Follow up to stat question

[msherman]

Dear list:  A continuation of the evacuation question. I went ahead and
looked at the time for evacuation (started to evacuate to exited onto
the street). The correlations between floor started and time was .75 for
one building and .77 for the other building. Next I did a regression
analysis allowing for linear and quadratic. In both instances the linear
and quadratic functions were significant. Next I allowed for a cubic
function and this is what happened.  For building 1 Linear was
significant, quadratic and cubic were not significant.  For building 2
linear was not significant, but quadratic and cubic were significant.
My question is how would I lose significance for the quadratic when the
cubic was allowed to enter for building 1. Also why would I lose
significance for linear  (given the very large zero-order correlation-my
expectation was that the linear would stay in) for building 2 while
picking up the cubic (besides the quadratic). Befuddled.   TIA.
P.S. A colleague recommended a Loess fitting curve. Does anyone have
any thoughts about using the Loess?

martin sherman

[Swank, Paul R]

Did you center the time variable before doing the analyses?

Paul

________________________________

From: SPSSX(r) Discussion on behalf of Martin Sherman
Sent: Sun 6/25/2006 11:02 AM
To: [hidden email]
Subject: Follow up to stat question



Dear list:  A continuation of the evacuation question. I went ahead and
looked at the time for evacuation (started to evacuate to exited onto
the street). The correlations between floor started and time was .75 for
one building and .77 for the other building. Next I did a regression
analysis allowing for linear and quadratic. In both instances the linear
and quadratic functions were significant. Next I allowed for a cubic
function and this is what happened.  For building 1 Linear was
significant, quadratic and cubic were not significant.  For building 2
linear was not significant, but quadratic and cubic were significant.
My question is how would I lose significance for the quadratic when the
cubic was allowed to enter for building 1. Also why would I lose
significance for linear  (given the very large zero-order correlation-my
expectation was that the linear would stay in) for building 2 while
picking up the cubic (besides the quadratic). Befuddled.   TIA.
P.S. A colleague recommended a Loess fitting curve. Does anyone have
any thoughts about using the Loess?

martin sherman

[Marc Halbrügge]

> My question is how would I lose significance for the quadratic when the
> cubic was allowed to enter for building 1. Also why would I lose
> significance for linear  (given the very large zero-order correlation-my
> expectation was that the linear would stay in) for building 2 while
> picking up the cubic (besides the quadratic). Befuddled.   TIA.
Did you test for multi-collinearity? The linear, quadratic and cubic
evacuation time should be highly intercorrelated.

[Hector Maletta]

Correlated, but not necessarily LINEARLY correlated.
Hector

-----Mensaje original-----
De: SPSSX(r) Discussion [mailto:[hidden email]] En nombre de Marc
Halbrügge
Enviado el: Sunday, June 25, 2006 3:10 PM
Para: [hidden email]
Asunto: Re: Follow up to stat question

> My question is how would I lose significance for the quadratic when the
> cubic was allowed to enter for building 1. Also why would I lose
> significance for linear  (given the very large zero-order correlation-my
> expectation was that the linear would stay in) for building 2 while
> picking up the cubic (besides the quadratic). Befuddled.   TIA.
Did you test for multi-collinearity? The linear, quadratic and cubic
evacuation time should be highly intercorrelated.

[Boonen Eliane]

It's too much.
Delete me on your list.
Thanks.

J. Schoeters

[Richard Ristow]

Kind of a summary; these are points that have been made

At 12:02 PM 6/25/2006, Martin Sherman wrote:

>A continuation of the evacuation question. I went ahead and looked at
>the time for evacuation (started to evacuate to exited onto the
>street). The correlations between floor started and time was .75 for
>one building and .77 for the other building.

It's a good idea to take a naive look. In this case, what the
correlation means is, it takes longer to walk down more stairs. It's
fine to look at the correlation, but in this case, I don't think it can
be regarded as telling you much you didn't know.

>Next I did a regression analysis allowing for linear and quadratic. In
>both instances the linear and quadratic functions were significant.
>Next I allowed for a cubic function and this is what happened.  For
>building 1 Linear was significant, quadratic and cubic were not
>significant.  For building 2 linear was not significant, but quadratic
>and cubic were significant. My question is how would I lose
>significance for the quadratic when the cubic was allowed to enter for
>building 1. Also why would I lose significance for linear  (given the
>very large zero-order correlation-my expectation was that the linear
>would stay in) for building 2 while
>picking up the cubic (besides the quadratic). Befuddled.   TIA.

You should probably post the exact model you fit, and means and SDs of
the dependent and independent variables.

To say again what others have said: The linear, quadratic, and cubic
functions of a variable are VERY HIGHLY CORRELATED under very ordinary
conditions. Having all values positive (as yours are) is enough. The
larger the mean is relative to the SD, the worse. Look at the
correlation matrix of the predictors - linear, quadratic, and cubic -
that you used.

As Paul Swank said, you can solve the correlation between linear and
quadratic terms by centering the independent variable. Choosing a
convenient point near the middle will do; it needn't be the exact mean.
In your case, if time to evacuate is the dependent and starting floor
the independent, I'd keep the linear term uncentered, so its
coefficient has the natural meaning, and the constant has a reasonable
interpretation: mean time to start evacuation. But for 75 or so floors
to evacuate, I'd use, say, (Floor-40)**2 as the quadratic term. You can
interpret this as taking time per floor from the 40th floor as the
norm, and the quadratic term as the systematic change in time per floor
above and below the 40th.

Centering won't remove the correlation between linear and cubic terms.
As a cubic term, you might try subtracting the linear component:

(Floor-40)**3 - (Floor-40)

Notice that, here, I'm centering both the linear and the cubic
components of the variable. It make its shape, if plot it, much more
meaningful.

Finally, it's a common rule, in fitting polynomials, that if any term
is included, all lower terms must also be included. Keep the linear
term, whether it loses 'significance' or not. But I think, if you
transform like this, that the linear term will stay dominant.

Has the question of data censoring been settled? One would think this
involved censored data, since there's no observation for people who
failed to make it out of the buildings. However, as I understand it,
the pattern was peculiar: there was enough time to evacuate, and little
or no cutoff for people who were lost because the building collapsed
before they completed evacuation. The losses were people above the
points of impact, who were cut off from evacuation altogether, and need
to be excluded from this model.

A sad business, this. It is worth knowing about, though.

[Judit Lindqvist]

Delete me on your list.
Thanks.

J. Lindqvist

[Marta García-Granero]

Hi Judit,

JL> Delete me on your list.

When you subscribed to the list, you received a message (copied below)
with instructions on how to unsubscribe yourself (we, users, CAN'T do
that for you, if we could start unsubscribing each other this would be
chaos). The message also instructed you to keep it, I see you didn't.

HTH,
Marta

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