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[R-meta] residuals in lmer versus rma.mv

2 messages · Martineau, Roger, Wolfgang Viechtbauer

Martineau, Roger
# 
Dear list-members,

I extracted residuals from a lmer model and would like to get the same (or very similar) numbers from an equivalent rma.mv model. The example is reported below and the residuals from lmer and rma.mv are different:
1        2        3        4        5        6
 0.20559  0.03306 -0.12163 -0.30483  0.10283  0.35307
1         2         3         4         5         6

 0.438639  0.238639  0.089245 -0.111968  0.338639  0.586820

What should I do to get 0.205, 0.033, -0.122, etc as the residuals from the rma.mv model ?

Thanks in advance,

Roger  :)

Dr Roger Martineau, DVM PhD
Centre de recherche et de d?veloppement de Sherbrooke / Sherbrooke Research and Development Centre
Agriculture et Agroalimentaire Canada/Agriculture and Agri-Food Canada
2000 rue College / 2000 College Street
Sherbrooke, Qu?bec, Canada,  J1M 0C8
R?ceptionniste/Receptionist: 819-565-9171

# Example
dat <- iris
dat <- within(dat, {
  Y       <- Sepal.Length
  X       <- Petal.Length
  TID     <- 1:nrow(dat)
  PubID   <- rep(c(1:5), times = 30)
  Paper   <- rep(c(1:10), each = 15)
  TID     <- as.factor(TID)
  PubID   <- as.factor(PubID)
  Paper   <- as.factor(Paper)
  Wgt     <- round(Sepal.Length)^0.5
  ID      <- 1:nrow(dat)
})
dat <- subset (dat, select = -c(Sepal.Length,Sepal.Width,Petal.Length,Petal.Width,Species))
str(dat)

# lmer model
m.lmer <- lmer(Y ~ X + (1|Paper/PubID), weight = Wgt, data=dat)
summary(m.lmer)
Res.lmer <- residuals(m.lmer)
head(Res.lmer)

# rma.mv model
Rmat <- diag(1/dat$Wgt)
rownames(Rmat) <- colnames(Rmat) <- dat$ID
m.rma <- rma.mv(Y  ~ X,
                V=0, random = list(~ 1|Paper, ~ 1|PubID, ~ 1|ID),
                R=list(ID = Rmat), Rscale=FALSE,
                data=dat, method = "REML", digits=5, sparse = TRUE)
summary(m.rma)
Res.rma <- residuals.rma(m.rma)
head(Res.rma)
Wolfgang Viechtbauer
# 
Hi Martin,

For rma.mv(), you should use:

m.rma <- rma.mv(Y  ~ X,
                V=0, random = list(~ 1|Paper/PubID, ~ 1|ID),
                R=list(ID = Rmat), Rscale=FALSE,
                data=dat, method = "REML", digits=5, sparse = TRUE)

But you still won't get the same residuals, because residuals(m.lmer) computes 'conditional residuals' (Y minus 'fitted values based on the fixed effects plus random effects'), while residuals(m.rma) computes 'marginal residuals' (Y minus 'fitted values based on the fixed effects').

For 'rma.uni' models, rstandard(<model>, type="conditional") also computes conditional residuals, but I have not yet implemented this for 'rma.mv' models. But you can get these manually as follows:

dat$`Paper/PubID` <- paste0(dat$Paper, "/", dat$PubID)
re <- ranef(m.rma)
Res.rma <- dat$Y - (fitted(m.rma) +
re$`Paper`$intrcpt[match(dat$`Paper`, row.names(re$Paper))] + 
re$`Paper/PubID`$intrcpt[match(dat$`Paper/PubID`, row.names(re$`Paper/PubID`))])
head(Res.rma)

The minor differences arise due to slightly different parameter estimates, but that can be ignored.

If you install the 'devel' version, you can do the slightly simpler:

re <- ranef(m.rma, expand=TRUE)
Res.rma <- dat$Y - (fitted(m.rma) + re$`Paper`$intrcpt + re$`Paper/PubID`$intrcpt)
head(Res.rma)

(note that the 'expand' argument is not currently documented).

Best,
Wolfgang