Model Terms in iglm

Key Definitions

Before stating all statistics, we introduce the formal notation and definitions used throughout this vignette:

Population and Dyads:
- \(𝒫 = \{1, \ldots, N\}\) denotes the population of \(N\) units.
- \(𝒟\) denotes the set of dyads (pairs of distinct units): \(𝒟 = \{(i,j) : 1 \le i \neq j \le N\}\) for directed connections and \(𝒟 = \{(i,j) : 1 \le i < j \le N\}\) for undirected connections.
Variables and Attributes:
- \(x_i\): Exogenous (or secondary) predictor attribute of unit \(i \in 𝒫\).
- \(y_i\): Endogenous outcome attribute of unit \(i \in 𝒫\).
- \(z_{i,j} \in \{0, 1\}\): Binary connection indicator from unit \(i\) to unit \(j\) for \((i,j) \in 𝒟\), collected in the connection matrix \(\mathbf{z}\).
- \(v_i\): Optional unit-level exogenous covariate.
- \(w_{i,j}\): Optional dyadic exogenous covariate.
Neighbourhoods and Local Structure:
- \(𝒩_i \subset 𝒫\) denotes the local neighbourhood of unit \(i\) (with \(i \in 𝒩_i\)).
- \(c_{i,j} \in \{0, 1\}\) is the neighbourhood overlap indicator, taking the value 1 if \(𝒩_i \cap 𝒩_j \neq \emptyset\), and 0 otherwise.
Connections: Different types of indicators for connections:
- Overlapping: \(u_{i,j} = c_{i,j} z_{i,j}\), a connection between units \(i\) and \(j\) where \(𝒩_i \cap 𝒩_j \neq \emptyset\).
- Non-overlapping: \(k_{i,j} = (1-c_{i,j}) z_{i,j}\), a connection between units \(i\) and \(j\) where \(𝒩_i \cap 𝒩_j = \emptyset\).
- \(e_{i,j}^{(\mathtt{s})}\) for \(\mathtt{s} \in \{\mathtt{global}, \mathtt{local}, \mathtt{alocal}\}\) is defined by: \[ e_{i,j}^{(\mathtt{s})} = \begin{cases} z_{i,j} & \text{if } \mathtt{s} = \mathtt{global}\\ u_{i,j} & \text{if } \mathtt{s} = \mathtt{local} \\ k_{i,j} & \text{if } \mathtt{s} = \mathtt{alocal} \end{cases} \] The mode parameter \(\mathtt{s}\) is generally defined as \(\mathtt{s} \in \{\mathtt{global}, \mathtt{local}, \mathtt{alocal}\}\), but note that for the terms gwesp, gwdsp, gwodegree, gwidegree, edges_x_match, and edges_y_match (defined in the summary table), only the options \(\mathtt{s} \in \{\mathtt{global}, \mathtt{local}\}\) are implemented as their \(\mathtt{alocal}\) version is not very useful.
Degree Statistics: For unit \(i \in 𝒫\) and mode \(\mathtt{s} \in \{\mathtt{global}, \mathtt{local}\}\):
- Out-degree: \(\operatorname{deg}(i, \mathtt{s}) = \sum_{j \in 𝒫 \setminus \{i\}} e_{i,j}^{(\mathtt{s})}\) with \(\operatorname{deg}(i) = \operatorname{deg}(i, \mathtt{global})\).
- In-degree: \(\operatorname{ideg}(i, \mathtt{s}) = \sum_{j \in 𝒫 \setminus \{i\}} e_{j,i}^{(\mathtt{s})}\) with \(\operatorname{ideg}(i) = \operatorname{ideg}(i, \mathtt{global})\).
Common Partners (CP): For a dyad \((i,j) \in 𝒟\) and mode \(\mathtt{s} \in \{\mathtt{global}, \mathtt{local}\}\), the number of shared partners via distinct path structures is defined as:
- Outgoing Two-Paths (OTP): \(\operatorname{CP}(i, j, \mathtt{s}, \mathtt{OTP}) = \sum_{h \in 𝒫 \setminus \{i,j\}} e_{i,h}^{(\mathtt{s})}\, e_{h,j}^{(\mathtt{s})}\).
- Incoming Shared Partners (ISP): \(\operatorname{CP}(i, j, \mathtt{s}, \mathtt{ISP}) = \sum_{h \in 𝒫 \setminus \{i,j\}} e_{h,i}^{(\mathtt{s})}\, e_{h,j}^{(\mathtt{s})}\).
- Outgoing Shared Partners (OSP): \(\operatorname{CP}(i, j, \mathtt{s}, \mathtt{OSP}) = \sum_{h \in 𝒫 \setminus \{i,j\}} e_{i,h}^{(\mathtt{s})}\, e_{j,h}^{(\mathtt{s})}\).
- Incoming Two-Paths (ITP): \(\operatorname{CP}(i, j, \mathtt{s}, \mathtt{ITP}) = \sum_{h \in 𝒫 \setminus \{i,j\}} e_{h,i}^{(\mathtt{s})}\, e_{j,h}^{(\mathtt{s})}\).
- Undirected Version: \(\operatorname{CP}(i, j, \mathtt{s}) = \sum_{h \in 𝒫 \setminus \{i,j\}} e_{i,h}^{(\mathtt{s})}\, e_{h,j}^{(\mathtt{s})}\).
Miscellaneous:
- Geometrically-weighted weight: \(w_k(\alpha) = \exp(\alpha) \left[ 1 - (1 - \exp(-\alpha))^k \right]\).
- Indicator for directionality: \(\mathbb{I}_U(\mathbf{z})\), taking the value 1 if connections in \(\mathbf{z}\) are undirected, and 0 otherwise.
- Indicator for transitive connection: \(d_{i,j}(\mathbf{z}) = \mathbb{I}(\exists\, k \in 𝒩_i \cap 𝒩_j: z_{i,k} = z_{k,j} = 1)\).

