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Liviu Andronic

2010-Mar-16 22:24 UTC

[R] plm "within" models: is the correct F-statistic reported?

Dear R users
I get different F-statistic results for a "within" model, when using
"time" or "twoways" effects in plm() [1] and when manually
specifying
the time control dummies [2].
[1] vignette("plm")
[2] http://cran.r-project.org/doc/contrib/Farnsworth-EconometricsInR.pdf

Two examples below:
library("AER")
data("Grunfeld", package = "AER")
library("plm")
gr <- subset(Grunfeld, firm %in% c("General Electric",
  "General Motors", "IBM"))
pgr <- plm.data(gr, index = c("firm",
"year"))> dim(pgr)[1] 60  5


## the first example is actually on "individual"
effects> gr_fe <- plm(invest ~ value + capital, data = pgr,+  model = "within",
effect="individual")> summary(gr_fe)Oneway (individual) effect Within Model

Call:
plm(formula = invest ~ value + capital, data = pgr, effect =
"individual",
    model = "within")

Balanced Panel: n=3, T=20, N=60

Residuals :
   Min. 1st Qu.  Median 3rd Qu.    Max.
-167.00  -26.10    2.09   26.80  202.00

Coefficients :
        Estimate Std. Error t-value    Pr(>|t|)
value     0.1049     0.0163    6.42 0.000000033 ***
capital   0.3453     0.0244   14.16     < 2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05
'.' 0.1 ' ' 1

Total Sum of Squares:    1890000
Residual Sum of Squares: 244000
F-statistic: 185.407 on 2 and 55 DF, p-value: <2e-16> summary(fixef(gr_fe))                 Estimate Std. Error t-value Pr(>|t|)
General Motors      -70.6       67.8   -1.04     0.30
General Electric   -239.6       32.8   -7.29    3e-13 ***
IBM                 -24.6       16.2   -1.52     0.13
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05
'.' 0.1 ' ' 1> gr_lm <- lm(invest ~ 0+value + capital + firm, data = pgr)
> summary(gr_lm)
Call:
lm(formula = invest ~ 0 + value + capital + firm, data = pgr)

Residuals:
    Min      1Q  Median      3Q     Max
-167.33  -26.14    2.09   26.84  201.68

Coefficients:
                      Estimate Std. Error t value     Pr(>|t|)
value                   0.1049     0.0163    6.42 0.0000000330 ***
capital                 0.3453     0.0244   14.16      < 2e-16 ***
firmGeneral Motors    -70.5629    67.8196   -1.04         0.30
firmGeneral Electric -239.5560    32.8400   -7.29 0.0000000012 ***
firmIBM               -24.6480    16.1726   -1.52         0.13
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05
'.' 0.1 ' ' 1

Residual standard error: 66.6 on 55 degrees of freedom
Multiple R-squared: 0.974,	Adjusted R-squared: 0.972
F-statistic:  420 on 5 and 55 DF,  p-value: <2e-16

In the first case, plm(..., effect="individual"), F-statistic: 185.407
and in the second F-statistic:  420, while all other regression
coefficients and standard errors are the same. Which F-statistic
should be considered?


## A second example with "twoways" effects> gr_fe1 <- plm(invest ~ value + capital, data = pgr,+   model = "within",
effect="twoways")> summary(gr_fe1)Twoways effects Within Model

Call:
plm(formula = invest ~ value + capital, data = pgr, effect =
"twoways",
    model = "within")

Balanced Panel: n=3, T=20, N=60

Residuals :
   Min. 1st Qu.  Median 3rd Qu.    Max.
-153.00  -29.10    2.23   34.80  125.00

Coefficients :
        Estimate Std. Error t-value Pr(>|t|)
value     0.1295     0.0224    5.77  1.4e-06 ***
capital   0.4184     0.0353   11.85  5.5e-14 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05
'.' 0.1 ' ' 1

Total Sum of Squares:    957000
Residual Sum of Squares: 138000
F-statistic: 107.246 on 2 and 36 DF, p-value: 6.84e-16> #summary(fixef(gr_fe1, "time"))
> gr_fe2 <- plm(invest ~ value + capital + year, data = pgr,+   model = "within",
effect="individual")> summary(gr_fe2)Oneway (individual) effect Within Model

Call:
plm(formula = invest ~ value + capital + year, data = pgr, effect
"individual",
    model = "within")

Balanced Panel: n=3, T=20, N=60

Residuals :
   Min. 1st Qu.  Median 3rd Qu.    Max.
-153.00  -29.10    2.23   34.80  125.00

