Optimal model search strategies — modelSearch • SEMgraph

Four model search strategies are implemented combining SEMdag(), SEMbap(), and resizeGraph() functions. All strategies estimate a new graph by 1) adjusting (BAP deconfounding) the the data matrix and 2) re-sizing the output DAG.

modelSearch(
  graph,
  data,
  gnet = NULL,
  d = 2,
  search = "basic",
  beta = 0,
  method = "BH",
  alpha = 0.05,
  verbose = FALSE,
  ...
)

Arguments

graph

Input graph as an igraph object.

data

A matrix or data.frame. Rows correspond to subjects, and columns to graph nodes (variables).

gnet

Reference directed network used to validate and import nodes and interactions.

d

Maximum allowed geodesic distance for directed or undirected shortest path search. A distance d = 0 disables shortest path search (fixed in search = "basic"), while d = 1 (fixed in search = "direct") only search for directed links (i.e., no mediators are allowed). A distance d > 1 (defaults to d = 2 for "outer" and "inner" strategies), will search for shortest paths with at most d - 1 mediators between nodes sharing a significant estimated interaction. Connectors are imported from the reference interactome, as specified by the argument gnet. If the edges of the reference interactome are weighted by P-value, as defined by the E(gnet)$pv attribute, the shortest path with the smallest sum of weights will be chosen (e.g., see weightGraph for graph weighting options).

search

Search strategy. Four model search strategies are available:

"outer". The estimated DAG is re-sized using resizeGraph to find new indirect paths (i.e., inferred directed connections that may hide new mediators). New interactions and connectors will be searched and imported from the reference network (argument gnet, see above). Both DAG and extended graph complexity can be controlled with beta > 0 and d > 1 arguments, respectively. The term "outer" means that new model mediator variables are imported from an external resource (i.e., the reference network).
"inner". This strategy is analogous to the "outer" one, but disables external mediator search. In other words, new indirect paths are generated by adding new interactions of the input model, so that mediators will be nodes already present in the input graph. The reference network is still used to validate new model paths. Also in this case, beta > 0 and d > 1 are used.
"direct". The input graph structure is improved through direct (i.e., adjacent) link search, followed by interaction validation and import from the reference network, with no mediators (i.e., d = 1).
"basic" (default). While the previous strategies rely on the input graph and the reference network to integrate knowledge to the final model, the "basic" strategy is data-driven. The input graph is needed to define the topological order. The argument gnet is set to NULL (i.e., no reference network is needed) and argument d = 0. Model complexity can be still controlled by setting beta > 0.

beta

Numeric value. Minimum absolute LASSO beta coefficient for a new interaction to be retained in the estimated DAG backbone. Lower beta values correspond to more complex DAGs. By default, beta is set to 0 (i.e., maximum complexity).

method

Multiple testing correction method. One of the values available in p.adjust. By default, method is set to "BH" (i.e., Benjamini-Hochberg multiple test correction).

alpha

Significance level for false discovery rate (FDR) used for local d-separation tests. This argument is used to control data de-correlation. A higher alpha level includes more hidden covariances, thus considering more sources of confounding. If alpha = 0, data de-correlation is disabled. By default, alpha = 0.05.

verbose

If TRUE, it shows intermediate graphs during the execution (not recommended for large graphs).

...

Currently ignored.

Value

The output model as well as the adjusted dataset are returned as a list of 2 objects:

"graph", the output model as an igraph object;
"data", the adjusted dataset.

Details

Search strategies can be ordered by decreasing conservativeness respect to the input graph, as: "direct", "inner", "outer", and "basic". The first three strategies are knowledge-based, since they require an input graph and a reference network, together with data, for knowledge-assisted model improvement. The last one does not require any reference and the output model structure will be data-driven. Output model complexity can be limited using arguments d and beta. While d is fixed to 0 or 1 in "basic" or "direct", respectively; we suggest starting with d = 2 (only one mediator) for the other two strategies. For knowledge-based strategies, we suggest to to start with beta = 0. Then, beta can be relaxed (0 to < 0.1) to improve model fitting, if needed. Since data-driven models can be complex, we suggest to start from beta = 0 when using the "basic" strategy. The beta value can be relaxed until a good model fit is obtained. Argument alpha determines the extent of data adjustment: lower alpha values for FDR correction correspond to a smaller number of significant confounding factors, hence a weaker correction (default alpha = 0.05).

Author

Mario Grassi mario.grassi@unipv.it

Examples


# \donttest{

# Comparison among different model estimation strategies

# Nonparanormal(npn) transformation
als.npn <- transformData(alsData$exprs)$data
#> Conducting the nonparanormal transformation via shrunkun ECDF...done.

# Models estimation
m1 <- modelSearch(graph = alsData$graph, data = als.npn, gnet = kegg,
      search = "direct", beta = 0, alpha = 0.05)
#> Step1: BAP deconfounding...
#> Step2: DAG estimation...
#> Step3: DAG resize (remove edges/add nodes)...
#> 
#> Done.
m2 <- modelSearch(graph = alsData$graph, data = als.npn, gnet = kegg,
      d = 2, search = "inner", beta = 0, alpha = 0.05)
#> Step1: BAP deconfounding...
#> Step2: DAG estimation...
#> Step3: DAG resize (remove edges/add nodes)...
#> 
#> Done.
m3 <- modelSearch(graph = alsData$graph, data = als.npn, gnet = kegg,
      d = 2, search = "outer", beta = 0, alpha = 0.05)
#> Step1: BAP deconfounding...
#> Step2: DAG estimation...
#> Step3: DAG resize (remove edges/add nodes)...
#> 
#> Done.
m4 <- modelSearch(graph = alsData$graph, data = als.npn, gnet = NULL,
      search = "basic", beta = 0.1, alpha = 0.05)
#> Step1: BAP deconfounding...
#> Step2: DAG estimation...
#> Step3: DAG resize (remove edges/add nodes)...
#> 
#> None DAG resize for basic search ! 
#> 
#> Done.

# Graphs
#old.par <- par(no.readonly = TRUE)
#par(mfrow=c(2,2), mar= rep(1,4))
gplot(m1$graph, main = "direct graph")

gplot(m2$graph, main = "inner graph")

gplot(m3$graph, main = "outer graph")

gplot(m4$graph, main = "basic graph")

#par(old.par)

# }