The sections below and the summary table list all implemented terms as of iglm version 1.2.6 and will be extended in future releases.

Category 1: Attribute Dependence Terms (\(g_i\) Terms)

These terms capture how individual predictors \(x_i\) (exogenous) and \(y_i\) (endogenous) relate to each other, without reference to the network.

`attribute_x`

Description: Intercept for the endogenous \(x\)-attribute.

\[ g_i(x_i, y_i) = x_i \]

formula <- object ~ attribute_x

`attribute_y`

Description: Intercept for the endogenous \(y\)-attribute.

\[ g_i(x_i, y_i) = y_i \]

formula <- object ~ attribute_y

`cov_x(data = v)`

Description: Effect of a unit-level exogenous covariate \(v_i\) on attribute \(x_i\).

\[ g_i(x_i, y_i) = v_i\, x_i \]

formula <- object ~ cov_x(data = v)

`cov_y(data = v)`

Description: Effect of a unit-level exogenous covariate \(v_i\) on attribute \(y_i\).

\[ g_i(x_i, y_i) = v_i\, y_i \]

formula <- object ~ cov_y(data = v)

`attribute_xy(mode = "global" | "local" | "alocal")`

Description: Interaction between the two attributes \(x_i\) and \(y_i\), optionally mediated by the neighbourhood structure.

Mode	Formula
`global`	\(x_i\, y_i\)
`local`	\(x_i \sum_{j \in 𝒩_i} y_j + y_i \sum_{j \in 𝒩_i} x_j\)
`alocal`	\(x_i \sum_{j \notin 𝒩_i} y_j + y_i \sum_{j \notin 𝒩_i} x_j\)

formula <- object ~ attribute_xy(mode = "local")

Category 2: Network Dependence Terms (\(h_{i,j}\) Terms)

These terms capture how the network topology \(z\) drives edge formation. All are pair-level statistics.

