osdsm | R Documentation |

`osdsm`

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

```
osdsm(
B,
alpha = 0.05,
trials = NULL,
missing.as.zero = FALSE,
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 |

`missing.as.zero` |
boolean: should missing edges be treated as edges with zero weight and tested for significance |

`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. |

`...` |
optional arguments |

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. The resulting backbone
contains edges whose weights are significantly *stronger* than expected in the null model. When `signed = TRUE`

, a
two-tailed test (is the weight stronger or weaker?) is performed for each edge. The resulting backbone contains
positive edges for those whose weights are significantly *stronger*, and negative edges for those whose weights are
significantly *weaker*, than expected in the null model.

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. This precision impacts the confidence that a given edge's p-value
is less than the desired `alpha`

level, and therefore represents a statistically significant edge that should be retained in
the backbone. When `trials = NULL`

, `trials.needed()`

is used to estimate the required number of trials to evaluate the
statistical significance of an edges' p-values.

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. \Sexpr[results=rd]{tools:::Rd_expr_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. \Sexpr[results=rd]{tools:::Rd_expr_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
```

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