Regression Testing

On 1/21/2011 9:13 AM, Achim Zeileis wrote:

On Fri, 21 Jan 2011, Mojo wrote:

On 1/20/2011 4:42 PM, Achim Zeileis wrote:

On Thu, 20 Jan 2011, Mojo wrote:

I'm new to R and some what new to the world of stats.  I got frustrated 
with excel and found R.  Enough of that already.

I'm trying to test and correct for Heteroskedasticity

I have data in a csv file that I load and store in a dataframe.

ds <- read.csv("book2.csv")
df <- data.frame(ds)

I then preform a OLS regression:

lmfit <- lm(df$y~df$x)

Just btw: lm(y ~ x, data = df) is somewhat easier to read and also easier 
to write when the formula involves more regressors.

To test for Heteroskedasticity, I run the BPtest:

bptest(lmfit)

       studentized Breusch-Pagan test

data:  lmfit
BP = 11.6768, df = 1, p-value = 0.0006329

From the above, if I'm interpreting this correctly, there is 
Heteroskedasticity present.  To correct for this, I need to calculate 
robust error terms.

That is one option. Another one would be using WLS instead of OLS - or 
maybe FGLS. As the model just has one regressor, this might be possible 
and result in a more efficient estimate than OLS.

I thought that WLS (which I guessing is a weighted regression) is really 
only useful when you know or at least have an idea of what is causing the 
Heteroskedasticity?

Yes. But with only a single variable that shouldn't be too hard to do. Also 
in the Breusch-Pagan test you specify a hypothesized functional form for 
the variance.

I'm not familiar with FGLS.

There is a worked example in

  demo("Ch-LinearRegression", package = "AER")

The corresponding book has some more details.

hth,
Z

I plan on adding additional independent variables as I get more 
comfortable with everything.

From my reading on this list, it seems like I need to vcovHC.

That's another option, yes.

vcovHC(lmfit)

             (Intercept)         df$x
(Intercept)  1.057460e-03 -4.961118e-05
df$x       -4.961118e-05  2.378465e-06

I'm having a little bit of a hard time following the help pages.

Yes, the manual page is somewhat technical but the first thing the 
"Details" section does is: It points you to some references that should 
be easier to read. I recommend starting with

     Zeileis A (2004), Econometric Computing with HC and HAC Covariance
     Matrix Estimators. _Journal of Statistical Software_, *11*(10),
     1-17. URL <URL: http://www.jstatsoft.org/v11/i10/>.

I will look into that.

Thanks,
Mojo

If I were to use vcovHAC instead of vcovHC, does that correct for serial 
correlation as well as Heteroskedasticity?

Thanks,
Mojo