mlVAR: Multilevel VAR Estimation for Multiple Time Series

Description

The function mlVAR computes estimates of the multivariate vector autoregression model as introduced by Bringmann et al. (2013) which can be extended through treatment effects, covariates and pre- and post assessment effects.

Usage

mlVAR(data, vars, idvar, dayvar, beepvar, periodvar, lags = 1, treatmentvar, covariates, 
        control = list(optimizer = "bobyqa"))

Arguments

data

Data frame

vars

Vectors of variables to include in the analysis

idvar

String indicating the subject ID

dayvar

String indicating assessment day (if missing, every assessment is set to one day)

beepvar

String indicating assessment beep per day (if missing, is added)

periodvar

String indicating the period (baseline, treatment period, etc.) of assessment (if missing, every assessment is set to one period)

lags

Vector indicating the lags to include

treatmentvar

Character vector indicating treatment

covariates

Character indicating covariates independent of assessment.

control

A list of arguments sent to lmerControl

Value

mlVAR returns a 'mlVAR' object containing
fixedEffectsA matrix that contains all fixed effects coefficients with dependent variables as rows and the lagged independent variables as columns.
se.fixedEffectsA matrix that contains all standard errors of the fixed effects.
randomEffectsA list of matrices that contain the random effects coefficients.
randomEffectsVarianceA matrix containing the estimated variances between the random-effects terms
pvalsA matrix that contains p-values for all fixed effects.
pseudologlikThe pseudo log-likelihood.
BICBayesian Information Criterion, i.e. the sum of all univariate models' BICs
inputList containing the names of variables used in the analysis

Details

mlVAR has been built to extract individual network dynamics by estimating a multilevel vector autoregression model that models the time dynamics of selected variables both within an individual and on group level. For example, in a lag-1-model each variable at time point t is regressed to a lagged version of itself at time point t-1 and all other variables at time point t-1. In psychological research, for example, this analysis can be used to relate the dynamics of symptoms on one day (as assessed by experience sampling methods) to the dynamics of these symptoms on the consecutive day.

References

Bringmann, L. F., Vissers, N., Wichers, M., Geschwind, N., Kuppens, P., Peeters, F., Borsboom, D. and Tuerlinckx, F. (2013). A network approach to psychopathology: New insights into clinical longitudinal data. PloS one, 8(4): e60188.

Examples

Run this code

# True L1 structure:
L1 <- matrix(c(
  0.5,0.25,0,
  0,0.5,0.25,
  0,0,0.5),3,3,byrow=TRUE)

# True L2 structure:
L2 <- matrix(c(
  0.1,0,-0.2,
  0,0.1,0,
  0,0,0.1),3,3,byrow=TRUE)

# Error variance:
error <- 0.1

# Number of subjects:
Np <- 10

# Number of measurements per subject:
Nt <- 30

# Generate random effects:
L1_RF <- lapply(1:Np, function(x) L1 + rnorm(prod(dim(L1)),0,error))
L2_RF <- lapply(1:Np, function(x) L2 + rnorm(prod(dim(L1)),0,error))

# Generate data:
Data <- do.call(rbind,lapply(1:Np, function(p) {
  subjectData <- simulateVAR(list(L1_RF[[p]], L2_RF[[p]]), 1:2, 100)
  names(subjectData) <- paste0("x",1:3)
  subjectData$ID <- p
  subjectData
  }))

# Run analysis:
Res <- mlVAR(Data, paste0('x',1:3), "ID", lags = c(1, 2))

  library("qgraph")
  
  # Plot true fixed VAR network vs estimated fixed VAR network:
  # Lag-1
  layout(t(1:2))
  qgraph(t(L1), labels = paste0('x',1:3), layout = "circle", title = "True Lag-1", diag = TRUE,
         mar = c(8,8,8,8))
  plot(Res, "fixed", lag=1, labels = paste0('x',1:3), layout = "circle", title = "Estimated Lag-1",
       mar = c(8,8,8,8))
  
  # Lag-2
  layout(t(1:2))
  qgraph(t(L2), labels = paste0('x',1:3), layout = "circle", title = "True Lag-2", diag = TRUE,
         mar = c(8,8,8,8))
  plot(Res, "fixed", lag=2, labels = paste0('x',1:3), layout = "circle", title = "Estimated Lag-2",
       mar = c(8,8,8,8))

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