Gram Schmidt orthogonalization procedure

[Dulce Subida]

Hi everyone!

I need to get a Gaussian logistic model in SPSS, to predict the
probability of occurence of a species (binary dependent variable) as a
function of an environmental variable (x: continuous independent
variable). I thought I could simply perform the binary logistic
regression, using x and x2 as independent variables in the model. However
in such case I think I will have a severe problem of multicollinearity
(between x and x2). I thought I could orthogonalize both independent
variables in order to surpass that problem. Does anyone know how can I run
the Gram Schmidt orthogonalization procedure in SPSS, or does anyone know
the syntaxis for it?

Thank you a lot for your help!

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[Peck, Jon]

-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Dulce Subida
Sent: Wednesday, December 17, 2008 6:07 AM
To: [hidden email]
Subject: [SPSSX-L] Gram Schmidt orthogonalization procedure

Hi everyone!

I need to get a Gaussian logistic model in SPSS, to predict the
probability of occurence of a species (binary dependent variable) as a
function of an environmental variable (x: continuous independent
variable). I thought I could simply perform the binary logistic
regression, using x and x2 as independent variables in the model. However
in such case I think I will have a severe problem of multicollinearity
(between x and x2). I thought I could orthogonalize both independent
variables in order to surpass that problem. Does anyone know how can I run
the Gram Schmidt orthogonalization procedure in SPSS, or does anyone know
the syntaxis for it?
[>>>Peck, Jon] Orthogonalizing the predictors first is not going to help.  The regression calculations already partial out the variable effects.  Imagine, for example, that your predictors are perfectly correlated.  One would then be zero after orthogonalization, and you still would not get any better coefficient estimates.

The MATRIX procedure can handle this sort of calculation, but the problem you have is not one of calculation.

HTH,
Jon Peck

Thank you a lot for your help!

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[Art Kendall]

I have never seen centering done for adding a power term.  However, a
power term is a form of interaction of a variable with itself.   Based
on this definition perhaps you should do what you would do with any
other interaction term and center the x before squaring.

compute squareterm= (x-xmean) **2.

Is there a way for you to get a dependent variable at a better level of
measurement?


Art Kendall
Social Research Consultants

Dulce Subida wrote:

> Hi everyone!
>
> I need to get a Gaussian logistic model in SPSS, to predict the
> probability of occurence of a species (binary dependent variable) as a
> function of an environmental variable (x: continuous independent
> variable). I thought I could simply perform the binary logistic
> regression, using x and x2 as independent variables in the model. However
> in such case I think I will have a severe problem of multicollinearity
> (between x and x2). I thought I could orthogonalize both independent
> variables in order to surpass that problem. Does anyone know how can I run
> the Gram Schmidt orthogonalization procedure in SPSS, or does anyone know
> the syntaxis for it?
>
> Thank you a lot for your help!
>
> =====================
> To manage your subscription to SPSSX-L, send a message to
> [hidden email] (not to SPSSX-L), with no body text except the
> command. To leave the list, send the command
> SIGNOFF SPSSX-L
> For a list of commands to manage subscriptions, send the command
> INFO REFCARD
>
>
>

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[Dulce Subida]

Thank you for your help!

Yes I have continuous measures of the dependent variable (abudances per
m3), however my purpose at the moment is to model the presence/absence of
the species.
The Gaussian logistic model is ecologically meaningful and has been
already applied a few times to data sets similar to the one I am handling,
however I could not find any information about the problem of the
multicollinearity between the independent variable and its interaction
with itself. This problem is mentioned in some textbooks for polynomial
regression, and to me it seems that the gaussian logistic regression has
implicit a polynomial (of second order) regression (in the quadratic
response function that is fitted to the logistic equation). I will
probably perform the procedure with and without transformation of the data
and compare the estimates of the parameters... it is working the double
however...

Thank you again!

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[Art Kendall]

One exploratory approach that might help is to do an x by abundance
scatterplot and then fit a loess line to see that it looks like.

In the GPL documentation that comes with SPSS  there is a way to do a
line chart from an equation.
It should be possible if someone were up on GPL, to put it all together
and have a scatterplot with the linear regression line, a line from an
equation, and a loess curve all on the same graph.

But for now you could do the 3 separately and compare them.


Art Kendall
Social Research Consultants

Dulce Subida wrote:

> Thank you for your help!
>
> Yes I have continuous measures of the dependent variable (abudances per
> m3), however my purpose at the moment is to model the presence/absence of
> the species.
> The Gaussian logistic model is ecologically meaningful and has been
> already applied a few times to data sets similar to the one I am handling,
> however I could not find any information about the problem of the
> multicollinearity between the independent variable and its interaction
> with itself. This problem is mentioned in some textbooks for polynomial
> regression, and to me it seems that the gaussian logistic regression has
> implicit a polynomial (of second order) regression (in the quadratic
> response function that is fitted to the logistic equation). I will
> probably perform the procedure with and without transformation of the data
> and compare the estimates of the parameters... it is working the double
> however...
>
> Thank you again!
>
> =====================
> To manage your subscription to SPSSX-L, send a message to
> [hidden email] (not to SPSSX-L), with no body text except the
> command. To leave the list, send the command
> SIGNOFF SPSSX-L
> For a list of commands to manage subscriptions, send the command
> INFO REFCARD
>
>
>

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