curve estimation function-cubic

[msherman]

Dear list:  I have the following non-spss situation. I am looking for a cubic relation between years as a home health care worker and job satisfaction. My prediction is that the relation is basically cubic. One starts out somewhat satisfied (excited about the job) but over the next two years there are all kinds of issues are dealt with and thus one becomes somewhat less satisfied. But after getting through the first couple of years and learning the tricks of the trade one begins to feel better about one's job and thus job satisfaction starts to increase again and then after about 20 years in the field one begins to get dissatisfied again because of demands of the job are stressful for someone who is now quite older and less physically capable of carrying out all of the job responsibilities of a home health care worker.  Hence, the s shaped or cubic relation. I now use the curve estimation function under the regression procedure and click on linear, quadratic, and cubic. The !
 results for the final analysis (linear, quadratic, and cubic all in the model) indicate that the linear is not significant (standardized beta = .34), but the quadratic is significant (standardized beta is -1.21, p=.036), and the cubic is also significant (standardized beta eq .797, p=.021). Now, my concern is the standardized beta for the quadratic which has a value of -1.21. To me this indicates a multi-collinearity problem. In fact the tolerance levels are: Linear = .02, Quadratic= .004, and for Cubic = .012).  I am not certain whether this is problem or not.  Would one always have mutlicollinear problems when all three functions are included in the model?  I would appreciate reactions. thanks,  martin sherman

Martin F. Sherman, Ph.D.
Professor of Psychology
Director of Masters Education: Thesis Track
Loyola College
Psychology Department
222 B Beatty Hall
4501 North Charles Street
Baltimore, MD 21210

410 617-2417 (office)
410 617-5341 (fax)

[hidden email]

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[Richard Ristow]

At 03:40 PM 2/21/2008, Martin Sherman wrote:

>I am looking for a cubic relation between years as a home health
>care worker and job satisfaction. I use the curve estimation
>function under the regression procedure and click on linear,
>quadratic, and cubic. The results (linear, quadratic, and cubic all
>in the model) indicate that the linear is not significant
>(standardized beta = .34), but the quadratic is significant
>(standardized beta is -1.21, p=.036), and the cubic is also
>significant (standardized beta eq .797, p=.021). Now, my concern is
>the standardized beta for the quadratic which has a value of -1.21.
>To me this indicates a multi-collinearity problem. Would one always
>have multi-collinearity problems when all three functions are
>included in the model?

Not quite always; but, very often, under ordinary circumstances.

Quantities are usually highly correlated with their own powers. The
correlation of the linear and quadratic terms can be reduced a lot,
usually enough, by mean-centering the variable before estimating. You
can then replace the cubic by the difference of the cubic and an
appropriate multiple of the linear term. After mean-centering, try

x**3-x*SQRT(SD)

where 'SD' is the standard deviation of the variable 'x'.

(Those are rough ways of doing it. You can also calculate
mathematically quadratic and cubic terms that are uncorrelated with
the linear term and with each other; it's called 'orthogonalization'.
But you probably don't need to go that far.)

-Best of luck,
  Richard

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[Peck, Jon]

A late response to this.  A cubic fit may tell you what you want, but you might consider using a more general procedure to see what might be missing.  If you have the Categories option, you could use CATREG (Regression/Optimal Scaling) to fit a more flexible model and get a better picture of the appropriate functional form.  You would tell Catreg to discretize the explanatory variable in an optimal way and then fit the regression.  The default discretization will give you seven segments, but you might also try the "Multiplying" method.  Ask for a transformation plot of the predictor to get a good picture of the shape, and Category quantifications in the output subdialog.

Although Catreg might seem from the name to be just for categorical data, it can do lots of other things.

HTH,
Jon Peck

-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Martin Sherman
Sent: Thursday, February 21, 2008 1:41 PM
To: [hidden email]
Subject: [SPSSX-L] curve estimation function-cubic

Dear list:  I have the following non-spss situation. I am looking for a cubic relation between years as a home health care worker and job satisfaction. My prediction is that the relation is basically cubic. One starts out somewhat satisfied (excited about the job) but over the next two years there are all kinds of issues are dealt with and thus one becomes somewhat less satisfied. But after getting through the first couple of years and learning the tricks of the trade one begins to feel better about one's job and thus job satisfaction starts to increase again and then after about 20 years in the field one begins to get dissatisfied again because of demands of the job are stressful for someone who is now quite older and less physically capable of carrying out all of the job responsibilities of a home health care worker.  Hence, the s shaped or cubic relation. I now use the curve estimation function under the regression procedure and click on linear, quadratic, and cubic. The !

