[R-sig-Geo] spautolm - standard errors of regression paramters

[Roger Bivand]

On Mon, 5 Nov 2007, Sam Field wrote:

> thanks Roger!
>
>
> In my haste, I mistyped.  I meant to write:
>
>
> sqrt(diag(mod1$fit[["imat"]]))
>
>
> which should be equivalent to
>
>
> summary(mod1)$Coef[,2],
>
> the standard errors of the regression coefficients.

No, because the fit[["imat"]] matrix has not been multiplied by s^2 (in 
summary.spautolm):

     object$resvar <- object$fit$s2 * object$fit$imat

So:

> summary(mod1)$Coef[,2]
(Intercept)       HOVAL      DISCBD
  4.68573631  0.09017431  1.47045126
> sqrt(diag(mod1$fit$s2 * mod1$fit[["imat"]]))
(Intercept)       HOVAL      DISCBD
  4.68573631  0.09017431  1.47045126

And it is not multiplied in spautolm() because of the adj.se= argument to 
summary.spautolm, so that the SE values in Waller and Gotway - adjusting 
s^2 for the number of fitted coefficients - could be reproduced.

Roger

>
>
> In any case, I have managed to replicate the case where the two commands produce
> different results. Using the "columbus data"...
>
>
> library(spdep)
> data(columbus)
>
> #defining W
>
> columbus_poly <- readShapePoly(system.file("etc/shapes/columbus.shp",
> package="spdep")[1])
> columbus_nb <- poly2nb(columbus_poly)
> columbus_listw <- nb2listw(columbus_nb)
>
> #running spautolm()
>
> mod1 <- spautolm(CRIME ~ HOVAL +  DISCBD,listw=columbus_listw,data =
> columbus,family="SAR")
>
>
> sqrt(diag(mod1$fit[["imat"]]))
>
> summary(mod1)$Coef[,2]
>
>
>
> and the result:
>
>
>> sqrt(diag(mod1$fit[["imat"]]))
> (Intercept)       HOVAL      DISCBD
> 0.468345807 0.009013047 0.146973631
>
>
>> summary(mod1)$Coef[,2]
> (Intercept)       HOVAL      DISCBD
> 4.68573639  0.09017431  1.47045128
>
>
> looks like the decimal place is shifted over one place.  If you add more
> variables to the model, the results differ by more then a decimal place in this
> case (in my case the results are very different). For example,
>
>
> mod2 <- spautolm(CRIME ~ HOVAL +  DISCBD + INC + PLUMB,listw=columbus_listw,data
> = columbus,family="SAR")
>
> sqrt(diag(mod2$fit[["imat"]]))
>
> summary(mod2)$Coef[,2]
>
>
> results in:
>
>> sqrt(diag(mod2$fit[["imat"]]))
> (Intercept)       HOVAL      DISCBD         INC       PLUMB
> 0.52884967  0.01002545  0.17186710  0.03379109  0.04940024
>>
>> summary(mod2)$Coef[,2]
> (Intercept)       HOVAL      DISCBD         INC       PLUMB
> 4.86800598  0.09228322  1.58201870  0.31104348  0.45472408
>
>
> Initially, I just wanted the standard errors so that I could write them out in a
> text file and put them in a table for a MSWord document.  However, I will also
> need the covariances of the parameters and, thus, need the off diagonal elements
> of the variance covariance matrix.   Am I reading this matrix incorrectly?
>
>
> thanks for all of your help!
>
> Sam
>
>
>
>
>
>
>
>
>
> Quoting Roger Bivand <Roger.Bivand at nhh.no>:
>
>> On Mon, 5 Nov 2007, Sam Field wrote:
>>
>>> List,
>>>
>>> I would like to grab the standard errors of the regression parameters from
>> an
>>> spautolm object.  Currently I am using...
>>>
>>> mod1 <- spautolm(y~var1 + var2,....)
>>>
>>> mod1_sd <-  (diag(mod1$fit[["imat"]])^2
>>
>> As with most model fitting functions, you use the summary method, so
>>
>> summary(mod1)$Coef
>>
>> is a four-column matrix, and
>>
>> summary(mod1)$Coef[,2]
>>
>> is the column you want.
>>
>> Roger
>>
>> PS. Reading summary.spautolm shows that the diagonal values of the matrix
>> you refer to are the squares of the SE values.
>>
>>>
>>>
>>> This does produce a vector of the diagonal elements of a matrix that look
>> like a
>>> variance covariance matrix (correct dimensions and row and column labels),
>> but
>>> the values I get do not agree with what the summary() function displays --
>> they
>>> also seem implausibly small.
>>>
>>> any hints?
>>>
>>> Thanks!
>>>
>>> Sam
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>
>> --
>> Roger Bivand
>> Economic Geography Section, Department of Economics, Norwegian School of
>> Economics and Business Administration, Helleveien 30, N-5045 Bergen,
>> Norway. voice: +47 55 95 93 55; fax +47 55 95 95 43
>> e-mail: Roger.Bivand at nhh.no
>>
>>
>
>
>

-- 
Roger Bivand
Economic Geography Section, Department of Economics, Norwegian School of
Economics and Business Administration, Helleveien 30, N-5045 Bergen,
Norway. voice: +47 55 95 93 55; fax +47 55 95 95 43
e-mail: Roger.Bivand at nhh.no