`degrees`

Description: Node-level degree fixed effects. One parameter per unit, capturing heterogeneity in activity not explained by other terms. Estimation relies on an MM algorithm constraint.

formula <- object ~ degrees

`edges(mode = "global" | "local" | "alocal")`

Description: Baseline propensity for a tie \(z_{i,j}\) to form; the network analogue of an intercept.

\[ h_{i,j}(x, y, z) = e_{i,j}^{(\mathtt{s})} \]

Suitable for both directed and undirected networks.

formula <- object ~ edges(mode = "global")
formula <- object ~ edges(mode = "local")
formula <- object ~ edges(mode = "alocal")

`mutual(mode = "global" | "local" | "alocal")`

Description: Reciprocity in directed networks. Counts pairs where \(i \to j\) and \(j \to i\) both exist (counted once per unordered pair, hence the factor \(1/2\)).

\[ h_{i,j}(x, y, z) = \frac{e_{i,j}^{(\mathtt{s})}\, e_{j,i}^{(\mathtt{s})}}{2} \]

Only valid for directed networks.

formula <- object ~ mutual(mode = "global")

`cov_z(data = w, mode = "global" | "local" | "alocal")`

Description: Dyadic covariate — exogenous edge-level covariate \(w_{i,j}\) influences tie formation.

\[ h_{i,j}(x, y, z) = w_{i,j}\, e_{i,j}^{(\mathtt{s})} \]

Suitable for both directed and undirected networks.

formula <- object ~ cov_z(data = W, mode = "global")

`cov_z_out(data = v, mode = "global" | "local" | "alocal")`

Description: Sender covariate — exogenous nodal attribute \(v_i\) influences the propensity to send a tie.

\[ h_{i,j}(x, y, z) = v_i\, e_{i,j}^{(\mathtt{s})} \]

Only valid for directed networks.

formula <- object ~ cov_z_out(data = v, mode = "global")

`cov_z_in(data = v, mode = "global" | "local" | "alocal")`

Description: Receiver covariate — exogenous nodal attribute \(v_j\) influences the propensity to receive a tie.

\[ h_{i,j}(x, y, z) = v_j\, e_{i,j}^{(\mathtt{s})} \]

Only valid for directed networks.

formula <- object ~ cov_z_in(data = v, mode = "global")

`isolates`

Description: Captures the proportion of units with no connections at all (total degree zero).

\[ h_{i,j}(x, y, z) = \mathbb{I}\!\left(\sum_{j \in 𝒫 \setminus \{i\}} z_{i,j} + z_{j,i} = 0\right) \]

Suitable for both directed and undirected networks.

formula <- object ~ isolates

`nonisolates`

Description: Captures the proportion of units that have at least one connection.

\[ h_{i,j}(x, y, z) = \mathbb{I}\!\left(\sum_{j \in 𝒫 \setminus \{i\}} z_{i,j} + z_{j,i} \ne 0\right) \]

Suitable for both directed and undirected networks.

formula <- object ~ nonisolates

`gwdegree(mode = "global" | "local", decay = α)`

Description: Geometrically Weighted Degree — captures the overall degree distribution with exponential decay parameter \(\alpha\).

\[ h_{i,j}(x, y, z) = w_{\operatorname{deg}(i)}(\alpha) + w_{\operatorname{deg}(j)}(\alpha) \]

Suitable for both directed and undirected networks. Only mode %in% c("global", "local") is available.

formula <- object ~ gwdegree(mode = "global", decay = 0.5)

`gwodegree(mode = "global" | "local", decay = α)`

Description: Geometrically Weighted Out-Degree — captures the out-degree distribution in directed networks.

\[ h_{i,j}(x, y, z) = w_{\operatorname{deg}(i,\,\mathtt{s})}(\alpha) \]

Only valid for directed networks. Only mode %in% c("global", "local") is available.

formula <- object ~ gwodegree(mode = "global", decay = 0.5)

`gwidegree(mode = "global" | "local", decay = α)`

Description: Geometrically Weighted In-Degree — captures the in-degree distribution in directed networks.

\[ h_{i,j}(x, y, z) = w_{\operatorname{ideg}(i,\,\mathtt{s})}(\alpha) \]

Only valid for directed networks. Only mode %in% c("global", "local") is available.

