CTMA: Transforms the lagged effect estimates for a given interval...

In rebeccakuiper/CTmeta: Continuous-time meta-analysis (CTmeta) on standarized lagged effects taking into account the various time-intervals used in the primary studies

Transforms the lagged effect estimates for a given interval to the ones corresponding to a different time-interval

Description

Transforms the lagged effect estimates for a given interval to the ones corresponding to a different time-interval

Usage

CTMA(N, TypeMx, Phi, SigmaVAR, Gamma, DeltaTStar, DeltaT, Moderators = 0,
  Mod = NULL, FEorRE = 1, alpha = 0.05)

Arguments

N	Number of persons (panel data) or measurement occasions - 1 (time series data) used in the S studies. Matrix of size S times 1.
TypeMx	Indicator of type of matrix for Phi, SigmaVAR, and Gamma: 0) Stacked matrix of size S q times q; 2) Array with dimensions q times q times S; with S the number of studies in the meta-analysis and q the number of variables (leading to an q times q lagged effects matrix Phi).
Phi	Stacked matrix (TypeMx == 0) or array (TypeMx == 1) of (un)standardized lagged effects matrices for all S studies in the meta-analysis.
SigmaVAR	Stacked matrix (TypeMx == 0) or array (TypeMx == 1) of residual covariance matrices of the first-order discrete-time vector autoregressive (DT-VAR(1)) model.
Gamma	Stacked matrix (TypeMx == 0) or array (TypeMx == 1) of stationary covariance matrices, that is, the contemporaneous covariance matrices of the data sets.
DeltaTStar	The time interval (scalar) to which the standardized lagged effects matrix should be transformed to.
DeltaT	The time intervals used in the S studies. Matrix of size S times 1.
Moderators	Indicator whether there are moderators to be included (1) or not (0; default).
Mod	Matrix of moderators to be included in the analysis when Moderators == 1. By default, Mod = NULL.
FEorRE	Indicator whether continuous-time meta-analysis (CTmeta) should use a fixed-effects model (1; default) or random-effects model (2).
alpha	The alpha level in determining the (1-alpha)*100 percent confidence interval (CI). By default, alpha is set to 0.05, resulting in a 95 percent CI.

Value

vectorized transformed standardized lagged effects, their covariance matrix, and the corresponding elleptical/multivariate 95 percent CI.

Examples

###########################################################
### Input for examples ###
q = 2 # Number of variables in the process/system
S = 3 # Number of studies included in the meta-analysis

## Phi as S q times q matrix (TypeMx == 0) ##

# Based on discrete-time model #
Phi <- matrix(c(0.25, 0.10,
                0.20, 0.36,
                0.35, 0.20,
                0.30, 0.46,
                0.15, 0.00,
                0.10, 0.26), byrow = T, ncol = q)

# Based on correlation matrix #
corr_YXYX <- matrix(c(1.00, 0.40, 0.63, 0.34,
                      0.40, 1.00, 0.31, 0.63,
                      0.63, 0.31, 1.00, 0.41,
                      0.34, 0.63, 0.41, 1.00), byrow = T, ncol = 2*q)
out <- calc.TransPhi_Corr(12, 24, 2235, corr_YXYX)
Phi_1 <- matrix(out$vecStandPhi_DeltaTStar, byrow = T, ncol = q)
Phi_2 <- matrix(out$vecStandPhi_DeltaTStar, byrow = T, ncol = q)
Phi_3 <- matrix(out$vecStandPhi_DeltaTStar, byrow = T, ncol = q)
Phi <- rbind(Phi_1, Phi_2, Phi_3)


## SigmaVAR and Gamma as S q times q matrix (TypeMx == 0) ##
# Based on discrete-time model, using SigmaVAR #
SigmaVAR_s <- diag(q) # for ease
SigmaVAR <- rbind(SigmaVAR_s, SigmaVAR_s, SigmaVAR_s)
# If Phi and SigmaVAR are known, one can calculate Gamma:
Gamma <- array(data=NA, dim=c(S*q,q))
teller <- 1
for(s in 1:S){
  Gamma[teller:(teller+1),] <- calc.Gamma.fromVAR(Phi[teller:(teller+1),], SigmaVAR[teller:(teller+1),])
  teller <- teller + q
}

