Subsetting by Cascade

selected_policies <- subset_cascade(cascade = policy_cascades, 
                                    selection = c('clinic_access', 'cogrowman'))
selected_policies[1:2]
#> $cascade_nodes
#> $cascade_nodes$clinic_access
#>  [1] "Oregon"         "Wisconsin"      "Kansas"         "Maryland"      
#>  [5] "California"     "Nevada"         "Colorado"       "Connecticut"   
#>  [9] "Massachusetts"  "Minnesota"      "North Carolina" "Washington"    
#> [13] "Maine"          "Michigan"       "New York"       "Montana"       
#> 
#> $cascade_nodes$cogrowman
#>  [1] "Hawaii"       "Vermont"      "Oregon"       "Florida"      "New Jersey"  
#>  [6] "Rhode Island" "Washington"   "Maryland"     "Arizona"      "Tennessee"   
#> 
#> 
#> $cascade_times
#> $cascade_times$clinic_access
#>  [1] 1973 1985 1988 1989 1990 1991 1993 1993 1993 1993 1993 1993 1995 1995 1999
#> [16] 2005
#> 
#> $cascade_times$cogrowman
#>  [1] 1961 1970 1973 1985 1986 1988 1990 1992 1998 1998

Visually Inspecting Cascades

It’s always good practice to visually inspect the data before working with it. The NetworkInference package provides functionality to visualize the cascade data.

The function summary.cascades() provides quick summary statistics on the cascade data:

summary(policy_cascades)
#> # cascades: 728
#> # nodes: 50
#> # nodes in cascades: 50
#> # possible edges: 2450
#> 
#> Summary statistics for cascade length and number of ties:
#>           length     ties
#> Min.     1.00000  0.00000
#> 1st Qu. 11.00000  4.00000
#> Median  23.00000 11.00000
#> Mean    24.49863 14.53571
#> 3rd Qu. 40.00000 23.00000
#> Max.    50.00000 48.00000

The first four lines provide the number of cascades, the number of nodes in the system, the number of nodes involved in cascades (there might be states that we don’t have diffusion data on, but we still want them represented in the dataset) and the possible number of edges in a potential diffusion network (a diffusion edge between nodes u and v only makes sense if there is at least one cascade in which u experiences an event before v). In this example there are 187 policies and 50 states. Each state is involved in at least one policy cascade and a fully connected diffusion network would have 2450 edges.

It also provides summary statistics on the distribution of the cascade lengths (number of nodes involved in each cascade) and the number of ties in the cascades (two nodes experiencing the same event at the same time). For our example, we can see that the ‘smallest’ policy was adopted by 10 states and the ‘largest’ by all 50 states. From the tie summaries we see that there is at least one policy that was adopted by 45 states in the same year.

The plot() method allows to plot cascades with varying degrees of detail. The argument label_nodes (TRUE/FALSE) provides node labels which require more space but provide more detail. The argument selection allows to pick a subset of cascades to visualize in case there are too many to plot. If label_nodes is set to FALSE each event is depicted by a dot, which allows to visualize more cascades simultaneously.

Let’s first look at the visualization with labels. Here we plot two cascades, selected by their name:

selection <- c('guncontrol_assaultweapon_ba', 'guncontrol_licenses_dealer')
plot(policy_cascades, label_nodes = TRUE, selection = selection)
#> Warning: The `guide` argument in `scale_*()` cannot be `FALSE`. This was deprecated in
#> ggplot2 3.3.4.
#> ℹ Please use "none" instead.
#> ℹ The deprecated feature was likely used in the NetworkInference package.
#>   Please report the issue at
#>   <https://github.com/desmarais-lab/NetworkInference/issues>.
#> This warning is displayed once every 8 hours.
#> Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
#> generated.
#> Warning: ggrepel: 17 unlabeled data points (too many overlaps). Consider
#> increasing max.overlaps

We can also plot more cascades with less detail:

selection <- c('waiting', 'threestrikes', 'unionlimits', 'smokeban', 
               'paperterror', 'miglab', 'methpre', 'lott', 'lemon', 'idtheft',
               'harass', 'hatecrime', 'equalpay')
plot(policy_cascades, label_nodes = FALSE, selection = selection)

This produces a ‘violin plot’ for each cascade with the single diffusion events overplotted as dots. As we already saw in the previous visualization, the policy data has a lot of ties (i.e. many states adopted a policy in the same year) which is indicated by the areas of higher density in the violin plot.

Classic Netinf

In the original implementation the number of edges to infer had to be fixed and chosen by the researcher. If you want to run netinf in this classic way you can do so by specifiying all parameters and the number of edges:

results <- netinf(policy_cascades, trans_mod = "exponential", n_edges = 100, 
                  params = 0.5, quiet = TRUE)

The exponential model has only one parameter (lambda or the rate). If there are more parameters the details section in the documentation of the netinf function (?netinf) has more detail on how to specify parameters and on the specific parametrization used by the implementation.

n_edges specifies how many edges should be inferred. See @gomez2010inferring and @desmarais2015persistent for guidance on choosing this parameter if running netinf in classic mode. If the number of edges is specified manually, it has to be lower than the maximum number of possible edges. An edge u->v is only possible if in at least one cascade u experiences an event before v. This means, that the maximum number of edges depends on the data. The function count_possible_edges() allows us to compute the maximum number of edges in advance:

npe <- count_possible_edges(policy_cascades)
npe
#> [1] 2450

Automatic Parameter Selection

With version 1.2.0 netinf can be run without manually specifying the number of edges or the parameters of the diffusion model.

results <- netinf(policy_cascades, trans_mod = "exponential", 
                  p_value_cutoff = 0.1, params = 0.5, quiet = TRUE)
nrow(results)
#> [1] 872

results <- netinf(policy_cascades, trans_mod = "exponential", 
                  p_value_cutoff = 0.1, quiet = TRUE)
nrow(results)
#> [1] 866

Netinf output

Let’s take a look at the output of the algorithm. The output is a dataframe containing the inferred latent network in the form of an edgelist:

head(results)

Each row corresponds to a directed edge. The first column indicates the origin node, the second the destination node. The third column displays the gain in model fit from each added edge. The last column displays the p-value from the Vuong test of each edge. There is a generic plot method to inspect the results. If more tweaking is required, the results are a dataframe so it should be easy for the more experienced users to make your own plot. With type = "improvement" the improvement from each edge can be plotted:

plot(results, type = "improvement")

We can also quickly check the p-value from the Vuong test associated with each edge addition:

plot(results, type = 'p-value')

In order to produce a quick visualization of the resulting diffusion network we can use the plot method again, this time with type = "network". Note that in order to use this functionality the igraph package has to be installed.

#install.packages('igraph')
# For this functionality the igraph package has to be installed
# This code is only executed if the package is found:
if(requireNamespace("igraph", quietly = TRUE)) {
    plot(results, type = "network")
}

If additional tweaking of the plot is desired, the network can be visualized using igraph explicitly. We refer you you to the igraph documentation for details on how to customize the plot.

if(requireNamespace("igraph", quietly = TRUE)) {
    library(igraph) 
    g <- graph_from_data_frame(d = results[, 1:2])
    plot(g, edge.arrow.size=.3, vertex.color = "grey70")
}