formula <- object ~ gwidegree(mode = "global", decay = 0.5)

`transitive`

Description: Transitivity indicator — rewards edges that close a locally transitive triple.

\[ h_{i,j}(x, y, z) = d_{i,j}(\mathbf{z})\, z_{i,j} \]

Suitable for both directed and undirected networks.

formula <- object ~ transitive

`gwesp_symm(mode = "global" | "local", decay = α)`

Description: Geometrically Weighted Edgewise Shared Partners (undirected) — the classic GWESP statistic for undirected networks.

\[ h_{i,j}(x, y, z) = e_{i,j}^{(\mathtt{s})}\, w_{\operatorname{CP}(i,j,\mathtt{s})}(\alpha) \]

Suitable for undirected networks only.

formula <- object ~ gwesp_symm(mode = "global", decay = 0.5)

`gwesp(mode = "global" | "local", type = "OTP" | "ISP" | "OSP" | "ITP", decay = α)`

Description: Geometrically Weighted Edgewise Shared Partners (directed) — conditions shared partners on a specific path type.

\[ h_{i,j}(x, y, z) = e_{i,j}^{(\mathtt{s})}\, w_{\operatorname{CP}(i,j,\mathtt{s},\mathtt{type})}(\alpha) \]

Only valid for directed networks. Only mode %in% c("global", "local") is available.

formula <- object ~ gwesp(mode = "global", type = "OTP", decay = 0.5)

`gwdsp_symm(mode = "local", decay = α)`

Description: Geometrically Weighted Dyadwise Shared Partners (undirected) — models triadic potential irrespective of the closing edge.

\[ h_{i,j}(x, y, z) = w_{\operatorname{CP}(i,j,\mathtt{local})}(\alpha) \]

Suitable for undirected networks only.

formula <- object ~ gwdsp_symm(mode = "local", decay = 0.5)

`gwdsp(mode = "global" | "local", type = "OTP" | "ISP" | "OSP" | "ITP", decay = α)`

Description: Geometrically Weighted Dyadwise Shared Partners (directed) — models directed triadic potential irrespective of the closing edge.

\[ h_{i,j}(x, y, z) = w_{\operatorname{CP}(i,j,\mathtt{s},\mathtt{type})}(\alpha) \]

Only valid for directed networks. Only mode %in% c("global", "local") is available.

formula <- object ~ gwdsp(mode = "global", type = "OTP", decay = 0.5)

Category 3: Joint Attribute/Network Dependence Terms (\(h_{i,j}\) Terms)

These terms capture the interplay between nodal attributes and network position. They are the key building blocks for studying spillover effects.

`attribute_xz(mode = "local")`

Description: Additive effect of \(x_i\) and \(x_j\) on local edge formation.

\[ h_{i,j}(x, y, z) = (x_i + x_j)\, u_{i,j} \]

Suitable for both directed and undirected networks.

formula <- object ~ attribute_xz(mode = "local")

`attribute_yz(mode = "local")`

Description: Additive effect of \(y_i\) and \(y_j\) on local edge formation.

\[ h_{i,j}(x, y, z) = (y_i + y_j)\, u_{i,j} \]

Suitable for both directed and undirected networks.

formula <- object ~ attribute_yz(mode = "local")

`edges_x_match(mode = "global" | "local")`

Description: Homophily on \(x\) — rewards edges between units with equal \(x\)-values.

\[ h_{i,j}(x, y, z) = \mathbb{I}(x_i = x_j)\, e_{i,j}^{(\mathtt{s})} \]

Suitable for both directed and undirected networks.

formula <- object ~ edges_x_match(mode = "global")

`edges_y_match(mode = "global" | "local")`

Description: Homophily on \(y\) — rewards edges between units with equal \(y\)-values.

\[ h_{i,j}(x, y, z) = \mathbb{I}(y_i = y_j)\, e_{i,j}^{(\mathtt{s})} \]

Suitable for both directed and undirected networks.

formula <- object ~ edges_y_match(mode = "global")

