var1 {psychonetrics}

Lag-1 vector autoregression family of psychonetrics models

Description

This is the family of models that models time-series data using a lag-1 vector autoregressive model (VAR; Epskamp,Waldorp, Mottus, Borsboom, 2018). The model is fitted to the Toeplitz matrix, but unlike typical SEM software the block of covariances of the lagged variables is not used in estimating the temporal and contemporaneous relationships (the block is modeled completely separately using a cholesky decomposition, and does not enter the model elsewise). The contemporaneous argument can be used to define what contemporaneous model is used: contemporaneous = "cov" (default) models a variance-covariance matrix, contemporaneous = "chol" models a Cholesky decomposition, contemporaneous = "prec" models a precision matrix, and contemporaneous = "ggm" (alias: gvar()) models a Gaussian graphical model, also then known as a graphical VAR model.

Usage

var1(data, contemporaneous = c("cov", "chol", "prec",
                   "ggm"), beta = "full", omega_zeta = "full", delta_zeta
                   = "full", kappa_zeta = "full", sigma_zeta = "full",
                   lowertri_zeta = "full", mu, beepvar, dayvar, idvar,
                   vars, groups, covs, means, nobs, missing = "listwise",
                   equal = "none", baseline_saturated = TRUE, estimator =
                   "ML", optimizer, storedata = FALSE, covtype =
                   c("choose", "ML", "UB"), standardize = c("none", "z",
                   "quantile"), sampleStats, verbose = FALSE, bootstrap =
                   FALSE, boot_sub, boot_resample)

gvar(...)

Arguments

data

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

contemporaneous

The type of contemporaneous model used. See description.

beta

A model matrix encoding the temporal relationships (transpose of temporal network). A 0 encodes a fixed to zero element, a 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. Can also be "full" for a full temporal network or "zero" for an empty temporal network.

omega_zeta

Only used when contemporaneous = "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.

delta_zeta

Only used when contemporaneous = "ggm". Either "diag" to estimate all scalings or "zero" (not recommended) 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.

kappa_zeta

Only used when contemporaneous = "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.

sigma_zeta

Only used when contemporaneous = "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.

lowertri_zeta

Only used when contemporaneous = "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.

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.

beepvar

Optional string indicating assessment beep per day. Adding this argument will cause non-consecutive beeps to be treated as missing!

dayvar

Optional string indicating assessment day. Adding this argument makes sure that the first measurement of a day is not regressed on the last measurement of the previous day. IMPORTANT: only add this if the data has multiple observations per day.

idvar

Optional string indicating the subject ID

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.

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.

sampleStats

An optional sample statistics object. Mostly used internally.

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.

verbose

Logical, should messages be printed?

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 var1

Details

This will be updated in a later version.

Value

An object of the class psychonetrics

Author(s)

Sacha Epskamp

References

Epskamp, S., Waldorp, L. J., Mottus, R., & Borsboom, D. (2018). The Gaussian graphical model in cross-sectional and time-series data. Multivariate Behavioral Research, 53(4), 453-480.

See Also

lvm, varcov, dlvm1

Examples

library("dplyr")
library("graphicalVAR")

beta <- matrix(c(
  0,0.5,
  0.5,0
),2,2,byrow=TRUE)
kappa <- diag(2)
simData <- graphicalVARsim(50, beta, kappa)

# Form model:
model <- gvar(simData)

# Evaluate model:
model <- model %>% runmodel

# Parameter estimates:
model %>% parameters

# Plot the CIs:
CIplot(model,  "beta")

# Note: this example is wrapped in a dontrun environment because the data is not 
# available locally.
## Not run: 
# Longer example:
#
# Obtain the data from:
#
# Epskamp, S., van Borkulo, C. D., van der Veen, D. C., Servaas, M. N., Isvoranu, A. M., 
# Riese, H., & Cramer, A. O. (2018). Personalized network modeling in psychopathology: 
# The importance of contemporaneous and temporal connections. Clinical Psychological 
# Science, 6(3), 416-427.
# 
# Available here: https://osf.io/c8wjz/

tsdata <- read.csv("Supplementary2_data.csv")

# Encode time variable in a way R understands:
tsdata$time <- as.POSIXct(tsdata$time, tz = "Europe/Amsterdam")

# Extract days:
tsdata$Day <- as.Date(tsdata$time, tz = "Europe/Amsterdam")

# Variables to use:
vars <- c("relaxed", "sad", "nervous", "concentration", "tired", "rumination", 
          "bodily.discomfort")

# Estimate, prune with FDR, and perform stepup search:
model_FDRprune <- gvar(
  tsdata, 
  vars = vars, 
  dayvar = "Day",
  estimator = "FIML"
  ) %>% 
  runmodel %>% 
  prune(adjust = "fdr", recursive = FALSE) %>% 
  stepup(criterion = "bic")

# Estimate with greedy stepup search:
model_stepup <- gvar(
  tsdata, 
  vars = vars, 
  dayvar = "Day",
  estimator = "FIML",
  omega_zeta = "zero",
  beta = "zero"
) %>% 
  runmodel %>% 
  stepup(greedy = TRUE, greedyadjust = "bonferroni", criterion = "bic")

# Compare models:
compare(
  FDRprune = model_FDRprune,
  stepup = model_stepup
)
# Very similar but not identical. Stepup is prefered here according to AIC and BIC

# Stepup results:
temporal <- getmatrix(model_stepup, "PDC") # PDC = Partial Directed Correlations
contemporaneous <- getmatrix(model_stepup, "omega_zeta")

# Average layout:
library("qgraph")
L <- averageLayout(temporal, contemporaneous)

# Labels:
labs <- gsub("\\.","\n",vars)

# Plot:
layout(t(1:2))
qgraph(temporal, layout = L, theme = "colorblind", directed=TRUE, diag=TRUE,
       title = "Temporal", vsize = 12, mar = rep(6,4), asize = 5,
       labels = labs)
qgraph(contemporaneous, layout = L, theme = "colorblind", 
       title = "Contemporaneous", vsize = 12, mar = rep(6,4), asize = 5,
       labels = labs)

## End(Not run)