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Re: st: Normally distributed error term & testing normality of residuals


From   Maarten Buis <maartenlbuis@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Normally distributed error term & testing normality of residuals
Date   Mon, 15 Oct 2012 10:33:14 +0200

--- On Sun, Oct 14, 2012 at 9:54 AM, Ebru Ozturk <ebru_0512@hotmail.com> wrote:
>> Thank you. So, there is no possibility to check heteroscedasticity graphically?

--- On Sun, Oct 14, 2012 at 1:53 PM, Nick Cox <njcoxstata@gmail.com> wrote:
> No one said that. You can plot the residuals, or their squares, or
> their absolute values, or roots of absolute values -- there are
> arguments for each -- against anything of interest, e.g. a predictor
> or fitted values.

The challenge with a model like Tobit is to know what kind of patter
in such a graph represents a problem, as you would expect the raw
residuals to be heteroskedastic in a Tobit model. One solution that
has been mentioned several times in this thread is to simulate from
the model to see what is "normal". An example is given below:

*--------------- begin example ----------------
// prepare data
sysuse auto, clear
gen wgt = weight/2000
label var wgt "weight in short tons"
replace mpg = 17 if mpg <= 17

// estimate Tobit model
tobit mpg wgt, ll

// To make the graphing and simulation easier I
// am going to change the data radically, so I
// first preserve the data
preserve

// only plot those observatin used in the model
keep if e(sample)

// I want 6 simulations, identified by the
// variable samp
gen id = _n
expand 6
bys id : gen samp = _n

// simulate outcome from the model
predict xb, xb
set seed 123456
gen sim = xb + rnormal(0, [sigma]_b[_cons])
replace sim = 17 if sim <= 17

// predict resiudals for both the observed
// data and the simulations
predict yhat, ystar(17,.)
replace sim = yhat - sim
gen resid = yhat - mpg

// plot the results
scatter sim resid wgt, by(samp)           ///
        msymbol(Oh o) msize(medium small) ///
        mcolor(gs8 black)
restore
*---------------- end example -----------------
(For more on examples I sent to the Statalist see:
http://www.maartenbuis.nl/example_faq )

Hope this helps,
Maarten

---------------------------------
Maarten L. Buis
WZB
Reichpietschufer 50
10785 Berlin
Germany

http://www.maartenbuis.nl
---------------------------------
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