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Using minTriadicClosure in LOLOG Models

Introduction

The minTriadicClosure() function defines a smoothed triadic closure statistic for use in LOLOG models. It counts how many nodes are part of at least k closed triangles, using a sigmoid function for smoothing.

Integration with LOLOG

This statistic can be added to LOLOG model formulas. Below is an example using a small toy network.

# Load required libraries
library(MinTriadic)
library(lolog)
library(network)

# Register the triadic change statistic
registerMinTriadicClosure()

# Load the Lazega collaboration network
data(lazega, package = "lolog")

# Fit LOLOG model with edges and minTriadicClosure
model <- lolog(lazega ~ edges + minTriadicClosure(k = 2, alpha = 1.5), verbose = FALSE)

## Error in solve.default(var(auxStats)) : 
##   Lapack routine dgesv: system is exactly singular: U[2,2] = 0

## Warning in lolog(lazega ~ edges + minTriadicClosure(k = 2, alpha = 1.5), :
## Singular statistic covariance matrix. Using diagnoal.

## Error in solve.default(var(auxStats)) : 
##   Lapack routine dgesv: system is exactly singular: U[2,2] = 0

## Warning in lolog(lazega ~ edges + minTriadicClosure(k = 2, alpha = 1.5), :
## Singular statistic covariance matrix. Using diagnoal.

## Error in solve.default(var(auxStats)) : 
##   Lapack routine dgesv: system is exactly singular: U[2,2] = 0

## Warning in lolog(lazega ~ edges + minTriadicClosure(k = 2, alpha = 1.5), :
## Singular statistic covariance matrix. Using diagnoal.

## Error in solve.default(var(auxStats)) : 
##   Lapack routine dgesv: system is exactly singular: U[2,2] = 0

## Warning in lolog(lazega ~ edges + minTriadicClosure(k = 2, alpha = 1.5), :
## Singular statistic covariance matrix. Using diagnoal.

## Error in solve.default(var(auxStats)) : 
##   Lapack routine dgesv: system is exactly singular: U[2,2] = 0

## Warning in lolog(lazega ~ edges + minTriadicClosure(k = 2, alpha = 1.5), :
## Singular statistic covariance matrix. Using diagnoal.

## Error in solve.default(var(auxStats)) : 
##   Lapack routine dgesv: system is exactly singular: U[2,2] = 0

## Warning in lolog(lazega ~ edges + minTriadicClosure(k = 2, alpha = 1.5), :
## Singular statistic covariance matrix. Using diagnoal.

## Error in solve.default(var(auxStats)) : 
##   Lapack routine dgesv: system is exactly singular: U[2,2] = 0

## Warning in lolog(lazega ~ edges + minTriadicClosure(k = 2, alpha = 1.5), :
## Singular statistic covariance matrix. Using diagnoal.

## Error in solve.default(var(auxStats)) : 
##   Lapack routine dgesv: system is exactly singular: U[2,2] = 0

## Warning in lolog(lazega ~ edges + minTriadicClosure(k = 2, alpha = 1.5), :
## Singular statistic covariance matrix. Using diagnoal.

# View model summary
summary(model)

##                   observed_statistics     theta        se pvalue
## edges                             115  2.929975 0.7146951      0
## minTriadicClosure                  28 70.941143 5.4321625      0

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