Is there a predict function for PLM in R?

Question

I have a small N large T panel which I am estimating via plm (panel linear regression model), with fixed effects.

Is there any way to get predicted values for a new dataset? (I want to estimate parameters on a subset of my sample, and then use these to calculate model-implied values for the whole sample).

Thanks!

Answer 1

There are (at least) two methods in the package to produce estimates from plm objects:

-- fixef.plm: Extract the Fixed Effects

-- pmodel.response: A function to extract the model.response

It appears to me that the author(s) are not interested in providing estimates for the "random effects". It may be a matter of "if you don't know how to do it on your own, then we don't want to give you a sharp knife to cut yourself too deeply."

Answer 2

I wrote a function called predict.out.plm that can create predictions for the original data and for a manipulated data set (with equal column names).

The predict.out.plm calculates a) the predicted (fitted) outcome of the transformed data and b) constructs the according to level outcome. The function works for First Difference (FD) estimations and Fixed Effects (FE) estimations using plm. For FD it creates the differenced outcome over time and for FE it creates the time-demeaned outcome.

The function is largely untested, and probably only works with strongly balanced data frames.

Any suggestions and corrections are very welcome. Help to develop a small R package would be very appreciated.

The function predict.out.plm

predict.out.plm<-function(
  estimate,
  formula,
  data,
  model="fd",
  pname="y",
  pindex=NULL,
  levelconstr=T
){
  # estimate=e.fe
  # formula=f
  # data=d
  # model="within"
  # pname="y"
  # pindex=NULL
  # levelconstr=T
  #get index of panel data
  if (is.null(pindex) && class(data)[1]=="pdata.frame") {
    pindex<-names(attributes(data)$index)
  } else {
    pindex<-names(data)[1:2]
  }
  if (class(data)[1]!="pdata.frame") { 
    data<-pdata.frame(data)
  }
  #model frame
  mf<-model.frame(formula,data=data)
  #model matrix - transformed data
  mn<-model.matrix(formula,mf,model)

  #define variable names
  y.t.hat<-paste0(pname,".t.hat")
  y.l.hat<-paste0(pname,".l.hat")
  y.l<-names(mf)[1]

  #transformed data of explanatory variables 
  #exclude variables that were droped in estimation
  n<-names(estimate$aliased[estimate$aliased==F])
  i<-match(n,colnames(mn))
  X<-mn[,i]

  #predict transformed outcome with X * beta
  # p<- X %*% coef(estimate)
  p<-crossprod(t(X),coef(estimate))
  colnames(p)<-y.t.hat

  if (levelconstr==T){
    #old dataset with original outcome
    od<-data.frame(
      attributes(mf)$index,
      data.frame(mf)[,1]
    )
    rownames(od)<-rownames(mf) #preserve row names from model.frame
    names(od)[3]<-y.l

    #merge old dataset with prediciton
    nd<-merge(
      od,
      p,
      by="row.names",
      all.x=T,
      sort=F
    )
    nd$Row.names<-as.integer(nd$Row.names)
    nd<-nd[order(nd$Row.names),]

    #construct predicted level outcome for FD estiamtions
    if (model=="fd"){
      #first observation from real data
      i<-which(is.na(nd[,y.t.hat]))
      nd[i,y.l.hat]<-NA
      nd[i,y.l.hat]<-nd[i,y.l]
      #fill values over all years
      ylist<-unique(nd[,pindex[2]])[-1]
      ylist<-as.integer(as.character(ylist))
      for (y in ylist){
        nd[nd[,pindex[2]]==y,y.l.hat]<-
          nd[nd[,pindex[2]]==(y-1),y.l.hat] + 
          nd[nd[,pindex[2]]==y,y.t.hat]
      }
    } 
    if (model=="within"){
      #group means of outcome
      gm<-aggregate(nd[, pname], list(nd[,pindex[1]]), mean)
      gl<-aggregate(nd[, pname], list(nd[,pindex[1]]), length)
      nd<-cbind(nd,groupmeans=rep(gm$x,gl$x))
      #predicted values + group means
      nd[,y.l.hat]<-nd[,y.t.hat] + nd[,"groupmeans"]
    } 
    if (model!="fd" && model!="within") {
      stop('funciton works only for FD and FE estimations')
    }
  }
  #results
  results<-p
  if (levelconstr==T){
    results<-list(results,nd)
    names(results)<-c("p","df")
  }
  return(results)
}

