12  Crime data

So we have some crime data. The data will not be uploaded, I will just include the code here you can copy and paste to run the data cleaning / model fitting yourself.

To briefly describe it

12.1 BA-Bipartite Network Specification

Recall under the BA-Bipartite network specification we are assuming that marks are structured in the following way:

  • Nodes have two possible classifications - event and perp.

  • Each mark consists of exactly 1 new event node arriving, which connects to old perp nodes according to the same degree-based weighting as the BA kernel.

  • The number of perp nodes is distributed Poisson(lambda_new)

Under this specification, perp-perp edges are not allowed to exist (is this correct?). Hence we can ignore the edges present in the perps.df (we will revisit when trying different model specs).

12.1.1 Data prep

Now, looking at the perps.df data:

summary(as.numeric(perps$person_id))
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
      5  426537  863430  868561 1307976 1742898

It looks like the person_id’s stretch all the way from 5 to 1742898. We will just treat these as node ID’s. And in order to prevent any clashes, we will just prepend “event_” on to the event_id to use as the node ID’s of the event nodes.

First converting to long format.

library(tidyr)
library(dplyr)

# Love how easy this is
long_df <- events %>%
  unnest(people) %>%
  rename(person = people)

Now need to make sure the names don’t clash as mentioned above (will prepend “perp_” to the perp ID’s aswell just for consistency):

edges <- long_df %>% 
  mutate(
    event_id = paste0("event_", event_id),
    person = paste0("perp_", person)
    ) %>% 
  rename(
    i = event_id, # Doesn't matter what order we choose i/j
    j = person,
    time = diff_date
  ) %>% 
  select(i, j, time) %>% 
  distinct() %>%  # The way the original data set was constructed, we end up with
  filter(time < 5)                  # two identical rows per edge sometimes

# Only considering a small sub net for example

Lastly, we need to make sure we include the perp-event node classification.

This is easier if we use make_events() first, as it will automatically generate a nodes data frame, and then we can just add a column to this.

Note

Not sure if I like this manipulation after-the-fact. Wondering how you guys prepared your data.

ev <- make_events(edges = edges)

Looks like 14000-ish events, 27000-ish node arrivals, and 19000-ish edges.

Now just add a “role” column to ev$nodes:

ev$nodes$role <- ifelse(
  grepl("event", ev$nodes$id),
  "event",
  "perp"
)

And we are good to fit.

12.1.2 Model fitting

Only gonna consider a SMALL time window, just trying to demonstrate here.

sum(ev$times < 5)
[1] 147

We’ll set T_end = 5.

params_bip_init <- list(
  mu = 1,
  K = 1,
  beta = 1,
  beta_edges = 1,
  lambda_new = 3.5
)

fit <- fit_hawkesNet(
      ev = ev,
      params_init = params_bip_init,
      mark_type = "ba_bip",
      debug = T
    )