model_graph {modelbpp}

Generate a Graph of Models

Description

Generate an 'igraph' object from a 'model_set' object.

Usage

model_graph(
  object,
  node_size_by_x = TRUE,
  x = NULL,
  node_size = 5,
  min_size = 5,
  max_size = 35,
  color_original = "lightblue",
  color_add = "burlywood1",
  color_drop = "lightgreen",
  color_others = "lightgrey",
  color_label = "black",
  node_label_size = 1,
  original = "original",
  drop_redundant_direct_paths = TRUE,
  label_arrow_by_df = NULL,
  arrow_label_size = 1,
  weight_arrows_by_df = c("inverse", "normal", "none"),
  arrow_min_width = 0.5,
  arrow_max_width = 2,
  progress = TRUE,
  short_names = FALSE,
  ...
)

Arguments

object

Must be a model_set-class object for now.

node_size_by_x

Logical. Whether node (vertex) sizes are determined by a variable. Default is TRUE. See x below on how size is determined.

x

If not NULL, it should be a numeric vector of length equal to the number of models. The node sizes will be proportional to the values of x, offset by min_size. If NULL, the default, the BIC posterior probabilities stored in object will be retrieved.

node_size

If node_size_by_x is FALSE, this is the size for all nodes.

min_size

The minimum size of a node. Default is 5.

max_size

The maximum size of a node. Default is 35.

color_original

The color of node of the original model. Default is "lightblue".

color_add

The color of the nodes of models formed by adding one or more free parameters to the original model. Default is "burlywood1".

color_drop

The color of the nodes of models formed by dropping one or more free parameters from the original model. Default is "lightgreen".

color_others

The color of other models not specified above. Default is "grey50".

color_label

The color of the text labels of the nodes. Default is "black".

node_label_size

The size of the labels of the nodes. Default is 1.

original

String. The name of the original model (target model). Default is "original".

drop_redundant_direct_paths

Logical. Whether the redundant direct path between two models. A direct path is redundant if two models are also connected through at least one another model. Default is TRUE.

label_arrow_by_df

If TRUE, then an arrow (edge) is always labelled by the difference in model dfs. If FALSE, then no arrows are labelled. If NULL, then arrows are labelled when not all differences in model dfs are equal to one. Default is NULL.

arrow_label_size

The size of the labels of the arrows (edges), if labelled. Default is 1.

weight_arrows_by_df

String. Use if model df differences are stored. If "inverse", larger the difference in model df, narrower an arrow. That is, more similar two models are, thicker the arrow. If "normal", larger the difference in model df, wider an arrow. If "none", then arrow width is constant, set to arrow_max_width. Default is "inverse".

arrow_min_width

If weight_arrows_by_df is not "none", this is the minimum width of an arrow.

arrow_max_width

If weight_arrows_by_df is not "none", this is the maximum width of an arrow. If weight_arrows_by_df is "none", this is the width of all arrows.

progress

Whether a progress bar will be displayed for some steps (e.g., checking for nested relations). Default is TRUE.

short_names

If TRUE and short model names are stored, they will be used as model labels. Please print the object with short_names = TRUE to find the corresponding full model names.

...

Optional arguments. Not used for now.

Details

It extracts the model list stored in object, creates an adjacency matrix, and then creates an igraph object customized for visualizing model relations.

Construction of the Graph

This is the default way to construct the graph when the model set is automatically by model_set().

• Each model is connected by an arrow, pointing from one model to another model that

  a. can be formed by adding one or more free parameter, or

  b. can be formed by releasing one or more equality constraint between two parameters.

  c. has nested relation with this model as determined by the method proposed by Bentler and Satorra (2010), if the models are not generated internally.

That is, it points to a model with more degrees of freedom (more complicated), and is nested within that model in either parameter sense or covariance sense.

• By default, the size of the node for each model is scaled by its BIC posterior probability, if available. See The Size of a Node below.

• If a model is designated as the original (target) model, than he original model, the models with more degrees of freedom than the original model, and the models with fewer degrees of freedom than the original models, are colored differently.

• The default layout is the Sugiyama layout, with simpler models (models with fewer degrees of freedom) on the top. The lower a model is in the network, the more the degrees of freedom it has. This layout is suitable for showing the nested relations of the models. Models on the same level (layer) horizontally have the same model df.

The output is an igraph object. Users can customize it in any way they want using functions from the igraph package.

If a model has no nested relation with all other model, it will not be connected to other models.

If no model is named original (default is "original"), then no model is colored as the original model.

User-Provided Models

If object contained one or more user-provided models which are not generated automatically by model_set() or similar functions (e.g., gen_models()), then the method by Bentler and Satorra (2010) will be used to determine model relations. Models connected by an arrow has a nested relation based on the NET method by Bentler and Satorra (2010). An internal function inspired by semTools::net() is used to implement the NET method.

The Size of a Node

When a model is scaled by x, which usually is the BIC posterior probability, its size is determined by:

max_size * (x - min(x))/(max(x) - min(x)) + min_size

Value

A model_graph-class object that can be used as as an igraph-object, with a plot method (plot.model_graph()) with settings suitable for plotting a network of models with BIC posterior probabilities computed.

Author(s)

Shu Fai Cheung https://orcid.org/0000-0002-9871-9448 The internal function for nesting inspired by semTools::net(), which was developed by Terrence D. Jorgensen.

References

Bentler, P. M., & Satorra, A. (2010). Testing model nesting and equivalence. Psychological Methods, 15(2), 111–123. doi:10.1037/a0019625 Asparouhov, T., & Muthén, B. (2019). Nesting and Equivalence Testing for Structural Equation Models. Structural Equation Modeling: A Multidisciplinary Journal, 26(2), 302–309. doi:10.1080/10705511.2018.1513795

Examples

library(lavaan)

mod <-
"
m1 ~ x
y ~ m1
"

fit <- sem(mod, dat_serial_4, fixed.x = TRUE)

out <- model_set(fit)
out

g <- model_graph(out)
plot(g)