Description Usage Arguments Details Value Author(s) References See Also Examples

This function utilizes OpenMx (Boker et al., 2011, 2014) to confirmatory test latent variable network models between P manifests and M latents. See the details section for information about the modeling framework used. All the input matrices can be assigned R matrices with numbers indicating fixed values and NA indicating a value is free to estimate.

1 2 3 4 |

`data` |
An N (sample size) x P matrix or data frame containing the raw data, or a P x P variance-covariance matrix. |

`lambda` |
A P x M matrix indicating factor loadings. Defaults to a full NA P x M matrix if psi or omega_psi is not missing, or a P x 0 dummy matrix. |

`beta` |
An M x M matrix indicating linear effects between latent variables. Defaults to an M x M matrix containing only zeroes. |

`omega_theta` |
A P x P matrix encoding the residual network structure. By default, theta is modeled instead. |

`delta_theta` |
A P x P diagonal scaling matrix. Defaults to NA on all diagonal elements. Only used if omega_theta is modeled. |

`omega_psi` |
An M x M matrix containing the latent network structure. Dy default, psi is modeled instead. |

`delta_psi` |
A diagonal M x M scaling matrix. Defaults to an identity matrix. Only used if omega_psi is modeled. |

`psi` |
An M x M variance-covariance matrix between latents and latent residuals. Defaults to a full NA matrix. |

`theta` |
A P x P variance-covariance matrix of residuals of the observed variables. Defaults to a diagonal matrix containing NAs |

`sampleSize` |
The sample size, only used if |

`fitInd` |
The fit of the independence model. Used to speed up estimation fitting multiple models. |

`fitSat` |
The fit of the saturated model. Used to speed up estimation fitting multiple models. |

`startValues` |
An optional named list containing starting values of each model. e.g., |

`scale` |
Logical, should data be standardized before running lvnet? |

`nLatents` |
The number of latents. Allows for quick specification when |

`lasso` |
The LASSO tuning parameter. |

`lassoMatrix` |
Character vector indicating the names of matrices to apply LASSO regularization on. e.g., |

`lassoTol` |
Tolerance for absolute values to be treated as zero in counting parameters. |

`ebicTuning` |
Tuning parameter used in extended Bayesian Information Criterion. |

`mimic` |
If set to |

`fitFunction` |
The fit function to be used. |

`exogenous` |
Numeric vector indicating which variables are exogenous. |

The modeling framework follows the all-y LISREL framework for Structural Equation Models (SEM; Hayduk, 1987) to model relationships between P observed variables and M latent variables:

sigma = lambda * (I - beta)^(-1) psi (I - beta)^(-1 T) * lambda^T + theta

Where Sigma is the P x P model-implied covariance matrix, lambda a P x M matrix of factor loadings, B an M x M matrix containing regression effects between latent variables, Psi a M x M covariance matrix of the latent variables/residuals and Theta a P x P covariance matrix of residuals of the observed indicators.

The lvnet function allows for two extensions of this modeling framework. First, psi can be chosen to be modeled as follows:

psi = delta_psi (I - omega_psi)^(-1) delta_psi

In which delta_psi is a M x M diagonal scaling matrix and omega_psi a M x M matrix containing zeroes on the diagonal and partial correlation coefficients on the offdiagonal values of two latent variables conditioned on all other latent variables. omega_psi therefore corresponds to a Gaussian Graphical Model, or a network structure.

Similarly, theta can be chosen to be modeled as follows:

theta = delta_theta (I - omega_theta)^(-1) delta_theta

In which delta_theta is a P x P diagonal scaling matrix and omega_theta a P x P matrix containing zeroes on the diagonal and partial correlation coefficients on the offdiagonal values of two residuals conditioned on all other residuals.

Modeling omega_psi is termed Latent Network Modeling (LNM) and modeling omega_theta is termed Residual Network Modeling (RNM). lvnet automatically chooses the appropriate modeling framework based on the input.

