statistics for testing multivariate normality

[E. Bernardo]

What statistics are available in PASW/SPSS that  are used for testing multivariate normality?

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[Marta Garcia-Granero]

Eins Bernardo wrote:
> What statistics are available in PASW/SPSS that  are used for testing
> multivariate normality?
>
Couple of things you can do

1) Try this link (a macro with multivariate tests for skewness and
kurtosis):
http://www.columbia.edu/~ld208/

2) Multivariate normality can be tested by getting the residuals of all
the variables involved when predicted by the rest, by means of Multiple
Linear Regression (MLR) models. For example, if you have 3 variables
involved, you must run  3 MLR models (x1 predicted by x2&x3, x2 by
x1&x3, x3 by x1&x2), save the residuals and check their normality (using
EXAMINE, checking skewness&kurtosis, box-plot, histograms, Shapiro-Wilk
tests... all the stuff).

HTH,
Marta García-Granero

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[E. Bernardo]

Thank you, Marta.

 

I have concern in item#2 of your comment.  For reference, I pasted that comment as follows:

2) Multivariate normality can be tested by getting the residuals of all
the variables involved when predicted by the rest, by means of Multiple
Linear Regression (MLR) models.. For example, if you have 3 variables
involved, you must run  3 MLR models (x1 predicted by x2&x3, x2 by
x1&x3, x3 by x1&x2), save the residuals and check their normality (using
EXAMINE, checking skewness&kurtosis, box-plot, histograms, Shapiro-Wilk
tests... all the stuff).

Are the residuals correct if there is multicollinearity, outliers/extreme values, etc.

 

Eins.

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[Marta Garcia-Granero]

>
> I have concern in item#2 of your comment.  For reference, I
> pasted that comment as follows:
>
>     /2) Multivariate normality can be tested by getting the residuals
>     of all
>     the variables involved when predicted by the rest, by means of
>     Multiple
>     Linear Regression (MLR) models.. For example, if you have 3 variables
>     involved, you must run  3 MLR models (x1 predicted by x2&x3, x2 by
>     x1&x3, x3 by x1&x2), save the residuals and check their normality
>     (using
>     EXAMINE, checking skewness&kurtosis, box-plot, histograms,
>     Shapiro-Wilk
>     tests... all the stuff).
>     /
>
> Are the residuals correct if there is multicollinearity,
>

I don't know, the book I read on the topic did not mention that, but I'd
guess that yes, since you are not interested in estimating slopes, but
just in studying residuals behavior. Anyway, perhaps someone else at the
list has something to add.
>
> outliers/extreme values, etc
>
The presence of outliers is cause of non normality. If you are
interested in verifying normality, then outliers are part of what you
are trying to see.

Marta

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