Extracting coefficients and their standard error for each unit in an lme model fit

Question

How could I extract coefficients (b0 and b1) with their respectively standard errors for each experimental unit (plot )in a linear mixed model such as this one:

Better fits for a linear model

with this same dataset(df), and for the fitted model (fitL1): how could I get a data frame as this one...

   plot    b0      b0_se   b1    b1_se 
    1    2898.69   53.85   -7.5  4.3

   ...    ...       ...     ...   ...

Answer 1

The first comment is that this is actually a non-trivial theoretical question: there is a rather long thread on r-sig-mixed-models that goes into some of the technical details; you should definitely have a look, even though it gets a bit scary. The basic issue is that the estimated coefficient values for each group are the sum of the fixed-effect parameter and the BLUP/conditional mode for that group, which are different classes of objects (one is a parameter, one is a conditional mean of a random variable), which creates some technical difficulties.

The second point is that (unfortunately) I don't know of an easy way to do this in lme, so my answer uses lmer (from the lme4 package).

If you are comfortable doing the easiest thing and ignoring the (possibly ill-defined) covariance between the fixed-effect parameters and the BLUPs, you can use the code below.

Two alternatives would be (1) to fit your model with a Bayesian hierarchical approach (e.g. the MCMCglmm package) and compute the standard deviations of the posterior predictions for each level (2) use parametric bootstrapping to compute the BLUPs/conditional modes, then take the standard deviations of the bootstrap distributions.

Please remember that as usual this advice comes with no warranty.

library(lme4)
fm1 <- lmer(Reaction ~ Days + (Days | Subject), sleepstudy)
cc <- coef(fm1)$Subject
## variances of fixed effects
fixed.vars <- diag(vcov(fm1))
## extract variances of conditional modes
r1 <- ranef(fm1,condVar=TRUE)
cmode.vars <- t(apply(cv <- attr(r1[[1]],"postVar"),3,diag))
seVals <- sqrt(sweep(cmode.vars,2,fixed.vars,"+"))
res <- cbind(cc,seVals)
res2 <- setNames(res[,c(1,3,2,4)],
                 c("int","int_se","slope","slope_se"))
##          int   int_se     slope slope_se
## 308 253.6637 13.86649 19.666258   2.7752
## 309 211.0065 13.86649  1.847583   2.7752
## 310 212.4449 13.86649  5.018406   2.7752
## 330 275.0956 13.86649  5.652955   2.7752
## 331 273.6653 13.86649  7.397391   2.7752
## 332 260.4446 13.86649 10.195115   2.7752

Answer 2

To get you partway there using nlme...

You can pull the components of summary() using:

summary(fitL1)$tTable[,1] #fixed-effect parameter estimates
summary(fitL1)$tTable[,2] #fixed-effect parameter standard errors

etc.

You can further subset those by rows:

summary(fitL1)$tTable[1,1] #the first fixed-effect parameter estimate
summary(fitL1)$tTable[1,2] #the first fixed-effect parameter standard error

to extract individual parameters or standard errors and combine them into a data frame using, for example:

df<-data.frame(cbind(summary(fitL1)$tTable[1,1], summary(fitL1)$tTable[1,2]))
names(df)<-c("Estimate","SE")
df

To adjust these parameters for each plot (the random effect, I presume), you can pull the random coefficients with:

fitL1$coefficients$random

and add them to the parameter estimates (B0 (intercept), B1, etc.). However, I am not sure how the standard errors should be adjusted for each plot.