`outedges_x(mode = "global" | "local" | "alocal")`

Description: Effect of sender attribute \(x_i\) on out-degree formation.

\[ h_{i,j}(x, y, z) = x_i\, e_{i,j}^{(\mathtt{s})} \]

Only valid for directed networks.

formula <- object ~ outedges_x(mode = "global")

`inedges_x(mode = "global" | "local" | "alocal")`

Description: Effect of receiver attribute \(x_j\) on in-degree reception.

\[ h_{i,j}(x, y, z) = x_j\, e_{i,j}^{(\mathtt{s})} \]

Only valid for directed networks.

formula <- object ~ inedges_x(mode = "global")

`outedges_y(mode = "global" | "local" | "alocal")`

Description: Effect of sender attribute \(y_i\) on out-degree formation.

\[ h_{i,j}(x, y, z) = y_i\, e_{i,j}^{(\mathtt{s})} \]

Only valid for directed networks.

formula <- object ~ outedges_y(mode = "global")

`inedges_y(mode = "global" | "local" | "alocal")`

Description: Effect of receiver attribute \(y_j\) on in-degree reception.

\[ h_{i,j}(x, y, z) = y_j\, e_{i,j}^{(\mathtt{s})} \]

Only valid for directed networks.

formula <- object ~ inedges_y(mode = "global")

`spillover_xx(mode = "local")`

Description: Symmetric \(x\)-to-\(x\) spillover — the product \(x_i x_j\) along local connections, capturing peer effects in the \(x\) attribute.

\[ h_{i,j}(x, y, z) = x_i\, x_j\, u_{i,j} \]

Suitable for both directed and undirected networks.

formula <- object ~ spillover_xx(mode = "local")

`spillover_xx_scaled(mode = "global" | "local")`

Description: Degree-normalised \(x\)-to-\(x\) spillover, accounting for the number of neighbours.

\[ h_{i,j}(x, y, z) = \left(\frac{x_i\, x_j}{\operatorname{deg}(i,\mathtt{s})} + \frac{x_j\, x_i}{\operatorname{deg}(j,\mathtt{s})}\,\mathbb{I}_U(\mathbf{z})\right) e_{i,j}^{(\mathtt{s})} \]

Suitable for both directed and undirected networks.

formula <- object ~ spillover_xx_scaled(mode = "global")

`spillover_yy(mode = "local")`

Description: Symmetric \(y\)-to-\(y\) spillover — the product \(y_i y_j\) along local connections.

\[ h_{i,j}(x, y, z) = y_i\, y_j\, u_{i,j} \]

Suitable for both directed and undirected networks.

formula <- object ~ spillover_yy(mode = "local")

`spillover_yy_scaled(mode = "global" | "local")`

Description: Degree-normalised \(y\)-to-\(y\) spillover.

\[ h_{i,j}(x, y, z) = \left(\frac{y_i\, y_j}{\operatorname{deg}(i,\mathtt{s})} + \frac{y_j\, y_i}{\operatorname{deg}(j,\mathtt{s})}\,\mathbb{I}_U(\mathbf{z})\right) e_{i,j}^{(\mathtt{s})} \]

Suitable for both directed and undirected networks.

formula <- object ~ spillover_yy_scaled(mode = "global")

`spillover_xy(mode = "local")`

Description: Symmetric cross-attribute spillover — \(x_i \to y_j\) and \(x_j \to y_i\) along local connections. For undirected networks both directions are summed.

\[ h_{i,j}(x, y, z) = x_i\, y_j\, u_{i,j} + x_j\, y_i\, u_{i,j}\, \mathbb{I}_U(\mathbf{z}) \]

Suitable for both directed and undirected networks.

formula <- object ~ spillover_xy(mode = "local")

`spillover_xy_scaled(mode = "global" | "local")`

Description: Degree-normalised symmetric cross-attribute spillover (\(x \to y\)).

\[ h_{i,j}(x, y, z) = \left(\frac{x_i\, y_j}{\operatorname{deg}(i,\mathtt{s})} + \frac{x_j\, y_i}{\operatorname{deg}(j,\mathtt{s})}\,\mathbb{I}_U(\mathbf{z})\right) e_{i,j}^{(\mathtt{s})} \]

