10,ncol=10) 
diag(A)=0 
colnames(A)=rownames(A)=LETTERS[1:10] 
# random data 
data=matrix(rnorm(1000),ncol=10) 
colnames(data)=colnames(A) 
snha_rsquare(data,A) 
# real data 
data(swiss) 
sw.s=snha(swiss,method='spearman') 
rsqs=snha_rsquare(sw.s) 
plot(sw.s,main=paste("r =",round(mean(rsqs,2))), 
   layout='star',star.center='Examination') 
# some colors for r-square values 
vcols=paste("grey",seq(80,40,by=-10),sep="") 
scols=as.character(cut(snha_rsquare(swiss,sw.s$theta), 
   breaks=c(0,0.1,0.3,0.5,0.7,1),labels=vcols)) 
plot(sw.s,main=paste("r =",round(mean(snha_rsquare(swiss,sw.s$theta)),2)), 
   vertex.color=scols ,layout='star',star.center='Examination', 
   vertex.size=10,edge.color=c('black','red'),edge.width=3) 
# random adjacency matrix 
A=matrix(rbinom(100,1, 0.2),nrow=10,ncol=10) 
diag(A)=0 
colnames(A)=rownames(A)=LETTERS[1:10] 
# random data 
data=matrix(rnorm(1000),ncol=10) 
colnames(data)=colnames(A) 
snha_rsquare(data,A) 
# real data 
data(swiss) 
sw.s=snha(swiss,method='spearman') 
rsqs=snha_rsquare(sw.s) 
plot(sw.s,main=paste("r =",round(mean(rsqs,2))), 
   layout='star',star.center='Examination') 
# some colors for r-square values 
vcols=paste("grey",seq(80,40,by=-10),sep="") 
scols=as.character(cut(snha_rsquare(swiss,sw.s$theta), 
   breaks=c(0,0.1,0.3,0.5,0.7,1),labels=vcols)) 
plot(sw.s,main=paste("r =",round(mean(snha_rsquare(swiss,sw.s$theta)),2)), 
   vertex.color=scols ,layout='star',star.center='Examination', 
   vertex.size=10,edge.color=c('black','red'),edge.width=3)

Package 'snha'

Help Index

snha package - association chain graphs from correlation networks

Description

Details

Value

Author(s)

References

Examples

return a list representation for an snha graph object

Description

Usage

Arguments

Value

See Also

Examples

Men Decathlon data from the 1988 Olympics

Description

Usage

Format

Source

Examples

create a mgraph object, an adjacency matrix of a specific type

Description

Usage

Arguments

Value

See Also

Examples

quality measures for a predicted graph

Description

Usage

Arguments

Value

Examples

create names for nodes and other data structures

Description

Usage

Arguments

Examples

create an undirected graph out of a directed graph

Description

Usage

Arguments

Examples

return the number of edges for each node

Description

Usage

Arguments

Examples

using linear models to check the create snha graph

Description

Usage

Arguments

Value

Examples

linear model backward variable selection

Description

Usage

Arguments

Value

Examples

network deconvolved data matrix using the algorithm of Feizi et. al. 2013

Description

Usage

Arguments

Value

Author(s)

References

Examples

create node colors for directed graphs

Description

Usage

Arguments

Examples

checking possible chains with 3 nodes for triad structures

Description

Usage

Arguments

Value