An `lvnet`

object, which is a list containing the following elements:

`matrices` |
A list containing thee estimated model matrices |

`sampleStats` |
A list containing the covariance matrix ( |

`mxResults` |
The OpenMx object of the fitted model |

`fitMeasures` |
A named list containing the fit measures of the fitted model |

Sacha Epskamp <mail@sachaepskamp.com>

Boker, S. M., Neale, M., Maes, H., Wilde, M., Spiegel, M., Brick, T., ... Fox, J. (2011). OpenMx: an open source extended structural equation modelingframework. Psychometrika, 76(2), 306-317

Boker, S. M., Neale, M. C., Maes, H. H., Wilde, M. J., Spiegel, M., Brick, T. R., ..., Team OpenMx. (2014). Openmx 2.0 user guide [Computer software manual].

Hayduk, L. A. (1987).Structural equation modeling with LISREL: Essentials advances. Baltimore, MD, USA: Johns Hopkins University Press.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 | ```
# Load dataset:
library("lavaan")
data(HolzingerSwineford1939)
Data <- HolzingerSwineford1939[,7:15]
# Measurement model:
Lambda <- matrix(0, 9, 3)
Lambda[1:3,1] <- NA
Lambda[4:6,2] <- NA
Lambda[7:9,3] <- NA
# Fit CFA model:
CFA <- lvnet(Data, lambda = Lambda)
# Latent network:
Omega_psi <- matrix(c(
0,NA,NA,
NA,0,0,
NA,0,0
),3,3,byrow=TRUE)
# Fit model:
LNM <- lvnet(Data, lambda = Lambda, omega_psi=Omega_psi)
# Compare fit:
lvnetCompare(cfa=CFA,lnm=LNM)
# Summary:
summary(LNM)
# Plot latents:
plot(LNM, "factorStructure")
``` |

```
Loading required package: OpenMx
To take full advantage of multiple cores, use:
mxOption(NULL, 'Number of Threads', parallel::detectCores())
This is lavaan 0.5-23.1097
lavaan is BETA software! Please report any bugs.
Attaching package: 'lavaan'
The following object is masked from 'package:OpenMx':
vech
sh: 1: cannot create /dev/null: Permission denied
sh: 1: wc: Permission denied
Df AIC BIC EBIC Chisq Chisq diff Df diff
Saturated 0 NA NA NA 0.00000 NA NA
cfa 24 7517.490 7595.339 7835.038 85.30552 85.305522 24
lnm 25 7516.494 7590.637 7818.921 86.31009 1.004565 1
Pr(>Chisq)
Saturated NA
cfa 8.502553e-09
lnm 3.162085e-01
========== lvnet ANALYSIS RESULTS ==========
Input:
Model:
Number of manifests: 9
Number of latents: 3
Number of parameters: 20
Number of observations 301
Test for exact fit:
Chi-square: 86.31
DF: 25
p-value: 0
Information criteria:
AIC: 7516.494
BIC: 7590.637
Adjusted BIC: 7527.208
Extended BIC: 7818.921
Fit indices:
CFI: 0.931
NFI: 0.906
TLI: 0.9
RFI: 0.865
IFI: 0.931
RNI: 0.931
RMR: 0.077
SRMR: 0.061
RMSEA:
RMSEA: 0.09
90% CI lower bound: 0.07
90% CI upper bound: 0.111
p-value: 0.001
Parameter estimates:
matrix row col name Estimate
lambda 1 1 lambda_1_1 0.708
lambda 2 1 lambda_2_1 0.393
lambda 3 1 lambda_3_1 0.517
lambda 4 2 lambda_4_2 0.874
lambda 5 2 lambda_5_2 0.971
lambda 6 2 lambda_6_2 0.809
lambda 7 3 lambda_7_3 0.537
lambda 8 3 lambda_8_3 0.639
lambda 9 3 lambda_9_3 0.587
theta 1 1 theta_1_1 0.559
theta 2 2 theta_2_2 1.135
theta 3 3 theta_3_3 0.848
theta 4 4 theta_4_4 0.370
theta 5 5 theta_5_5 0.448
theta 6 6 theta_6_6 0.356
theta 7 7 theta_7_7 0.805
theta 8 8 theta_8_8 0.487
theta 9 9 theta_9_9 0.563
omega_psi 1 2 omega_psi_1_2 0.422
omega_psi 1 3 omega_psi_1_3 0.442
```

Embedding an R snippet on your website

Add the following code to your website.

For more information on customizing the embed code, read Embedding Snippets.