# Based on discrete-time model, using Gamma #
# Use Gamma from above
# If Phi and SigmaVAR are known, one can calculate Gamma:
SigmaVAR <- array(data=NA, dim=c(S*q,q))
teller <- 1
for(s in 1:S){
  SigmaVAR[teller:(teller+1),] <- Gamma[teller:(teller+1),] - Phi[teller:(teller+1),] %*% Gamma[teller:(teller+1),] %*% t(Phi[teller:(teller+1),])
  teller <- teller + q
}

# Based on correlation matrix #
# Use 'out' from above. # out <- calc.TransPhi_Corr(12, 24, 2235, corr_YXYX)
SigmaVAR_1 <- out$SigmaVAR_DeltaTStar
Gamma_1 <- out$Gamma
# Do this for each study to make a stacked matrix out of this

## Phi as array with dimensions q times q times S (TypeMx == 1) ##

# Based on discrete-time model #
# Use Phi from above
Phi_studies <- array(data=NA, dim=c(q,q,S))
teller = 0
for(s in 1:S){
  Phi_studies[1:q,1:q,s] <- matrix(t(Phi)[(teller+1):(teller+q*q)], byrow = T, ncol=q*q)
  Phi_studies[1:q,1:q,s] <- t(Phi_studies[1:q,1:q,s])
  teller = teller + q*q
}
#Phi <- Phi_studies

# Use SigmaVAR from above
SigmaVAR_studies <- array(data=NA, dim=c(q,q,S))
teller = 0
for(s in 1:S){
  SigmaVAR_studies[1:q,1:q,s] <- SigmaVAR[(teller+1):(teller+q),1:q]
  teller = teller + q
}
#SigmaVAR <- SigmaVAR_studies
Gamma_studies <- array(data=NA, dim=c(q,q,S))
for(s in 1:S){
  Gamma_studies[,,s] <- calc.Gamma.fromVAR(Phi_studies[,,s], SigmaVAR_studies[,,s])
}
#Gamma <- CovMx_studies

# Use Gamma from above
Gamma_studies <- array(data=NA, dim=c(q,q,S))
teller = 0
for(s in 1:S){
  Gamma_studies[1:q,1:q,s] <- Gamma[(teller+1):(teller+q),1:q]
  teller = teller + q
}
#Gamma <- CovMx_studies
SigmaVAR_studies <- array(data=NA, dim=c(q,q,S))
for(s in 1:S){
  SigmaVAR_studies[,,s] <- Gamma_studies[,,s] - Phi_studies[,,s] %*% Gamma_studies[,,s] %*% t(Phi_studies[,,s])
}
#SigmaVAR <- SigmaVAR_studies


# The study-specific sampel size (N) and time interval (DeltaT)
DeltaT <- matrix(c(2, 3, 1))
N <- matrix(c(643, 651, 473))
###########################################################


# Based on input above, one can run one of these two CTmeta analyses
DeltaTStar <- 1
CTMA(N, 1, Phi_studies, SigmaVAR_studies, Gamma_studies, DeltaTStar, DeltaT)
CTMA(N, 0, Phi, SigmaVAR, Gamma, DeltaTStar, DeltaT)


# In case of moderators
Mod <- matrix(c(64,65,47)) # 1 moderator
#Mod <- matrix(cbind(c(64,65,47), c(78,89,34)), ncol = q); colnames(Mod) <- c("Mod1", "Mod2") # two moderators, in each column 1
CTMA(N, 1, Phi_studies, SigmaVAR_studies, Gamma_studies, DeltaTStar, DeltaT, Moderators = 1, Mod)


# Afterwards: Make PhiPlot of overallPhi
DeltaTStar <- 1
out_CTmeta <- CTMA(N, 0, Phi, SigmaVAR, Gamma, DeltaTStar, DeltaT, Moderators = 0, Mod = NULL, FEorRE = 1, alpha=0.05)
q <- sqrt(length(out_CTmeta$Overall_standPhi_DeltaTStar))
overallPhi <- matrix(out_CTmeta$Overall_standPhi_DeltaTStar, byrow = T, ncol = q)
overallDrift <- logm(overallPhi)/DeltaTStar # Use expm package
PhiPlot(DeltaTStar, overallDrift, Min = 0, Max = 40, Step = 0.5)

rebeccakuiper/CTmeta documentation built on Oct. 17, 2023, 7:01 a.m.