 results for the final analysis (linear, quadratic, and cubic all in the model) indicate that the linear is not significant (standardized beta = .34), but the quadratic is significant (standardized beta is -1.21, p=.036), and the cubic is also significant (standardized beta eq .797, p=.021). Now, my concern is the standardized beta for the quadratic which has a value of -1.21. To me this indicates a multi-collinearity problem. In fact the tolerance levels are: Linear = .02, Quadratic= .004, and for Cubic = .012).  I am not certain whether this is problem or not.  Would one always have mutlicollinear problems when all three functions are included in the model?  I would appreciate reactions. thanks,  martin sherman

Martin F. Sherman, Ph.D.
Professor of Psychology
Director of Masters Education: Thesis Track
Loyola College
Psychology Department
222 B Beatty Hall
4501 North Charles Street
Baltimore, MD 21210

410 617-2417 (office)
410 617-5341 (fax)

[hidden email]

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[Kooij, A.J. van der]

I have learned recently that the purpose of the Discretization subcommand in the Optimal Scaling procedures (CATREG and CATPCA) is not clear to everyone. So, following up on Jon's reply to the Curve Estimation function-cubic question, some explanation of Discretization:

 

First, to explain "CAT " in the procedure names:

In the Optimal Scaling approach, a continuous variable is considered as a categorical variable: a variable with N categories; N is the number of cases (or the number of distinct values if there are duplicate values).

CATREG and CATPCA require (positive) integer valued data. So, the main purpose of Discretization is to transform continuous valued variables into integer valued variables.

If you want to keep all the "categories" of the continous variables, use the Multiplying or the Ranking option.

(with Multiplying, the variable is first transformed to z-scores, then multiplied with 10,  the resulting values are rounded, and a value is added such that the lowest value is 1)

 

The second purpose is to recode (continuous or integer valued) variables into variables with less values/categories. For this purpose use the Grouping option, either to recode into K categories (you can specify K, default is 7), or to recode intervals of equal size into categories (you can specify the size of the intervals).

 

Anita van der Kooij

Data Theory Group

Leiden University


________________________________

From: SPSSX(r) Discussion on behalf of Peck, Jon
Sent: Thu 28/02/2008 23:55
To: [hidden email]
Subject: Re: curve estimation function-cubic



A late response to this.  A cubic fit may tell you what you want, but you might consider using a more general procedure to see what might be missing.  If you have the Categories option, you could use CATREG (Regression/Optimal Scaling) to fit a more flexible model and get a better picture of the appropriate functional form.  You would tell Catreg to discretize the explanatory variable in an optimal way and then fit the regression.  The default discretization will give you seven segments, but you might also try the "Multiplying" method.  Ask for a transformation plot of the predictor to get a good picture of the shape, and Category quantifications in the output subdialog.

Although Catreg might seem from the name to be just for categorical data, it can do lots of other things.

HTH,
Jon Peck

-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Martin Sherman
Sent: Thursday, February 21, 2008 1:41 PM
To: [hidden email]
Subject: [SPSSX-L] curve estimation function-cubic

Dear list:  I have the following non-spss situation. I am looking for a cubic relation between years as a home health care worker and job satisfaction. My prediction is that the relation is basically cubic. One starts out somewhat satisfied (excited about the job) but over the next two years there are all kinds of issues are dealt with and thus one becomes somewhat less satisfied. But after getting through the first couple of years and learning the tricks of the trade one begins to feel better about one's job and thus job satisfaction starts to increase again and then after about 20 years in the field one begins to get dissatisfied again because of demands of the job are stressful for someone who is now quite older and less physically capable of carrying out all of the job responsibilities of a home health care worker.  Hence, the s shaped or cubic relation. I now use the curve estimation function under the regression procedure and click on linear, quadratic, and cubic. The !

 results for the final analysis (linear, quadratic, and cubic all in the model) indicate that the linear is not significant (standardized beta = .34), but the quadratic is significant (standardized beta is -1.21, p=.036), and the cubic is also significant (standardized beta eq .797, p=.021). Now, my concern is the standardized beta for the quadratic which has a value of -1.21. To me this indicates a multi-collinearity problem. In fact the tolerance levels are: Linear = .02, Quadratic= .004, and for Cubic = .012).  I am not certain whether this is problem or not.  Would one always have mutlicollinear problems when all three functions are included in the model?  I would appreciate reactions. thanks,  martin sherman

Martin F. Sherman, Ph.D.
Professor of Psychology
Director of Masters Education: Thesis Track
Loyola College
Psychology Department
222 B Beatty Hall
4501 North Charles Street
Baltimore, MD 21210

410 617-2417 (office)
410 617-5341 (fax)

[hidden email]

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For a list of commands to manage subscriptions, send the command
INFO REFCARD

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