Coefficients :
              Estimate Std. Error t-value Pr(>|t|)
value           0.1295     0.0224    5.77  1.4e-06 ***
capital         0.4184     0.0353   11.85  5.5e-14 ***
year[T.1936]  -83.9625    53.6143   -1.57   0.1261
year[T.1937] -150.9206    58.3282   -2.59   0.0139 *
year[T.1938]  -81.2343    50.7175   -1.60   0.1180
year[T.1939] -137.4579    53.4385   -2.57   0.0144 *
year[T.1940]  -96.3584    53.9837   -1.78   0.0827 .
year[T.1941]  -56.5587    53.0089   -1.07   0.2931
year[T.1942]  -36.6539    50.9966   -0.72   0.4769
year[T.1943]  -78.0794    52.0249   -1.50   0.1421
year[T.1944]  -66.4725    52.5047   -1.27   0.2136
year[T.1945]  -89.5562    54.2876   -1.65   0.1077
year[T.1946]  -59.1147    55.3115   -1.07   0.2923
year[T.1947]  -87.5444    52.6530   -1.66   0.1051
year[T.1948] -119.9125    53.3167   -2.25   0.0307 *
year[T.1949] -167.9552    54.1999   -3.10   0.0038 **
year[T.1950] -172.7676    55.0212   -3.14   0.0034 **
year[T.1951] -191.1369    57.6114   -3.32   0.0021 **
year[T.1952] -195.4503    59.6377   -3.28   0.0023 **
year[T.1953] -174.6639    66.3451   -2.63   0.0124 *
year[T.1954] -181.1273    68.5794   -2.64   0.0121 *
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05
'.' 0.1 ' ' 1

Total Sum of Squares:    1890000
Residual Sum of Squares: 138000
F-statistic: 21.8327 on 21 and 36 DF, p-value: 1.32e-14

In the first case, F-statistic: 107.246 , while in the second
F-statistic: 21.8327. Again, which one is correct? Thank you
Liviu




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Achim Zeileis

2010-Mar-16 23:39 UTC

head link

[R] plm "within" models: is the correct F-statistic reported?

> Dear R users
> I get different F-statistic results for a "within" model, when
using
> "time" or "twoways" effects in plm() [1] and when
manually specifying
> the time control dummies [2].
> [1] vignette("plm")
> [2] http://cran.r-project.org/doc/contrib/Farnsworth-EconometricsInR.pdf
Well, the question is incomplete in a way. An F-statistic is always 
associated with testing a model against some restricted version of that 
model. And which restricted model is reasonable might vary with your 
application.

You used:

data("Grunfeld", package = "AER")
library("plm")
gr <- subset(Grunfeld, firm %in% c("General Electric",
"General Motors", "IBM"))
pgr <- plm.data(gr, index = c("firm", "year"))

and then considered

gr_fe <- plm(invest ~ value + capital, data = pgr, model =
"within",
   effect = "individual")

which you correctly pointed out is equivalent to

gr_lm <- lm(invest ~ 0 + value + capital + firm, data = pgr)

The difference between the two is that in "gr_fe" the model knows that
the
parameters of interest are "value" and "capital" and that
the
firm-specific intercepts are nuisance parameters (or at least of less 
importance than value/capital).

In "gr_lm" however, the fitted model does not know about that. It just
knows that you forced out the intercept (and doesn't check that a 
firm-specific intercept is in fact included).

Hence, when saying summary() different models with "no effects" are 
assumed. For gr_fe the model without effects just omits value/capital but 
keeps the firm-specific interecepts. For gr_lm not even the intercept is 
kept in the model. Thus:

gr_fe_null <- lm(invest ~ 0 + firm, data = pgr)
gr_lm_null <- lm(invest ~ 0, data = pgr)

Then, comparing the full model (gr_lm) against the different null models 
yields:

R> anova(gr_fe_null, gr_lm)
Analysis of Variance Table

Model 1: invest ~ 0 + firm
Model 2: invest ~ 0 + value + capital + firm
   Res.Df     RSS Df Sum of Sq      F    Pr(>F)
1     57 1888946
2     55  243985  2   1644961 185.41 < 2.2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05
'.' 0.1 ' ' 1
R> anova(gr_lm_null, gr_lm)
Analysis of Variance Table

Model 1: invest ~ 0
Model 2: invest ~ 0 + value + capital + firm
   Res.Df     RSS Df Sum of Sq      F    Pr(>F)
1     60 9553385
2     55  243985  5   9309400 419.71 < 2.2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05
'.' 0.1 ' ' 1
> In the first case, plm(..., effect="individual"), F-statistic:
185.407
> and in the second F-statistic:  420, while all other regression
> coefficients and standard errors are the same. Which F-statistic
> should be considered?
It depends what you want to test. But I doubt that the one reported in 
summary(gr_lm) tests a useful hypothesis/alternative.

Best,
Z

Liviu Andronic

2010-Mar-17 13:38 UTC

head link

[R] plm "within" models: is the correct F-statistic reported?

