varcov {psychonetrics}

Variance-covariance family of psychonetrics models

Description

This is the family of models that models only a variance-covariance matrix with mean structure. The type argument can be used to define what model is used: type = "cov" (default) models a variance-covariance matrix directly, type = "chol" (alias: cholesky()) models a Cholesky decomposition, type = "prec" (alias: precision()) models a precision matrix, type = "ggm" (alias: ggm()) models a Gaussian graphical model (Epskamp, Rhemtulla and Borsboom, 2017), and type = "cor" (alias: corr()) models a correlation matrix.

Usage

varcov(data, type = c("cov", "chol", "prec", "ggm", "cor"),
                   sigma = "full", kappa = "full", omega = "full",
                   lowertri = "full", delta = "diag", rho = "full", SD =
                   "full", mu, tau, vars, ordered = character(0), groups,
                   covs, means, nobs, missing = "listwise", equal =
                   "none", baseline_saturated = TRUE, estimator =
                   "default", optimizer, storedata = FALSE, WLS.W,
                   sampleStats, meanstructure, corinput, verbose = FALSE,
                   covtype = c("choose", "ML", "UB"), standardize =
                   c("none", "z", "quantile"), fullFIML = FALSE,
                   bootstrap = FALSE, boot_sub, boot_resample)
cholesky(...)
precision(...)
prec(...)
ggm(...)
corr(...)

Arguments

data

A data frame encoding the data used in the analysis. Can be missing if covs and nobs are supplied.

type

The type of model used. See description.

sigma

Only used when type = "cov". Either "full" to estimate every element freely, "diag" to only include diagonal elements, or a matrix of the dimensions node x node with 0 encoding a fixed to zero element, 1 encoding a free to estimate element, and higher integers encoding equality constrains. For multiple groups, this argument can be a list or array with each element/slice encoding such a matrix.

kappa

Only used when type = "prec". Either "full" to estimate every element freely, "diag" to only include diagonal elements, or a matrix of the dimensions node x node with 0 encoding a fixed to zero element, 1 encoding a free to estimate element, and higher integers encoding equality constrains. For multiple groups, this argument can be a list or array with each element/slice encoding such a matrix.

omega

Only used when type = "ggm". Either "full" to estimate every element freely, "zero" to set all elements to zero, or a matrix of the dimensions node x node with 0 encoding a fixed to zero element, 1 encoding a free to estimate element, and higher integers encoding equality constrains. For multiple groups, this argument can be a list or array with each element/slice encoding such a matrix.

lowertri

Only used when type = "chol". Either "full" to estimate every element freely, "diag" to only include diagonal elements, or a matrix of the dimensions node x node with 0 encoding a fixed to zero element, 1 encoding a free to estimate element, and higher integers encoding equality constrains. For multiple groups, this argument can be a list or array with each element/slice encoding such a matrix.

delta

Only used when type = "ggm". Either "diag" or "zero" (not recommended), or a matrix of the dimensions node x node with 0 encoding a fixed to zero element, 1 encoding a free to estimate element, and higher integers encoding equality constrains. For multiple groups, this argument can be a list or array with each element/slice encoding such a matrix.

rho

Only used when type = "cor". Either "full" to estimate every element freely, "zero" to set all elements to zero, or a matrix of the dimensions node x node with 0 encoding a fixed to zero element, 1 encoding a free to estimate element, and higher integers encoding equality constrains. For multiple groups, this argument can be a list or array with each element/slice encoding such a matrix.

SD

Only used when type = "cor". Either "diag" or "zero" (not recommended), or a matrix of the dimensions node x node with 0 encoding a fixed to zero element, 1 encoding a free to estimate element, and higher integers encoding equality constrains. For multiple groups, this argument can be a list or array with each element/slice encoding such a matrix.

mu

Optional vector encoding the mean structure. Set elements to 0 to indicate fixed to zero constrains, 1 to indicate free means, and higher integers to indicate equality constrains. For multiple groups, this argument can be a list or array with each element/column encoding such a vector.

tau

Optional list encoding the thresholds per variable.

vars

An optional character vector encoding the variables used in the analyis. Must equal names of the dataset in data.

groups

An optional string indicating the name of the group variable in data.

covs

A sample variance–covariance matrix, or a list/array of such matrices for multiple groups. Make sure covtype argument is set correctly to the type of covariances used.

means

A vector of sample means, or a list/matrix containing such vectors for multiple groups.

nobs

The number of observations used in covs and means, or a vector of such numbers of observations for multiple groups.

covtype

If 'covs' is used, this is the type of covariance (maximum likelihood or unbiased) the input covariance matrix represents. Set to "ML" for maximum likelihood estimates (denominator n) and "UB" to unbiased estimates (denominator n-1). The default will try to find the type used, by investigating which is most likely to result from integer valued datasets.