Suitable for both directed and undirected networks.

formula <- object ~ spillover_xy_scaled(mode = "global")

`spillover_yx(mode = "local")`

Description: Directed cross-attribute spillover — \(y_i \to x_j\) only (no symmetrisation). Only for directed networks.

\[ h_{i,j}(x, y, z) = y_i\, x_j\, u_{i,j} \]

Only valid for directed networks.

formula <- object ~ spillover_yx(mode = "local")

`spillover_yx_scaled(mode = "global" | "local")`

Description: Degree-normalised cross-attribute spillover (\(y \to x\)), with symmetrisation for undirected networks.

\[ h_{i,j}(x, y, z) = \left(\frac{y_i\, x_j}{\operatorname{deg}(i,\mathtt{s})} + \frac{y_j\, x_i}{\operatorname{deg}(j,\mathtt{s})}\,\mathbb{I}_U(\mathbf{z})\right) e_{i,j}^{(\mathtt{s})} \]

Suitable for both directed and undirected networks.

formula <- object ~ spillover_yx_scaled(mode = "global")

`spillover_yc(mode = "local", data = v)`

Description: Interaction of endogenous attribute \(y\) with exogenous covariate \(v\) along overlapping connections, with symmetrisation for undirected networks.

\[ h_{i,j}(x, y, z) = c_{i,j}\bigl(v_j\, y_i + \mathbb{I}_U(\mathbf{z})\, v_i\, y_j\bigr)\, z_{i,j} \]

Suitable for both directed and undirected networks.

formula <- object ~ spillover_yc(data = v, mode = "local")

Term	\(x\)	\(y\)	\(z\)	Undirected
`attribute_x`	✓			✓
`attribute_y`		✓		✓
`cov_x`	✓			✓
`cov_y`		✓		✓
`attribute_xy(mode = "s")`	✓	✓		✓
`degrees`			✓	✓
`edges(mode = "s")`			✓	✓
`mutual(mode = "s")`			✓	✗
`cov_z(mode = "s")`			✓	✓
`cov_z_out(mode = "s")`			✓	✗
`cov_z_in(mode = "s")`			✓	✗
`isolates`			✓	✓
`nonisolates`			✓	✓
`gwdegree(mode = "global")`			✓	✓
`gwodegree(mode = "s")`			✓	✗
`gwidegree(mode = "s")`			✓	✗
`transitive`			✓	✓
`gwesp_symm(mode = "s")`			✓	✓
`gwesp(mode = "s", type = "…")`			✓	✗
`gwdsp_symm(mode = "local")`			✓	✓
`gwdsp(mode = "s", type = "…")`			✓	✗
`attribute_xz(mode = "local")`	✓		✓	✓
`attribute_yz(mode = "local")`		✓	✓	✓
`edges_x_match(mode = "s")`	✓		✓	✓
`edges_y_match(mode = "s")`		✓	✓	✓
`outedges_x(mode = "s")`	✓		✓	✗
`inedges_x(mode = "s")`	✓		✓	✗
`outedges_y(mode = "s")`		✓	✓	✗
`inedges_y(mode = "s")`		✓	✓	✗
`spillover_xx(mode = "local")`	✓		✓	✓
`spillover_xx_scaled(mode = "s")`	✓		✓	✓
`spillover_yy(mode = "local")`		✓	✓	✓
`spillover_yy_scaled(mode = "s")`		✓	✓	✓
`spillover_xy(mode = "local")`	✓	✓	✓	✓
`spillover_xy_scaled(mode = "s")`	✓	✓	✓	✓
`spillover_yx(mode = "local")`	✓	✓	✓	✗
`spillover_yx_scaled(mode = "s")`	✓	✓	✓	✓
`spillover_yc(mode = "local")`		✓	✓	✓

