[R] definition of "dffits"

[John Fox]

Dear Kunio,

The approach in dffits() in R is equivalent to the definition of DFFITS_i in
Belsley, Kuh, and Welch, Regression Diagnostics (which is, I believe the
original source, or close to it), generalized to WLS. Possibly a more
transparent definition would be

dfs <- function(mod){
	rs <- rstudent(mod)
	h <- hatvalues(mod)
	sqrt(h/(1 - h))*rs
	}

I hope this helps,
 John

------------------------------
John Fox, Professor
Department of Sociology
McMaster University
Hamilton, Ontario, Canada
web: socserv.mcmaster.ca/jfox


> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org]
On
> Behalf Of Kunio takezawa
> Sent: October-19-08 1:27 AM
> To: r-help at r-project.org
> Subject: [R] definition of "dffits"
> 
> R-users
> E-mail: r-help at r-project.org
> 
>    Hi! R-users.
> 
>    I am just wondering what the definition of "dffits" in R language is.
> Let me show you an simple example.
> 
> function() {
>   library(MASS)
> 
>   xx <- c(1,2,3,4,5)
>   yy <- c(1,3,4,2,4)
> 
>   data1 <- data.frame(x=xx, y=yy)
>   lm.out <- lm(y~., data=data1, x=T)
>   lev1 <- lm.influence(lm.out)$hat
>   sig1 <- lm.influence(lm.out)$sigma
>   res1 <- residuals(lm.out)
> 
>   ey <- fitted(lm.out)
>   py <- ey + res1/(1-lev1)
> 
>   df1 <- dffits(lm.out, infl = lm.influence(lm.out))
>   df1 <- dffits(lm.out)
>   print("df1: dffits")
>   print(df1)
> 
>   my_df1 <- (ey-py)/(sig1*sqrt(lev1))
>   print("my_df1")
>   print(my_df1)
> 
>   my_df2 <- -lev1*(ey-py)/(sig1*sqrt(lev1))
> 
>   print("my_df2")
>   print(my_df2)
> }
> 
> 
> [1] "df1: dffits"
>          1          2          3          4          5
> -1.3333333  0.4082483  0.6000000 -1.0475699  0.2672612
> [1] "my_df1"
>          1          2          3          4          5
>  2.2222222 -1.3608276 -3.0000000  3.4918995 -0.4454354
> [1] "my_df2"
>          1          2          3          4          5
> -1.3333333  0.4082483  0.6000000 -1.0475699  0.2672612
> 
> I think that "my_df1" is "dffits"( http://en.wikipedia.org/wiki/DFFITS ),
> but in R language, "my_df2" gives the difinition of "dffits".
>    Please let me know why.
> 
> --
> *****    r.otasuke at gmail.com    *****
> http://cse.naro.affrc.go.jp/takezawa/intro.html
> 
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