Dear Achim

On 3/16/10, Achim Zeileis <Achim.Zeileis at uibk.ac.at>
wrote:>  Hence, when saying summary() different models with "no effects"
are
> assumed. For gr_fe the model without effects just omits value/capital but
> keeps the firm-specific interecepts. For gr_lm not even the intercept is
> kept in the model. Thus:
>
>  gr_fe_null <- lm(invest ~ 0 + firm, data = pgr)
>  gr_lm_null <- lm(invest ~ 0, data = pgr)
>What would be the more useful "no effects" model in the plm(...,
effect="twoways") case? Considering the same setting,
library("AER")
data("Grunfeld", package = "AER")
library("plm")
gr <- subset(Grunfeld, firm %in% c("General Electric",
"General Motors", "IBM"))
pgr <- plm.data(gr, index = c("firm", "year"))

I am fitting a "twoways" model and an "individual" with
manually
specified time effects.> gr_fe1 <- plm(invest ~ value + capital, data = pgr,+    model = "within",
effect="twoways")> summary(gr_fe1)Twoways effects Within Model

Call:
plm(formula = invest ~ value + capital, data = pgr, effect =
"twoways",
    model = "within")

Balanced Panel: n=3, T=20, N=60

Residuals :
   Min. 1st Qu.  Median 3rd Qu.    Max.
-153.00  -29.10    2.23   34.80  125.00

Coefficients :
        Estimate Std. Error t-value Pr(>|t|)
value     0.1295     0.0224    5.77  1.4e-06 ***
capital   0.4184     0.0353   11.85  5.5e-14 ***
---
Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1

Total Sum of Squares:    957000
Residual Sum of Squares: 138000
F-statistic: 107.246 on 2 and 36 DF, p-value: 6.84e-16
>  gr_fe2 <- plm(invest ~ value + capital + year, data = pgr,+    model = "within",
effect="individual")>  summary(gr_fe2)Oneway (individual) effect Within Model

Call:
plm(formula = invest ~ value + capital + year, data = pgr, effect
"individual",
    model = "within")

Balanced Panel: n=3, T=20, N=60

Residuals :
   Min. 1st Qu.  Median 3rd Qu.    Max.
-153.00  -29.10    2.23   34.80  125.00

Coefficients :
          Estimate Std. Error t-value Pr(>|t|)
value       0.1295     0.0224    5.77  1.4e-06 ***
capital     0.4184     0.0353   11.85  5.5e-14 ***
year1936  -83.9625    53.6143   -1.57   0.1261
year1937 -150.9206    58.3282   -2.59   0.0139 *
year1938  -81.2343    50.7175   -1.60   0.1180
year1939 -137.4579    53.4385   -2.57   0.0144 *
year1940  -96.3584    53.9837   -1.78   0.0827 .
year1941  -56.5587    53.0089   -1.07   0.2931
year1942  -36.6539    50.9966   -0.72   0.4769
year1943  -78.0794    52.0249   -1.50   0.1421
year1944  -66.4725    52.5047   -1.27   0.2136
year1945  -89.5562    54.2876   -1.65   0.1077
year1946  -59.1147    55.3115   -1.07   0.2923
year1947  -87.5444    52.6530   -1.66   0.1051
year1948 -119.9125    53.3167   -2.25   0.0307 *
year1949 -167.9552    54.1999   -3.10   0.0038 **
year1950 -172.7676    55.0212   -3.14   0.0034 **
year1951 -191.1369    57.6114   -3.32   0.0021 **
year1952 -195.4503    59.6377   -3.28   0.0023 **
year1953 -174.6639    66.3451   -2.63   0.0124 *
year1954 -181.1273    68.5794   -2.64   0.0121 *
---
Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1

Total Sum of Squares:    1890000
Residual Sum of Squares: 138000
F-statistic: 21.8327 on 21 and 36 DF, p-value: 1.32e-14


Following the reasoning in your previous e-mail, I assume that the
(more useful) "no effects" model used in the "twoways" case
is> gr_fe1_null <- lm(invest ~ 0 + firm + year, data = pgr)
However I cannot replicate the F-statistic: 107.246.> anova(gr_fe1_null, gr_fe1)Analysis of Variance Table

Response: invest
          Df  Sum Sq Mean Sq F value Pr(>F)
firm       3 7664439 2554813  101.46 <2e-16 ***
year      19  932060   49056    1.95  0.040 *
Residuals 38  956886   25181
---
Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1
Warning message:
In anova.lmlist(object, ...) :
  models with response "NULL" removed because response differs from
model 1> anova(gr_fe1_null, gr_fe2)Analysis of Variance Table

Response: invest
          Df  Sum Sq Mean Sq F value Pr(>F)
firm       3 7664439 2554813  101.46 <2e-16 ***
year      19  932060   49056    1.95  0.040 *
Residuals 38  956886   25181
---
Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1
Warning message:
In anova.lmlist(object, ...) :
  models with response "NULL" removed because response differs from
model 1


In the case of "individual" with manually introduced time effects, I
assume the following null is used:> gr_fe2_null <- lm(invest ~ 0 + firm, data = pgr)
But even here I cannot replicate the F-statistic:
21.8327.> anova(gr_fe2_null, gr_fe2)Analysis of Variance Table

Response: invest
          Df  Sum Sq Mean Sq F value Pr(>F)
firm       3 7664439 2554813    77.1 <2e-16 ***
Residuals 57 1888946   33139
---
Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1
Warning message:
In anova.lmlist(object, ...) :
  models with response "NULL" removed because response differs from
model 1


Am I doing something wrong?
Liviu

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