Description Usage Arguments Details Value Discount rate Author(s) References See Also Examples

View source: R/infect_suscept.r

Calculates infectiousness and susceptibility for each node in the graph

1 2 3 4 5 6 7 | ```
infection(graph, toa, t0 = NULL, normalize = TRUE, K = 1L, r = 0.5,
expdiscount = FALSE, valued = getOption("diffnet.valued", FALSE),
outgoing = getOption("diffnet.outgoing", TRUE))
susceptibility(graph, toa, t0 = NULL, normalize = TRUE, K = 1L, r = 0.5,
expdiscount = FALSE, valued = getOption("diffnet.valued", FALSE),
outgoing = getOption("diffnet.outgoing", TRUE))
``` |

`graph` |
A dynamic graph (see |

`toa` |
Integer vector of length |

`t0` |
Integer scalar. See |

`normalize` |
Logical. Whether or not to normalize the outcome |

`K` |
Integer scalar. Number of time periods to consider |

`r` |
Numeric scalar. Discount rate used when |

`expdiscount` |
Logical scalar. When TRUE, exponential discount rate is used (see details). |

`valued` |
Logical scalar. When |

`outgoing` |
Logical scalar. When |

Normalization, `normalize=TRUE`

, is applied by dividing the
resulting number from the infectiousness/susceptibility stat
by the number of individuals who adopted the innovation at
time *t*.

Given that node *i* adopted the innovation in time *t*, its
Susceptibility is calculated as follows

*
S(i) = [∑_k ∑_j (x(ij,t-k+1) * z(j,t-k))/w(k)]/[∑_k ∑_j (x(ij,t-k+1) * z(j, 1<=t<=t-k))/w(k)] for j != i*

where *x(ij,t-k+1)* is 1 whenever there's a link from *i*
to *j* at time *t-k+1*, *z(j,t-k)*
is 1 whenever individual *j* adopted the innovation at time *t-k*,
*z(j, 1<=t<=t-k)* is 1 whenever
*j* had adopted the innovation up to *t-k*, and *w(k)* is
the discount rate used (see below).

Similarly, infectiousness is calculated as follows

*
I(i) = [∑_k ∑_j (x(ji,t) * z(j,t+1))/w(k)]/[∑_k ∑_j (x(ji,t) * z(j, t+1<=t<=T))/w(k)] for j != i*

It is worth noticing that, as we can see in the formulas, while susceptibility is from alter to ego, infection is from ego to alter.

When `outgoing=FALSE`

the algorithms are based on incoming edges, this is
the adjacency matrices are transposed swapping the indexes *(i,j)* by
*(j,i)*. This can be useful for some users.

Finally, by default both are normalized by the number of individuals who
adopted the innovation in time *t-k*. Thus, the resulting formulas,
when `normalize=TRUE`

, can be rewritten as

*
S(i)' = S(i)/[∑_k ∑_j z(j,t-k)/w(k)]
I(i)' = I(i)/[∑_k ∑_j z(j,t-k)/w(k)]*

For more details on these measurements, please refer to the vignette titled
*Time Discounted Infection and Susceptibility*.

A numeric column vector (matrix) of size *n* with either infection/susceptibility rates.

Discount rate, *w(k)* in the formulas above, can be either exponential
or linear. When `expdiscount=TRUE`

, *w(k) = (1+r)^(k-1)*, otherwise
it will be *w(k)=k*.

Note that when *K=1*, the above formulas are equal to the ones presented
in Valente et al. (2015).

George G. Vega Yon

Thomas W. Valente, Stephanie R. Dyal, Kar-Hai Chu, Heather Wipfli, Kayo Fujimoto Diffusion of innovations theory applied to global tobacco control treaty ratification, Social Science & Medicine, Volume 145, November 2015, Pages 89-97, ISSN 0277-9536 http://dx.doi.org/10.1016/j.socscimed.2015.10.001

Myers, D. J. (2000). The Diffusion of Collective Violence: Infectiousness, Susceptibility, and Mass Media Networks. American Journal of Sociology, 106(1), 173–208. https://doi.org/10.1086/303110

The user can visualize the distribution of both statistics
by using the function `plot_infectsuscep`

Other statistics: `bass`

,
`classify_adopters`

,
`cumulative_adopt_count`

, `dgr`

,
`ego_variance`

, `exposure`

,
`hazard_rate`

, `moran`

,
`struct_equiv`

, `threshold`

,
`vertex_covariate_dist`

1 2 3 4 5 6 7 8 9 10 11 12 | ```
# Creating a random dynamic graph
set.seed(943)
graph <- rgraph_er(n=100, t=10)
toa <- sample.int(10, 100, TRUE)
# Computing infection and susceptibility (K=1)
infection(graph, toa)
susceptibility(graph, toa)
# Now with K=4
infection(graph, toa, K=4)
susceptibility(graph, toa, K=4)
``` |

netdiffuseR documentation built on June 7, 2018, 5:05 p.m.

Embedding an R snippet on your website

Add the following code to your website.

For more information on customizing the embed code, read Embedding Snippets.