Linear trend test when using logistic regression model

[Margaret MacDougall]

Hello

  Using SPSS, is it possible to perform a chi-square test of linear trend within the context of a binary logistic regression model? The idea I have in mind here can best be illustrated by an example. Suppose I wish to determine whether there is a linear association between the factor ‘level of exposure’ (in categories) and the dependent variable ‘disease status’ (with categories ‘present’ or ‘absent’) whilst adjusting for the effect of other factors such as ‘family history of disease' and gender’.

  I suspect that that such a test exists but relevant output is not forthcoming from the output for a binary logistic regression analysis within SPSS (on assuming the 'point and click' approach). Some advice would be very much appreciated!

  Many thanks for your interest in this request.

  Best wishes

  Margaret

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[Marta García-Granero]

Hi Margaret

Monday, November 27, 2006, 2:04:05 PM, You wrote:

MM>   Using SPSS, is it possible to perform a chi-square test of
MM> linear trend within the context of a binary logistic regression
MM> model? The idea I have in mind here can best be illustrated by an
MM> example. Suppose I wish to determine whether there is a linear
MM> association between the factor ‘level of exposure’ (in categories)
MM> and the dependent variable ‘disease status’ (with categories
MM> ‘present’ or ‘absent’) whilst adjusting for the effect of other
MM> factors such as ‘family history of disease' and gender’.

use  /CONTRAST (LevelOfExposure)=Polynomial

It will decompose LevelOfExposure in k-1 (k:Nr. of levels) variables.
The first one will test the linear trend, the second one the quadratic
term, and so on.

MM>   I suspect that that such a test exists but relevant output
MM> is not forthcoming from the output for a binary logistic
MM> regression analysis within SPSS (on assuming the 'point and click'
MM> approach).


--
Regards,
Dr. Marta García-Granero,PhD           mailto:[hidden email]
Statistician

---
"It is unwise to use a statistical procedure whose use one does
not understand. SPSS syntax guide cannot supply this knowledge, and it
is certainly no substitute for the basic understanding of statistics
and statistical thinking that is essential for the wise choice of
methods and the correct interpretation of their results".

(Adapted from WinPepi manual - I'm sure Joe Abrahmson will not mind)

[Margaret MacDougall]

Dear Marta

  Thank you very much. This is most interesting and helpful.

  I take it that this test allows you to adjust for the other factors in the model so as to measure the strength of the independent linear relationship between a given factor and the dependent variable.

  Could somebody please guide me to a reference which explains the calculations involved in this particular version of the chi-square test of association.

  Many thanks

  Best wishes

  Margaret

Marta García-Granero <[hidden email]> wrote:

  Hi Margaret

Monday, November 27, 2006, 2:04:05 PM, You wrote:

MM> Using SPSS, is it possible to perform a chi-square test of
MM> linear trend within the context of a binary logistic regression
MM> model? The idea I have in mind here can best be illustrated by an
MM> example. Suppose I wish to determine whether there is a linear
MM> association between the factor ‘level of exposure’ (in categories)
MM> and the dependent variable ‘disease status’ (with categories
MM> ‘present’ or ‘absent’) whilst adjusting for the effect of other
MM> factors such as ‘family history of disease' and gender’.

use /CONTRAST (LevelOfExposure)=Polynomial

It will decompose LevelOfExposure in k-1 (k:Nr. of levels) variables.
The first one will test the linear trend, the second one the quadratic
term, and so on.

MM> I suspect that that such a test exists but relevant output
MM> is not forthcoming from the output for a binary logistic
MM> regression analysis within SPSS (on assuming the 'point and click'
MM> approach).


--
Regards,
Dr. Marta García-Granero,PhD mailto:[hidden email]
Statistician

---
"It is unwise to use a statistical procedure whose use one does
not understand. SPSS syntax guide cannot supply this knowledge, and it
is certainly no substitute for the basic understanding of statistics
and statistical thinking that is essential for the wise choice of
methods and the correct interpretation of their results".

(Adapted from WinPepi manual - I'm sure Joe Abrahmson will not mind)


 Send instant messages to your online friends http://uk.messenger.yahoo.com

[Marta García-Granero]

Hi Margaret

Back from short holidays...

