using predict with a list of lm() objects - r

Question

I have data which I regularly run regressions on. Each "chunk" of data gets fit a different regression. Each state, for example, might have a different function that explains the dependent value. This seems like a typical "split-apply-combine" type of problem so I'm using the plyr package. I can easily create a list of lm() objects which works well. However I can't quite wrap my head around how I use those objects later to predict values in a separate data.frame.
Here's a totally contrived example illustrating what I'm trying to do:
# setting up some fake data
set.seed(1)
funct <- function(myState, myYear){
rnorm(1, 100, 500) + myState + (100 * myYear)
}
state <- 50:60
year <- 10:40
myData <- expand.grid( year, state)
names(myData) <- c("year","state")
myData$value <- apply(myData, 1, function(x) funct(x[2], x[1]))
## ok, done with the fake data generation.
require(plyr)
modelList <- dlply(myData, "state", function(x) lm(value ~ year, data=x))
## if you want to see the summaries of the lm() do this:
# lapply(modelList, summary)
state <- 50:60
year <- 50:60
newData <- expand.grid( year, state)
names(newData) <- c("year","state")
## now how do I predict the values for newData$value
# using the regressions in modelList?
So how do I use the lm() objects contained in modelList to predict values using the year and state independent values from newData?

Answer 1

Here's my attempt:
predNaughty <- ddply(newData, "state", transform,
value=predict(modelList[[paste(piece$state[1])]], newdata=piece))
head(predNaughty)
# year state value
# 1 50 50 5176.326
# 2 51 50 5274.907
# 3 52 50 5373.487
# 4 53 50 5472.068
# 5 54 50 5570.649
# 6 55 50 5669.229
predDiggsApproved <- ddply(newData, "state", function(x)
transform(x, value=predict(modelList[[paste(x$state[1])]], newdata=x)))
head(predDiggsApproved)
# year state value
# 1 50 50 5176.326
# 2 51 50 5274.907
# 3 52 50 5373.487
# 4 53 50 5472.068
# 5 54 50 5570.649
# 6 55 50 5669.229
JD Long edit
I was inspired enough to work out an adply() option:
pred3 <- adply(newData, 1, function(x)
predict(modelList[[paste(x$state)]], newdata=x))
head(pred3)
# year state 1
# 1 50 50 5176.326
# 2 51 50 5274.907
# 3 52 50 5373.487
# 4 53 50 5472.068
# 5 54 50 5570.649
# 6 55 50 5669.229

Answer 2

You need to use mdply to supply both the model and the data to each function call:
dataList <- dlply(newData, "state")
preds <- mdply(cbind(mod = modelList, df = dataList), function(mod, df) {
mutate(df, pred = predict(mod, newdata = df))
})

Answer 3

A solution with just base R. The format of the output is different, but all the values are right there.
models <- lapply(split(myData, myData$state), 'lm', formula = value ~ year)
pred4 <- mapply('predict', models, split(newData, newData$state))

Answer 4

What is wrong with
lapply(modelList, predict, newData)
?
EDIT:
Thanks for explaining what is wrong with that. How about:
newData <- data.frame(year)
ldply(modelList, function(model) {
data.frame(newData, predict=predict(model, newData))
})
Iterate over the models, and apply the new data (which is the same for each state since you just did an expand.grid to create it).
EDIT 2:
If newData does not have the same values for year for every state as in the example, a more general approach can be used. Note that this uses the original definition of newData, not the one in the first edit.
ldply(state, function(s) {
nd <- newData[newData$state==s,]
data.frame(nd, predict=predict(modelList[[as.character(s)]], nd))
})
First 15 lines of this output:
year state predict
1 50 50 5176.326
2 51 50 5274.907
3 52 50 5373.487
4 53 50 5472.068
5 54 50 5570.649
6 55 50 5669.229
7 56 50 5767.810
8 57 50 5866.390
9 58 50 5964.971
10 59 50 6063.551
11 60 50 6162.132
12 50 51 5514.825
13 51 51 5626.160
14 52 51 5737.496
15 53 51 5848.832

Answer 5

I take it the hard part is matching each state in newData to the corresponding model.
Something like this perhaps?
predList <- dlply(newData, "state", function(x) {
predict(modelList[[as.character(min(x$state))]], x)
})
Here I used a "hacky" way of extracting the corresponding state model: as.character(min(x$state))
...There is probably a better way?
Output:
> predList[1:2]
$`50`
1 2 3 4 5 6 7 8 9 10 11
5176.326 5274.907 5373.487 5472.068 5570.649 5669.229 5767.810 5866.390 5964.971 6063.551 6162.132
$`51`
12 13 14 15 16 17 18 19 20 21 22
5514.825 5626.160 5737.496 5848.832 5960.167 6071.503 6182.838 6294.174 6405.510 6516.845 6628.181
Or, if you want a data.frame as output:
predData <- ddply(newData, "state", function(x) {
y <-predict(modelList[[as.character(min(x$state))]], x)
data.frame(id=names(y), value=c(y))
})
Output:
head(predData)
state id value
1 50 1 5176.326
2 50 2 5274.907
3 50 3 5373.487
4 50 4 5472.068
5 50 5 5570.649
6 50 6 5669.229

Answer 6

Maybe I'm missing something, but I believe lmList is the ideal tool here,
library(nlme)
ll = lmList(value ~ year | state, data=myData)
predict(ll, newData)
## Or, to show that it produces the same results as the other proposed methods...
newData[["value"]] <- predict(ll, newData)
head(newData)
# year state value
# 1 50 50 5176.326
# 2 51 50 5274.907
# 3 52 50 5373.487
# 4 53 50 5472.068
# 5 54 50 5570.649
# 6 55 50 5669.229