sktest : Normality Test

[Gabriella Miniero]

Hi Forum!
I have to test the normality of my linear multiple regression. I've chosen to use the Jacque Bera test and that's the result. First of all, is right to use it with only residuals? and then, can I say that my residuals are normally distributed?

. sktest e

                    Skewness/Kurtosis tests for Normality
                                                         ------- joint ------
    Variable |    Obs   Pr(Skewness)   Pr(Kurtosis)  adj chi2(2)    Prob>chi2
-------------+---------------------------------------------------------------
           e |    107      0.4790         0.6289         0.75         0.6882

[Carlo Lazzaro]

Gabriella:
yes, you can.
You can also visually inspecting residual distribution normality via -qnorm- and/or -kdensity-.
However, it is more important to check residual distribution homoskedasticity and, even more relevant, regression model misspecification (-linktest-).

[Gabriella Miniero]

Thank you for your helpful advice!

[carlton durrant]

Dear forum users

I have run a normality test using Jarque Bera and found it to be non normal. I decided to run try the Skewness Kurtosis test for panel data (stsktest) for four models as follows but I need assistance interpreting the meaning of the results for normality on the remainder term (e) and firm specific (u). If part is normal and the other not normal how do one interpret the test?




Model 1
Tests for skewness and kurtosis Number of obs = 370
Replications = 50

(Replications based on 37 clusters in CUID)
------------------------------------------------------------------------------
| Observed Bootstrap Normal-based
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
Skewness_e | -4.08e-07 3.50e-07 -1.17 0.244 -1.09e-06 2.78e-07
Kurtosis_e | 6.13e-08 1.49e-08 4.12 0.000 3.21e-08 9.05e-08
Skewness_u | 1.40e-08 1.87e-07 0.07 0.941 -3.53e-07 3.81e-07
Kurtosis_u | -4.18e-09 3.58e-09 -1.17 0.244 -1.12e-08 2.85e-09
------------------------------------------------------------------------------
Joint test for Normality on e: chi2(2) = 18.29 Prob > chi2 = 0.0001
Joint test for Normality on u: chi2(2) = 1.36 Prob > chi2 = 0.5055


model 2

Tests for skewness and kurtosis Number of obs = 370
Replications = 50

(Replications based on 37 clusters in CUID)

Observed Bootstrap Normal-based
Coef. Std. Err. z P>z [95% Conf. Interval]

Skewness_e -9.40e-09 2.53e-07 -0.04 0.970 -5.06e-07 4.87e-07
Kurtosis_e 2.84e-08 6.54e-09 4.33 0.000 1.55e-08 4.12e-08
Skewness_u -2.46e-07 1.47e-07 -1.68 0.093 -5.34e-07 4.14e-08
Kurtosis_u 3.74e-09 2.11e-09 1.77 0.076 -3.94e-10 7.88e-09

Joint test for Normality on e: chi2(2) = 18.79 Prob > chi2 = 0.0001
Joint test for Normality on u: chi2(2) = 5.96 Prob > chi2 = 0.0508

the summary table is below.

Skewness/ Kurtosis test for panel data
	Model 1	Model 2	Model 3	Model 4
Test of Normality(P values)
Joint test for Normality on e	0.0001	0.0001	0.0001	0.0035
Joint test for Normality on u:	0.5055	0.0508	0.061	0.0361

[Carlo Lazzaro]

Carlton:
as per FAQ, you're kindly requested to declare the source of community-contributed Stata programme like -xtsktest-.
That said, if you're concerned about heteroskedasticity, you can go visual inspect residual plots and decide to invoke -robust- or -vce(cluster clusterid)- standard errors.

[carlton durrant]

Hi Carlo

The source of the test is from an article "Tests for Normality in Linear Panel Data Models" I have enclosed the abstract as follows

Abstract. A new Stata command, xtsktest, is proposed to explore
non-normalities in linear panel data models. The tests explore skewness
and excess kurtosis allowing researchers to identify departures away from
gaussianity in both error components of a standard panel regression, sepa-
rately or jointly. The tests are based on recent results by Galvao, Montes-
Rojas, Sosa-Escudero and Wang (2013), and can be seen as extending the
classical Bera-Jarque normality test for the case of panel data.

[Carlo Lazzaro]

Carlton:
I did not mean you to show the abstract quoted from the community-contributed command helpfile, but simply to declare the source you got -xtsktest- from (SSC, I guess).
Far for being an unuseful inquiry, this habit, which is well covered in the FAQ, allow interested listers to understand which version of the community-contributed programme you're working with.