MM>   I take it that this test allows you to adjust for the other
MM> factors in the model so as to measure the strength of the
MM> independent linear relationship between a given factor and the
MM> dependent variable.

Answer: Yes

MM>  Could somebody please guide me to a reference which explains the
MM> calculations involved in this particular version of the chi-square
MM> test of association.

If you want to know more on polynomial contrasts, check specialised
books, like: Maxwell & Delaney "Designing Experiments and Analyzing
Data" Lawrence Erlbaum Associates.

If you Google a bit using this search key: "Polynomial contrasts
logistic regression", you will se that it is widely used in
experimental research to test for linear and non linear trends.

This table was extracted from that book:

**********************************************************
*         COEFFICIENTS OF ORTHOGONAL POLYNOMIALS         *
**********************************************************
*  K    Trend             Coefficients, c(i)             *
* ------------------------------------------------------ *
*  3    Linear   -1   0   1                              *
*       Quad      1  -2   1                              *
*       ------------------------------------------------ *
*  4    Linear   -3  -1   1   3                          *
*       Quad      1  -1  -1   1                          *
*       Cubic    -1   3  -3   1                          *
*       ------------------------------------------------ *
*  5    Linear   -2  -1   0   1   2                      *
*       Quad      2  -1  -2  -1   2                      *
*       Cubic    -1   2   0  -2   1                      *
*       Quartic   1  -4   6  -4   1                      *
*       ------------------------------------------------ *
*  6    Linear   -5  -3  -1   1   3   5                  *
*       Quad      5  -1  -4  -4   1   5                  *
*       Cubic    -5   7   4  -4  -7   5                  *
*       Quartic   1  -3   2   2  -3   1                  *
*       Quintic  -1   5 -10  10  -5   1                  *
*       ------------------------------------------------ *
*  7    Linear   -3  -2  -1   0   1   2   3              *
*       Quad      5   0  -3  -4  -3   0   5              *
*       Cubic    -1   1   1   0  -1  -1   1              *
*       Quartic   3  -7   1   6   1  -7   3              *
*       Quintic  -1   4  -5   0   5  -4   1              *
*       ------------------------------------------------ *
*  8    Linear   -7  -5  -3  -1   1   3   5  7           *
*       Quad      7   1  -3  -5  -5  -3   1  7           *
*       Cubic    -7   5   7   3  -3  -7  -5  7           *
*       Quartic   7 -13  -3   9   9  -3 -13  7           *
*       Quintic  -7  23 -17 -15  15  17 -23  7           *
*        ------------------------------------------------ *
*  9    Linear   -4  -3  -2  -1   0   1   2   3   4      *
*       Quad     28   7  -8 -17 -20 -17  -8   7  28      *
*       Cubic   -14   7  13   9   0  -9 -13  -7  14      *
*       Quartic  14 -21 -11   9  18   9 -11 -21  14      *
*       Quintic  -4  11  -4  -9   0   9   4 -11   4      *
*       ------------------------------------------------ *
* 10    Linear   -9  -7  -5  -3  -1   1   3   5   7   9  *
*       Quad      6   2  -1  -3  -4  -4  -3  -1   2   6  *
*       Cubic   -42  14  35  31  12 -12 -31 -35 -14  42  *
*       Quartic  18 -22 -17   3  18  18   3 -17 -22  18  *
*       Quintic  -6  14  -1 -11  -6   6  11   1 -14   6  *
* ------------------------------------------------------ *
**********************************************************
* Extracted from Table A.10 of Maxwell & Delaney "Designing
  Experiments and Analyzing Data" Lawrence Erlbaum Associates.






--
Regards,
Dr. Marta García-Granero,PhD           mailto:[hidden email]
Statistician

---
"It is unwise to use a statistical procedure whose use one does
not understand. SPSS syntax guide cannot supply this knowledge, and it
is certainly no substitute for the basic understanding of statistics
and statistical thinking that is essential for the wise choice of
methods and the correct interpretation of their results".

