Regression Iteration

Benny.owusuk · September 11, 2021, 1:01pm

Dear All,

Please I need support
I run a panel estimation (penalized spline fixed effects model), however there exist some form of serial correlation in the residuals (AR1 process). I am therefore using Cochrane-Orcutt style to transform my residuals to correct for serial correlation.
I have done this manually, however I need to iterate to get a consistent value of rho in my code below. I am a bit deficient regarding writing of functions for iteration. Below is my code and some explanation about what exactly I want to do.

Firstly, I estimate the panel model. Variables wrapped in parenthesis are non parametric. After estimating the model, I recovered the residuals and regressed over the lagged residuals (regression of AR1 process) using ols

library(plm)
library( Matrix)
library(nlme)
library(mgcv)
library(splines)


Raw_data <- read.csv("C:/Users/Benny/OneDrive/Documents/R/DataSet.csv", header = TRUE)
PanelS <- pdata.frame(Raw_data, index=c("Country","Year"))

mod1 <- pam(A ~  B + sfe(C) + D,  data = PanelS)

res_1 <-  ts((mod1$residuals))
res_Lag <- lag(res_1, -1)

lagdata1 <- ts.intersect(res_1, res_Lag)
rho_1 <- coef(lm(res_1 ~ res_Lag -1, data = lagdata1 )) # coefficient of regressing residual over lagged residual using ols

## Tranforming the variables with rho_1
A_bar = PanelS$A - rho_1*(lag( PanelS$A))
B_bar= PanelS$B - rho_1*(lag( PanelS$B))
C_bar= PanelS$C- rho_1*(lag( PanelS$C))
D_bar= PanelS$C- rho_1*(lag( PanelS$D))
PanelS1 <- pdata.frame(data.frame(cbind(PanelS$Country, PanelS$Year, A_bar,B_bar,C_bar, D_bar)), index=c("V1","V2"))

After transforming the variables with rho_1, I proceed to estimate model_2

mod_2 <- pam(A_bar ~ B_bar + sfe(C_bar)+ D_bar,data = PanelS1)

res_2 <- ts((mod_2$residuals))
resLag2 <- lag(res_2, -1)
lagdata2 <- ts.intersect(res_2, resLag2)
rho_2 <- coef(lm(res_2 ~ resLag2 -1, data = lagdata2 ))  #coefficient of regressing residual over lagged residual

## Tranforming the variables with rho_2
A_bar = PanelS$A - rho_2*(lag( PanelS$A))
B_bar= PanelS$B - rho_2*(lag( PanelS$B))
C_bar= PanelS$C- rho_2*(lag( PanelS$C))

PanelS2<- pdata.frame(data.frame(cbind(PanelS$Country, PanelS$Year, A_bar,B_bar,C_bar, D_bar)), index=c("V1","V2"))

mod_3 <- pam(A_bar ~ B_bar + sfe(C_bar)+ D_bar,data = PanelS2)

res_3 <- ts((mod_3$residuals))
resLag3 <- lag(res_3, -1)
lagdata3 <- ts.intersect(res_2, resLag2)
rho_3 <- coef(lm(res_3 ~ resLag3 -1, data = lagdata3 ))
rho_3

Now I am doing this until rho_3 converges (or rho_3 is equal to rho_2 )- so iteration until the rho value gets equal to the previous rho_value.
I would appreciate if someone can help me with a function to iterate until convergence.