Testing the the function:

##packages
library(plm)

##test dataframe
#data structure
N<-4
G<-2
M<-5
d<-data.frame(
  id=rep(1:N,each=M),
  year=rep(1:M,N)+2000,
  gid=rep(1:G,each=M*2)
)
#explanatory variable
d[,"x"]=runif(N*M,0,1)
#outcome
d[,"y"] = 2 * d[,"x"] + runif(N*M,0,1)
#panel data frame
d<-pdata.frame(d,index=c("id","year"))

##new data frame for out of sample prediction
dn<-d
dn$x<-rnorm(nrow(dn),0,2)

##estimate
#formula
f<- pFormula(y ~ x + factor(year))
#fixed effects or first difffernce estimation
e<-plm(f,data=d,model="within",index=c("id","year"))
e<-plm(f,data=d,model="fd",index=c("id","year"))
summary(e)

##fitted values of estimation
#transformed outcome prediction 
predict(e)
c(pmodel.response(e)-residuals(e))
predict.out.plm(e,f,d,"fd")$p
# "level" outcome prediciton 
predict.out.plm(e,f,d,"fd")$df$y.l.hat
#both
predict.out.plm(e,f,d,"fd")

##out of sampel prediciton 
predict(e,newdata=d) 
predict(e,newdata=dn) 
# Error in crossprod(beta, t(X)) : non-conformable arguments
# if plm omits variables specified in the formula (e.g. one year in factor(year))
# it tries to multiply two matrices with different length of columns than regressors
# the new funciton avoids this and therefore is able to do out of sample predicitons
predict.out.plm(e,f,dn,"fd")

Answer 3

plm has now a predict.plm() function, although it is not documented/exported.

Note also that predict works on the transformed model (i.e. after doing the within/between/fd transformation), not the original one. I speculate that the reason for this is that it is more difficult to do prediction in a panel data framework. Indeed, you need to consider whether you are predicting:

• new time periods, for existing individual and you used a individual-FE? Then you can add the prediction to the existing individual mean
• new time periods, for new individual? Then you need to figure out which individual mean you are going to use?
• the same is even more complicated is you use a random-effect model, as the effects are not easily derived

In the code below, I illustrate how to use fitted values, on the existing sample:

library(plm)
#> Loading required package: Formula
library(tidyverse)

data("Produc", package = "plm")
zz <- plm(log(gsp) ~ log(pcap) + log(pc) + log(emp) + unemp,
          data = Produc, index = c("state","year"))


## produce a dataset of prediction, added to the group means
Produc_means <- Produc %>% 
  mutate(y = log(gsp)) %>% 
  group_by(state) %>% 
  transmute(y_mean = mean(y),
            y = y, 
            year = year) %>% 
  ungroup() %>% 
  mutate(y_pred = predict(zz) + y_mean) %>% 
  select(-y_mean)

## plot it
Produc_means %>% 
  gather(type, value, y, y_pred) %>% 
  filter(state %in% toupper(state.name[1:5])) %>% 
  ggplot(aes(x = year, y = value, linetype = type))+
  geom_line() +
  facet_wrap(~state) +
  ggtitle("Visualising in-sample prediction, for 4 states")
#> Warning: attributes are not identical across measure variables;
#> they will be dropped

^{Created on 2018-11-20 by the reprex package (v0.2.1)}

Answer 4

Looks like there is a new package to do in-sample predictions for a variety of models including plm

https://cran.r-project.org/web/packages/prediction/prediction.pdf

Answer 5

You can calculate the residuals via residuals(reg_name). From here, you can subtract them from your response variable and get the predicted values.