osdsm {backbone} | R Documentation |

`osdsm`

extracts the backbone of a bipartite projection using the Ordinal Stochastic Degree Sequence Model.

```
osdsm(
B,
alpha = 0.05,
trials = NULL,
signed = FALSE,
mtc = "none",
class = "original",
narrative = FALSE,
progress = TRUE
)
```

`B` |
An ordinally weighted bipartite graph, as: (1) an incidence matrix in the form of a matrix or sparse |

`alpha` |
real: significance level of hypothesis test(s) |

`trials` |
integer: the number of bipartite graphs generated to approximate the edge weight distribution. If NULL, the number of trials is selected based on |

`signed` |
boolean: TRUE for a signed backbone, FALSE for a binary backbone (see details) |

`mtc` |
string: type of Multiple Test Correction to be applied; can be any method allowed by |

`class` |
string: the class of the returned backbone graph, one of c("original", "matrix", "Matrix", "igraph", "edgelist").
If "original", the backbone graph returned is of the same class as |

`narrative` |
boolean: TRUE if suggested text & citations should be displayed. |

`progress` |
boolean: TRUE if the progress of Monte Carlo trials should be displayed. |

The `osdsm`

function compares an edge's observed weight in the projection `B*t(B)`

to the distribution of weights
expected in a projection obtained from a random bipartite network where both the rows and the columns contain
approximately the same number of each value. The edges in `B`

must be integers, and are assumed to represent an
ordinal-level measure such as a Likert scale that starts at 0.

When `signed = FALSE`

, a one-tailed test (is the weight stronger) is performed for each edge with a non-zero weight. It
yields a backbone that perserves edges whose weights are significantly *stronger* than expected in the chosen null
model. When `signed = TRUE`

, a two-tailed test (is the weight stronger or weaker) is performed for each every pair of nodes.
It yields a backbone that contains positive edges for edges whose weights are significantly *stronger*, and
negative edges for edges whose weights are significantly *weaker*, than expected in the chosen null model.
*NOTE: Before v2.0.0, all significance tests were two-tailed and zero-weight edges were evaluated.*

The p-values used to evaluate the statistical significance of each edge are computed using Monte Carlo methods. The number of
`trials`

performed affects the precision of these p-values, and the confidence that a given p-value is less than the
desired `alpha`

level. Because these p-values are proportions (i.e., the proportion of times an edge is weaker/stronger
in the projection of a random bipartite graphs), evaluating the statistical significance of an edge is equivalent to
comparing a proportion (the p-value) to a known proportion (alpha). When `trials = NULL`

, the `power.prop.test`

function
is used to estimate the required number of trials to make such a comparison with a `alpha`

type-I error rate, (1-`alpha`

) power,
and when the riskiest p-value being evaluated is at least 5% smaller than `alpha`

. When any `mtc`

correction is applied,
for simplicity this estimation is based on a conservative Bonferroni correction.

If `alpha`

!= NULL: Binary or signed backbone graph of class `class`

.

If `alpha`

== NULL: An S3 backbone object containing (1) the weighted graph as a matrix, (2) upper-tail p-values as a
matrix, (3, if `signed = TRUE`

) lower-tail p-values as a matrix, (4, if present) node attributes as a dataframe, and
(5) several properties of the original graph and backbone model, from which a backbone can subsequently be extracted
using `backbone.extract()`

.

package: Neal, Z. P. (2022). backbone: An R Package to Extract Network Backbones. *PLOS ONE, 17*, e0269137. doi: 10.1371/journal.pone.0269137

osdsm: Neal, Z. P. (2017). Well connected compared to what? Rethinking frames of reference in world city network research. *Environment and Planning A, 49*, 2859-2877. doi: 10.1177/0308518X16631339

```
#A weighted binary bipartite network of 20 agents & 50 artifacts; agents form two communities
B <- rbind(cbind(matrix(sample(0:3, 250, replace = TRUE, prob = ((1:4)^2)),10),
matrix(sample(0:3, 250, replace = TRUE, prob = ((4:1)^2)),10)),
cbind(matrix(sample(0:3, 250, replace = TRUE, prob = ((4:1)^2)),10),
matrix(sample(0:3, 250, replace = TRUE, prob = ((1:4)^2)),10)))
P <- B%*%t(B) #An ordinary weighted projection...
plot(igraph::graph_from_adjacency_matrix(P, mode = "undirected",
weighted = TRUE, diag = FALSE)) #...is a dense hairball
bb <- osdsm(B, alpha = 0.05, narrative = TRUE, #An oSDSM backbone...
class = "igraph", trials = 100)
plot(bb) #...is sparse with clear communities
```

[Package *backbone* version 2.1.2 Index]