Below is the panel data

structure(list(Country = c("CountryA", "CountryA", "CountryA", 
"CountryA", "CountryA", "CountryA", "CountryA", "CountryA", "CountryA", 
"CountryA", "CountryA", "CountryA", "CountryA", "CountryA", "CountryA", 
"CountryA", "CountryA", "CountryA", "CountryA", "CountryA", "CountryB", 
"CountryB", "CountryB", "CountryB", "CountryB", "CountryB", "CountryB", 
"CountryB", "CountryB", "CountryB", "CountryB", "CountryB", "CountryB", 
"CountryB", "CountryB", "CountryB", "CountryB", "CountryB", "CountryB", 
"CountryB", "CountryC", "CountryC", "CountryC", "CountryC", "CountryC", 
"CountryC", "CountryC", "CountryC", "CountryC", "CountryC", "CountryC", 
"CountryC", "CountryC", "CountryC", "CountryC", "CountryC", "CountryC", 
"CountryC", "CountryC", "CountryC", "CountryD", "CountryD", "CountryD", 
"CountryD", "CountryD", "CountryD", "CountryD", "CountryD", "CountryD", 
"CountryD", "CountryD", "CountryD", "CountryD", "CountryD", "CountryD", 
"CountryD", "CountryD", "CountryD", "CountryD", "CountryD", "CountryE", 
"CountryE", "CountryE", "CountryE", "CountryE", "CountryE", "CountryE", 
"CountryE", "CountryE", "CountryE", "CountryE", "CountryE", "CountryE", 
"CountryE", "CountryE", "CountryE", "CountryE", "CountryE", "CountryE", 
"CountryE", "CountryF", "CountryF", "CountryF", "CountryF", "CountryF", 
"CountryF", "CountryF", "CountryF", "CountryF", "CountryF", "CountryF", 
"CountryF", "CountryF", "CountryF", "CountryF", "CountryF", "CountryF", 
"CountryF", "CountryF", "CountryF", "CountryG", "CountryG", "CountryG", 
"CountryG", "CountryG", "CountryG", "CountryG", "CountryG", "CountryG", 
"CountryG", "CountryG", "CountryG", "CountryG", "CountryG", "CountryG", 
"CountryG", "CountryG", "CountryG", "CountryG", "CountryG", "CountryH", 
"CountryH", "CountryH", "CountryH", "CountryH", "CountryH", "CountryH", 
"CountryH", "CountryH", "CountryH", "CountryH", "CountryH", "CountryH", 
"CountryH", "CountryH", "CountryH", "CountryH", "CountryH", "CountryH", 
"CountryH", "CountryI", "CountryI", "CountryI", "CountryI", "CountryI", 
"CountryI", "CountryI", "CountryI", "CountryI", "CountryI", "CountryI", 
"CountryI", "CountryI", "CountryI", "CountryI", "CountryI", "CountryI", 
"CountryI", "CountryI", "CountryI", "CountryJ", "CountryJ", "CountryJ", 
"CountryJ", "CountryJ", "CountryJ", "CountryJ", "CountryJ", "CountryJ", 
"CountryJ", "CountryJ", "CountryJ", "CountryJ", "CountryJ", "CountryJ", 
"CountryJ", "CountryJ", "CountryJ", "CountryJ", "CountryJ"), 
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    2018L, 2019L, 2000L, 2001L, 2002L, 2003L, 2004L, 2005L, 2006L, 
    2007L, 2008L, 2009L, 2010L, 2011L, 2012L, 2013L, 2014L, 2015L, 
    2016L, 2017L, 2018L, 2019L), A = c(0.051539, 0.064525, 0.014292, 
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-200L))

Thank you

HanOostdijk · September 13, 2021, 11:51am

Please provide a reprex. Without it, it is not clear to me which packages you use.

It is also not clear to me if you have actually run part of this code:
did a construct such as mod_3 <- pam(A_bar ~ B_bar + sfe(C_bar)data = PanelS1) actually run without errors ?

And not knowing anything about your subject I would think that mod_3 would be derived from PanelS2.
And res_2 is derived from mod1 ???
I think (but could be wrong) that these are errors that can be avoided by presenting code that has actually run.
At this moment I can not help you any further than suggesting that you pack the repeating parts of code in a function that returns in a list of data.frame all the elements that you need for the ongoing calculation.

Benny.owusuk · September 13, 2021, 9:26pm

Dear @HanOostdijk , I have made the necessary corrections and provided the datasets as well. Thank you and looking forward to your support

HanOostdijk · September 14, 2021, 8:03am

I can not run your code:

Error in pam(A ~ B + sfe(C) + D, data = PanelS) :
could not find function "pam"

I tried

library(cluster)

but then got the following error

Error in pam(A ~ B + sfe(C) + D, data = PanelS) :
unused argument (data = PanelS)

Can you indicate where the pam function comes from?

Edit: and the same goes for the sfe function (same package?)
Once again this proves the usefulness of a reprex!