(Adapted from WinPepi manual - I'm sure Joe Abrahmson will not mind)

[Margaret MacDougall]

Dear Marta

  Thank you very much for the clarification. I shall try to get a copy of the book that you recommend.

  Best wishes

  Margaret

Marta García-Granero <[hidden email]> wrote:
  Hi Margaret

Back from short holidays...

MM> I take it that this test allows you to adjust for the other
MM> factors in the model so as to measure the strength of the
MM> independent linear relationship between a given factor and the
MM> dependent variable.

Answer: Yes

MM> Could somebody please guide me to a reference which explains the
MM> calculations involved in this particular version of the chi-square
MM> test of association.

If you want to know more on polynomial contrasts, check specialised
books, like: Maxwell & Delaney "Designing Experiments and Analyzing
Data" Lawrence Erlbaum Associates.

If you Google a bit using this search key: "Polynomial contrasts
logistic regression", you will se that it is widely used in
experimental research to test for linear and non linear trends.

This table was extracted from that book:

**********************************************************
* COEFFICIENTS OF ORTHOGONAL POLYNOMIALS *
**********************************************************
* K Trend Coefficients, c(i) *
* ------------------------------------------------------ *
* 3 Linear -1 0 1 *
* Quad 1 -2 1 *
* ------------------------------------------------ *
* 4 Linear -3 -1 1 3 *
* Quad 1 -1 -1 1 *
* Cubic -1 3 -3 1 *
* ------------------------------------------------ *
* 5 Linear -2 -1 0 1 2 *
* Quad 2 -1 -2 -1 2 *
* Cubic -1 2 0 -2 1 *
* Quartic 1 -4 6 -4 1 *
* ------------------------------------------------ *
* 6 Linear -5 -3 -1 1 3 5 *
* Quad 5 -1 -4 -4 1 5 *
* Cubic -5 7 4 -4 -7 5 *
* Quartic 1 -3 2 2 -3 1 *
* Quintic -1 5 -10 10 -5 1 *
* ------------------------------------------------ *
* 7 Linear -3 -2 -1 0 1 2 3 *
* Quad 5 0 -3 -4 -3 0 5 *
* Cubic -1 1 1 0 -1 -1 1 *
* Quartic 3 -7 1 6 1 -7 3 *
* Quintic -1 4 -5 0 5 -4 1 *
* ------------------------------------------------ *
* 8 Linear -7 -5 -3 -1 1 3 5 7 *
* Quad 7 1 -3 -5 -5 -3 1 7 *
* Cubic -7 5 7 3 -3 -7 -5 7 *
* Quartic 7 -13 -3 9 9 -3 -13 7 *
* Quintic -7 23 -17 -15 15 17 -23 7 *
* ------------------------------------------------ *
* 9 Linear -4 -3 -2 -1 0 1 2 3 4 *
* Quad 28 7 -8 -17 -20 -17 -8 7 28 *
* Cubic -14 7 13 9 0 -9 -13 -7 14 *
* Quartic 14 -21 -11 9 18 9 -11 -21 14 *
* Quintic -4 11 -4 -9 0 9 4 -11 4 *
* ------------------------------------------------ *
* 10 Linear -9 -7 -5 -3 -1 1 3 5 7 9 *
* Quad 6 2 -1 -3 -4 -4 -3 -1 2 6 *
* Cubic -42 14 35 31 12 -12 -31 -35 -14 42 *
* Quartic 18 -22 -17 3 18 18 3 -17 -22 18 *
* Quintic -6 14 -1 -11 -6 6 11 1 -14 6 *
* ------------------------------------------------------ *
**********************************************************
* Extracted from Table A.10 of Maxwell & Delaney "Designing
Experiments and Analyzing Data" Lawrence Erlbaum Associates.






--
Regards,
Dr. Marta García-Granero,PhD mailto:[hidden email]
Statistician

---
"It is unwise to use a statistical procedure whose use one does
not understand. SPSS syntax guide cannot supply this knowledge, and it
is certainly no substitute for the basic understanding of statistics
and statistical thinking that is essential for the wise choice of
methods and the correct interpretation of their results".

(Adapted from WinPepi manual - I'm sure Joe Abrahmson will not mind)



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