#SEM Approach
#install and activate packages 

install.packages("metafor")
install.packages("meta")
install.packages("metaSEM")
library(metafor)
library(meta)
library(metaSEM)

#Two studies investigated the effect of precise diet goals vs round diet goals on weight loss. Both goal groups were compared to a control group, who did not set a goal.  

#Calculate effect sizes and covariances for Study 1 (control group vs precise group vs round group vs both goals groups on weight loss)

m <- c(0.06,0.57,0.93,0.78) #the last number is both goal groups togehter  
v <- c(1.14,1.41,1.57,1.51)
n <- c(41,32,48,80)

smdMTS(m, v, n, homogeneity=c("variance"), bias.adjust=TRUE, all.comparisons=TRUE, list.output=TRUE, lavaan.output=FALSE)

#Calculate effect sizes and covariances for Study 2 (control group vs round group vs precise group vs both goal groups on weight loss)

m <- c(0.30,0.71,0.41,0.55) 
v <- c(1.33,1.96,1.64,1.80)
n <- c(47,49,54,103)

smdMTS(m, v, n, homogeneity=c("variance"), bias.adjust=TRUE, all.comparisons=TRUE, list.output=TRUE, lavaan.output=FALSE)


#Create data frame in order to use meta function 

Study <-c(1,2) 
contrast1_control_vs_round <-c(0.422,0.311) # I put here "y", the effect size of the output of the smdMTS function 
contrast2_control_vs_precise <-c(0.720,0.083)
contrast3_round_vs_precise <-c(0.298,-0.228)
contrast4_control_vs_goal_groups <- c(0.598,0.190)
var_contrast1 <-c(0.056,0.0414) # I put here the number from the covariance matrix (y2_1 & y2_1). Is this correct? It should be the variance of the contrast, right?
cov_contrast1_contrast2 <-c(0.025,0.030)
var_contrast2 <-c(0.047,0.039) 
cov_contrast2_contrast3 <- c(0.021,0.018) 
var_contrast3 <- c(0.051,0.039)
cov_contrast1_contrast3 <-c(-0.030,-0.020) #Which covariance do I have to use when I have three groups and I compare all groups with each other? 
#The precise group is also used in contrast 2 and the round group also in contrast 1, so I would have to use two covariances?
var_contrast4 <- c(0.037,0.037)
cov_contrast1_contrast4 <-c (0.025,-0.021) 

dietGoals<- data.frame (Study,contrast1_control_vs_round,contrast2_control_vs_precise,contrast3_round_vs_precise,
                        contrast4_control_vs_goal_groups,var_contrast1,cov_contrast1_contrast2,var_contrast2,cov_contrast2_contrast3,
                        var_contrast3,cov_contrast1_contrast3,var_contrast4,cov_contrast1_contrast4) #In which order I have to put these variables in here?
View(dietGoals)

#Multivariate meta-analysis, fixed-effects

meta(y = cbind(contrast1_control_vs_round,contrast2_control_vs_precise,contrast3_round_vs_precise,contrast4_control_vs_goal_groups), v = cbind(var_contrast1,cov_contrast1_contrast2,var_contrast2,
                                                                                                cov_contrast2_contrast3,var_contrast3,cov_contrast1_contrast3,var_contrast4,cov_contrast1_contrast4), data = dietGoals,RE.constraints=0)