Model Terms in iglm

Overview

Key Definitions

Category 1: Attribute Dependence Terms (\(g_i\) Terms)

attribute_x

attribute_y

cov_x(data = v)

cov_y(data = v)

attribute_xy(mode = "global" | "local" | "alocal")

Category 2: Network Dependence Terms (\(h_{i,j}\) Terms)

degrees

edges(mode = "global" | "local" | "alocal")

mutual(mode = "global" | "local" | "alocal")

cov_z(data = w, mode = "global" | "local" | "alocal")

cov_z_out(data = v, mode = "global" | "local" | "alocal")

cov_z_in(data = v, mode = "global" | "local" | "alocal")

isolates

nonisolates

gwdegree(mode = "global" | "local", decay = α)

gwodegree(mode = "global" | "local", decay = α)

gwidegree(mode = "global" | "local", decay = α)

transitive

gwesp_symm(mode = "global" | "local", decay = α)

gwesp(mode = "global" | "local", type = "OTP" | "ISP" | "OSP" | "ITP", decay = α)

gwdsp_symm(mode = "local", decay = α)

gwdsp(mode = "global" | "local", type = "OTP" | "ISP" | "OSP" | "ITP", decay = α)

Category 3: Joint Attribute/Network Dependence Terms (\(h_{i,j}\) Terms)

attribute_xz(mode = "local")

attribute_yz(mode = "local")

edges_x_match(mode = "global" | "local")

edges_y_match(mode = "global" | "local")

outedges_x(mode = "global" | "local" | "alocal")

inedges_x(mode = "global" | "local" | "alocal")

outedges_y(mode = "global" | "local" | "alocal")

inedges_y(mode = "global" | "local" | "alocal")

spillover_xx(mode = "local")

spillover_xx_scaled(mode = "global" | "local")

spillover_yy(mode = "local")

spillover_yy_scaled(mode = "global" | "local")

spillover_xy(mode = "local")

spillover_xy_scaled(mode = "global" | "local")

spillover_yx(mode = "local")

spillover_yx_scaled(mode = "global" | "local")

spillover_yc(mode = "local", data = v)

Quick-Reference Table

References

`attribute_x`

`attribute_y`

`cov_x(data = v)`

`cov_y(data = v)`

`attribute_xy(mode = "global" | "local" | "alocal")`

`degrees`

`edges(mode = "global" | "local" | "alocal")`

`mutual(mode = "global" | "local" | "alocal")`

`cov_z(data = w, mode = "global" | "local" | "alocal")`

`cov_z_out(data = v, mode = "global" | "local" | "alocal")`

`cov_z_in(data = v, mode = "global" | "local" | "alocal")`

`isolates`

`nonisolates`

`gwdegree(mode = "global" | "local", decay = α)`

`gwodegree(mode = "global" | "local", decay = α)`

`gwidegree(mode = "global" | "local", decay = α)`

`transitive`

`gwesp_symm(mode = "global" | "local", decay = α)`

`gwesp(mode = "global" | "local", type = "OTP" | "ISP" | "OSP" | "ITP", decay = α)`

`gwdsp_symm(mode = "local", decay = α)`

`gwdsp(mode = "global" | "local", type = "OTP" | "ISP" | "OSP" | "ITP", decay = α)`

`attribute_xz(mode = "local")`

`attribute_yz(mode = "local")`

`edges_x_match(mode = "global" | "local")`

`edges_y_match(mode = "global" | "local")`

`outedges_x(mode = "global" | "local" | "alocal")`

`inedges_x(mode = "global" | "local" | "alocal")`

`outedges_y(mode = "global" | "local" | "alocal")`

`inedges_y(mode = "global" | "local" | "alocal")`

`spillover_xx(mode = "local")`

`spillover_xx_scaled(mode = "global" | "local")`

`spillover_yy(mode = "local")`

`spillover_yy_scaled(mode = "global" | "local")`

`spillover_xy(mode = "local")`

`spillover_xy_scaled(mode = "global" | "local")`

`spillover_yx(mode = "local")`

`spillover_yx_scaled(mode = "global" | "local")`

`spillover_yc(mode = "local", data = v)`