missing

How should missingness be handled in computing the sample covariances and number of observations when data is used. Can be "listwise" for listwise deletion, or "pairwise" for pairwise deletion.

equal

A character vector indicating which matrices should be constrained equal across groups.

baseline_saturated

A logical indicating if the baseline and saturated model should be included. Mostly used internally and NOT Recommended to be used manually.

estimator

The estimator to be used. Currently implemented are "ML" for maximum likelihood estimation, "FIML" for full-information maximum likelihood estimation, "ULS" for unweighted least squares estimation, "WLS" for weighted least squares estimation, and "DWLS" for diagonally weighted least squares estimation.

optimizer

The optimizer to be used. Can be one of "nlminb" (the default R nlminb function), "ucminf" (from the optimr package), and C++ based optimizers "cpp_L-BFGS-B", "cpp_BFGS", "cpp_CG", "cpp_SANN", and "cpp_Nelder-Mead". The C++ optimizers are faster but slightly less stable. Defaults to "nlminb".

storedata

Logical, should the raw data be stored? Needed for bootstrapping (see bootstrap).

standardize

Which standardization method should be used? "none" (default) for no standardization, "z" for z-scores, and "quantile" for a non-parametric transformation to the quantiles of the marginal standard normal distribution.

WLS.W

Optional WLS weights matrix.

sampleStats

An optional sample statistics object. Mostly used internally.

verbose

Logical, should progress be printed to the console?

ordered

A vector with strings indicating the variables that are ordered catagorical, or set to TRUE to model all variables as ordered catagorical.

meanstructure

Logical, should the meanstructure be modeled explicitly?

corinput

Logical, is the input a correlation matrix?

fullFIML

Logical, should row-wise FIML be used? Not recommended!

bootstrap

Should the data be bootstrapped? If TRUE the data are resampled and a bootstrap sample is created. These must be aggregated using aggregate_bootstraps! Can be TRUE or FALSE. Can also be "nonparametric" (which sets boot_sub = 1 and boot_resample = TRUE) or "case" (which sets boot_sub = 0.75 and boot_resample = FALSE).

boot_sub

Proportion of cases to be subsampled (round(boot_sub * N)).

boot_resample

Logical, should the bootstrap be with replacement (TRUE) or without replacement (FALSE)

...

Arguments sent to varcov

Details

The model used in this family is:

\mathrm{var}(\boldsymbol{y} ) = \boldsymbol{\Sigma}

\mathcal{E}( \boldsymbol{y} ) = \boldsymbol{\mu}

in which the covariance matrix can further be modeled in three ways. With type = "chol" as Cholesky decomposition:

\boldsymbol{\Sigma} = \boldsymbol{L}\boldsymbol{L},

with type = "prec" as Precision matrix:

\boldsymbol{\Sigma} = \boldsymbol{K}^{-1},

and finally with type = "ggm" as Gaussian graphical model:

\boldsymbol{\Sigma} = \boldsymbol{\Delta}(\boldsymbol{I} - \boldsymbol{\Omega})^(-1) \boldsymbol{\Delta}.

Value

An object of the class psychonetrics

Author(s)

Sacha Epskamp

References

Epskamp, S., Rhemtulla, M., & Borsboom, D. (2017). Generalized network psychometrics: Combining network and latent variable models. Psychometrika, 82(4), 904-927.

See Also

lvm, var1, dlvm1

Examples

# Load bfi data from psych package:
library("psychTools")
data(bfi)

# Also load dplyr for the pipe operator:
library("dplyr")

# Let's take the agreeableness items, and gender:
ConsData <- bfi %>% 
  select(A1:A5, gender) %>% 
  na.omit # Let's remove missingness (otherwise use Estimator = "FIML)

# Define variables:
vars <- names(ConsData)[1:5]

# Saturated estimation:
mod_saturated <- ggm(ConsData, vars = vars)

# Run the model:
mod_saturated <- mod_saturated %>% runmodel

# We can look at the parameters:
mod_saturated %>% parameters

# Labels:
labels <- c(
  "indifferent to the feelings of others",
  "inquire about others' well-being",
  "comfort others",
  "love children",
  "make people feel at ease")
  
# Plot CIs:
CIplot(mod_saturated,  "omega", labels = labels, labelstart = 0.2)



# We can also fit an empty network:
mod0 <- ggm(ConsData, vars = vars, omega = "zero")

# Run the model:
mod0 <- mod0 %>% runmodel

# We can look at the modification indices:
mod0 %>% MIs

# To automatically add along modification indices, we can use stepup:
mod1 <- mod0 %>% stepup

# Let's also prune all non-significant edges to finish:
mod1 <- mod1 %>% prune

# Look at the fit:
mod1 %>% fit

# Compare to original (baseline) model:
compare(baseline = mod0, adjusted = mod1)

# We can also look at the parameters:
mod1 %>% parameters

# Or obtain the network as follows:
getmatrix(mod1, "omega")