Benny.owusuk · September 14, 2021, 3:56pm

Hallo @HanOostdijk ,

pam is from R pamfe package which can be downloaded from the link below (same for sfe)

GitHub - peterpuetz2020/pamfe: R Package pamfe: Semiparametric Regression for Fixed Effects Panel Data Models with Simultaneous Confidence Bands

Thank you for the support

HanOostdijk · September 14, 2021, 6:42pm

I hope that the code below helps you in some way.
I removed from the code the definition of your input.
I also removed the warnings except the first one.
Your handling of one step in the iteration process I do in the function step .
To let it work over the iterations I made some changes at the point where PanelS1 is created.
And the result of the function is the updated panel and the rho (combined in a list)
The iterations are driven in the function iter.

I don't know what your stopping criteria would be. I chose a difference of less than 0.01 for the rho compared with the previous value and I stop when the number of iterations reaches max_step.
Of course with each iteration a time-point is lost, but the impact of that is out of my scope.

library(plm)
library(Matrix)
library(nlme)
library(mgcv)
#> This is mgcv 1.8-36. For overview type 'help("mgcv-package")'.
library(splines)
# devtools::install_github("peterpuetz2020/pamfe")
library(pamfe)  

# Raw_data definition removed

PanelS <- pdata.frame(Raw_data, index = c("Country", "Year"))

step <- function(PanelS) {
  mod1 <- pam(A ~  B + sfe(C) + D,  data = PanelS)
  
  res_1 <-  ts((mod1$residuals))
  res_Lag <- lag(res_1,-1)
  
  lagdata1 <- ts.intersect(res_1, res_Lag)
  rho_1 <-
    coef(lm(res_1 ~ res_Lag - 1, data = lagdata1)) # coefficient of regressing residual over lagged residual using ols
  
  ## Tranforming the variables with rho_1
  A_bar = PanelS$A - rho_1 * (lag(PanelS$A))
  B_bar = PanelS$B - rho_1 * (lag(PanelS$B))
  C_bar = PanelS$C - rho_1 * (lag(PanelS$C))
  D_bar = PanelS$C - rho_1 * (lag(PanelS$D))
  PanelS1 <-
    pdata.frame(data.frame(
      cbind(
        Country = PanelS$Country,
        Year = PanelS$Year,
        A = A_bar,
        B = B_bar,
        C = C_bar,
        D = D_bar
      )
    ),
    index = c("Country", "Year"))
  list(panel = PanelS1, rho = rho_1)
}

iter <- function(initial_panel,
                 max_step = 10 ,
                 max_diff = 1e-2) {
  res <- step(initial_panel)
  for (i in 1:max_step) {
    rho_0 <- res$rho
    cat("iteration ",sprintf("%3.0f",i-1)," rho ",sprintf("%11.8f",rho_0),"\n")
    res   <- step(res$panel)
    if (abs(res$rho - rho_0) < max_diff) {
      break
    }
  }
  cat("\nfinal rho           ",sprintf("%11.8f",res$rho),"\n")
  res$panel
}

PanelF <- iter(PanelS,max_step= 50,max_diff = 1e-2)
#> Warning: class 'pFormula' is deprecated, simply use class 'Formula'
Following similar warnings are removed
#> iteration    0  rho   0.58793314
#> iteration    1  rho   0.00236060
#> iteration    2  rho   0.01748666
#> iteration    3  rho  -0.02243658
#> iteration    4  rho  -0.03837618
#> iteration    5  rho   0.09225147
#> iteration    6  rho  -0.06636908
#> iteration    7  rho  -0.00593040
#> iteration    8  rho   0.08955411
#> iteration    9  rho   0.04562646
#> iteration   10  rho  -0.21484503
#> iteration   11  rho  -0.05549444
#> iteration   12  rho   0.01794597
#> iteration   13  rho   0.00284733
#> iteration   14  rho   0.18932160
#> iteration   15  rho   0.07687804
#> iteration   16  rho   0.00121799
#> 
#> final rho             0.00538761

^{Created on 2021-09-14 by the reprex package (v2.0.0)}

Benny.owusuk · September 14, 2021, 8:08pm

Thank you so much @HanOostdijk. Appreciated

system · September 21, 2021, 8:09pm

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