Using brms with BISoN

bisonR can fully integrate with the popular Bayesian modelling package brms. This means that any brms model can be fit to network data such as edge weights, node centrality, or even global metrics comparing networks. This is achieved by treating network posteriors as imputed data and running multiple Bayesian models on these imputed data. This function is implemented as bison_brm and uses largely the same arguments as brms. The function returns an object of type brm_multiple.

bisonR uses a special notation to include network data in a brms formula. To specify network data, the wrapper bison() is used to tell the function that this variable should come from network data with uncertainty. Network properties can be calculated at three different levels: edge, node, and global. See the network_metrics vignette for information on available metrics. Depending on the type of analysis, you will need to specify node IDs or network IDs to ensure the data in your dataframe align with the network properties calculated in bisonR. This information is included as arguments to the network property in the formula.

When running analyses comparing global properties of networks, multiple fitted edge models must be provided, corresponding to each network. bisonR introduces a preserved factor variable bison_network that can be used to reference the different networks. bison_network is an integer factor corresponding to the order that fitted edge models were provided to bison_brm.

This sounds a little complex, but is much easier to understand with examples. The table below shows some examples of how the analysis would be conducted in brms (or lm/lmer/etc) compared to bison_brm.

Standard formula	bison_brm formula
edge_weight ~ x	bison(edge_weight(node_1_id, node_2_id)) ~ x
y ~ edge_weight	y ~ bison(edge_weight(node_1_id, node_2_id))
strength ~ x	bison(strength(node_id)) ~ x
y ~ strength	y ~ bison(strength(node_id))
cv ~ x	global_cv(bison_network) ~ x
y ~ cv	y ~ global_cv(bison_network)

Examples

Dyadic regression

Edge weight as response

bison_brm(
  bison(edge_weight(node_1_id, node_2_id)) ~ age_diff,
  fit_edge,
  df_edge
)

Edge weight as predictor

bison_brm(
  mass ~ bison(edge_weight(node_1_id, node_2_id)),
  fit_edge,
  df_edge
)

Edge weight as response with multiple networks

When analysing multiple networks, we need to provide multiple fitted edge models and corresponding dataframes. If the network IDs are to be used, we can access them using the preserved variable bison_network.

bison_brm(
  bison(edge_weight(node_1_id, node_2_id)) ~ bison_network,
  list(fit_edge_control, fit_edge_treatment),
  list(df_edge_control, df_edge_treatment)
)

Nodal regression

Node metric as a predictor

bison_brm(
  trait ~ bison(node_eigen(node)),
  fit_edge,
  df_nodal
)

Node metric as a response

bison_brm(
  bison(node_eigen(node)) ~ trait,
  fit_edge,
  df_nodal
)

Node metric as a response, controlling for network ID

If running an analysis across multiple networks, it might sometimes be necessary to control for network ID. This could be done using a random effect (varying intercept) as follows:

bison_brm(
  bison(node_eigen(node)) ~ trait + (1 | bison_network),
  fit_edge_list,
  df_nodal_list
)

Global regression

Global metric as a response

When running regression on global metrics, the fitted edge models must again be provided as a list. However, the dataframes can be provided either as 1) a list where each dataframe has one row, describing its corresponding edge model or 2) a dataframe, where each row in the dataframe corresponds to an edge model (where ordering is maintained).

bison_brm(
  bison(global_cv(bison_network)) ~ bison_network,
  list(fit_edge_1, fit_edge_2),
  df_global
)

Priors

The prior structure for a model (in the form of a brmsprior object) can be retrieved using the bison_brm_get_prior function:

prior <- bison_brm_get_prior(
  bison(global_cv(bison_network)) ~ bison_network,
  list(fit_edge_1, fit_edge_2),
  df_global
)

This object is a brmsprior object from the brms package, and can be modified in exactly the same way. For example, from the brms documentation, population-level fixed effects could be set all at once using:

## define a prior on all population-level effects a once
prior$prior[1] <- "normal(0,10)"

Once priors are set, they can be fed to the bison_brm function in the prior= argument, as follows:

bison_brm(
  bison(global_cv(bison_network)) ~ bison_network,
  list(fit_edge_1, fit_edge_2),
  df_global,
  prior=prior
)

Conclusion

This is just a small subset of all the possible types of model that can be fitted using the bison_brm function. For more information on the wide range of functionality available, check out the brms documentation.