# Regression Iteration

Dear All,

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)

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"),
Year = c(2000L, 2001L, 2002L, 2003L, 2004L, 2005L, 2006L,
2007L, 2008L, 2009L, 2010L, 2011L, 2012L, 2013L, 2014L, 2015L,
2016L, 2017L, 2018L, 2019L, 2000L, 2001L, 2002L, 2003L, 2004L,
2005L, 2006L, 2007L, 2008L, 2009L, 2010L, 2011L, 2012L, 2013L,
2014L, 2015L, 2016L, 2017L, 2018L, 2019L, 2000L, 2001L, 2002L,
2003L, 2004L, 2005L, 2006L, 2007L, 2008L, 2009L, 2010L, 2011L,
2012L, 2013L, 2014L, 2015L, 2016L, 2017L, 2018L, 2019L, 2000L,
2001L, 2002L, 2003L, 2004L, 2005L, 2006L, 2007L, 2008L, 2009L,
2010L, 2011L, 2012L, 2013L, 2014L, 2015L, 2016L, 2017L, 2018L,
2019L, 2000L, 2001L, 2002L, 2003L, 2004L, 2005L, 2006L, 2007L,
2008L, 2009L, 2010L, 2011L, 2012L, 2013L, 2014L, 2015L, 2016L,
2017L, 2018L, 2019L, 2000L, 2001L, 2002L, 2003L, 2004L, 2005L,
2006L, 2007L, 2008L, 2009L, 2010L, 2011L, 2012L, 2013L, 2014L,
2015L, 2016L, 2017L, 2018L, 2019L, 2000L, 2001L, 2002L, 2003L,
2004L, 2005L, 2006L, 2007L, 2008L, 2009L, 2010L, 2011L, 2012L,
2013L, 2014L, 2015L, 2016L, 2017L, 2018L, 2019L, 2000L, 2001L,
2002L, 2003L, 2004L, 2005L, 2006L, 2007L, 2008L, 2009L, 2010L,
2011L, 2012L, 2013L, 2014L, 2015L, 2016L, 2017L, 2018L, 2019L,
2000L, 2001L, 2002L, 2003L, 2004L, 2005L, 2006L, 2007L, 2008L,
2009L, 2010L, 2011L, 2012L, 2013L, 2014L, 2015L, 2016L, 2017L,
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,
0.018774, 0.035449, 0.021988, 0.02396, 0.011415, 0.010358,
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0.031157, 0.023387, 0.024198, 0.035353, 0.053873, 0.038743,
0.042338, 0.034935, 0.015377, 0.010599, 0.015154, 0.002919,
0.024291, 0.043819, 0.015901, 0.01897, 0.027767, 0.015992,
0.041976, 0.011223, 0.006144, 0.000778, 0.005873, 0.007194,
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-0.008816, 0.011466, 0.020956, 0.021873, 0.021772, 0.024495,
0.021354, 0.015267, 0.018769, 0.016904), C = c(0.75345, 0.70657,
0.645051, 0.510055, 0.433786, 0.35728, 0.265817, 0.208721,
0.163261, 0.130248, 0.136607, 0.153873, 0.152275, 0.166592,
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0.138383, 0.13023, 0.141247, 0.146088, 0.119133, 0.100396,
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0.639942, 0.655222, 0.729901, 0.823816, 0.79801, 0.811354,
0.787169, 0.756694, 0.72207, 0.692768, 0.651024, 0.617801
), B = c(0.147502302, 0.043680673, -0.212478849, -0.266834333,
-0.228099071, -0.199890362, -0.968175801, 1.047500546, 1.273127656,
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0.975483583, 0.983073825, 0.988745617, 1, 1.005225593, 1.010468623,
1.020086873, 1.032605559)), class = "data.frame", row.names = c(NA,
-200L))

``````

Thank you

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.

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

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!

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

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)

Thank you so much @HanOostdijk. Appreciated

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