standardized odds ratio interpretation

[Greg]

I was hoping to get some clarification in terms of interpreting a set of standardized odds ratios (which SPSS calculated while running binary logistic regression). The following is a small hypothetical example of the results ( I will post the unstandardized and standardized results.)

Unstandardized results

                  beta      odds ratio
Group A:   -1.149     0.317
Group B:   -0.839     0.432
Group C:   -1.340     0.262
(group d reference group)
(dependent variable is binary: 1: happy/ 0: not happy

Standardized results

                  beta      odds ratio
Group A:   -0.433     0.648
Group B:   -0.339     0.713
Group C:   -0.119     0.888
(group d reference group)
(dependent variable is binary: 1: happy/ 0: not happy

Based on the unstandardized results, the odds of being happy for group C are 73.8% lower than those of group b (56.8%). Therefore, group b has higher odds of being happy than the odds of group c.

Based on the standardized results, the odds of being happy for group C are 11.2% lower than those of group b (28.7%). Therefore, group c has higher odds of being happy than the odds of group b. (I understand that this refers to standard deviation units.)

Is the above correct? This is the first time I'm using standardized odds ratios.

Also, the odds ratio (in terms of absolute numbers) for Group c is the lowest in the unstandardized version, but the highest in the standardized. Is this normal? (based on the hypothetical example I provided).

Thank you in advance for your help!

[Bruce Weaver]

I assume this is a follow-up to your earlier question (http://spssx-discussion.1045642.n5.nabble.com/Standardized-odds-ratios-td5732487.html).

How exactly did you obtain the standardized results you show below?  Based on the earlier thread, I'm guessing you converted both explanatory and outcome variables to z-scores before estimating your model.  That seems to me like a nonsensical thing to do when you have categorical variables.  (I'm not even sure how you would go about doing it for the 4-level variable.)  

In the original thread, I thought you were wanting to convert continuous (explanatory) variables to z-scores so that the odds ratio for a continuous variables showed odds ratios for a 1-SD increment in that variable.  I could imagine someone wanting to do this, although my preference would be to report odds ratios for some practically important increment in X that does not change from sample to sample (as the SD does).  

HTH.

Greg wrote

I was hoping to get some clarification in terms of interpreting a set of standardized odds ratios (which SPSS calculated while running binary logistic regression). The following is a small hypothetical example of the results ( I will post the unstandardized and standardized results.)

Unstandardized results

                  beta      odds ratio
Group A:   -1.149     0.317
Group B:   -0.839     0.432
Group C:   -1.340     0.262
(group d reference group)
(dependent variable is binary: 1: happy/ 0: not happy

Standardized results

                  beta      odds ratio
Group A:   -0.433     0.648
Group B:   -0.339     0.713
Group C:   -0.119     0.888
(group d reference group)
(dependent variable is binary: 1: happy/ 0: not happy

Based on the unstandardized results, the odds of being happy for group C are 73.8% lower than those of group b (56.8%). Therefore, group b has higher odds of being happy than the odds of group c.

Based on the standardized results, the odds of being happy for group C are 11.2% lower than those of group b (28.7%). Therefore, group c has higher odds of being happy than the odds of group b. (I understand that this refers to standard deviation units.)

Is the above correct? This is the first time I'm using standardized odds ratios.

Also, the odds ratio (in terms of absolute numbers) for Group c is the lowest in the unstandardized version, but the highest in the standardized. Is this normal? (based on the hypothetical example I provided).

Thank you in advance for your help!

[Greg]

Correct and thank you for the quick reply. I converted my variables to z-scores and then ran the log regression. (All the predictors are categorical.)

[Bruce Weaver]

I don't understand the results you posted, in that case.  How did you standardize the variables?  It would help of you posted your syntax for that, as well as syntax to estimate to estimate the two models.

Meanwhile, try the following demonstration.

* Change path below to where you store the sample datasets.
GET FILE='C:\SPSSdata\survey_sample.sav'.
COMPUTE Male = sex EQ 1.
FORMATS Male(F1).
CROSSTABS sex by Male.

* Get Z-score versions of Male and marital status.
DESCRIPTIVES Male marital /SAVE.

* Logistic regression with Y = Male, X = marital (as factor variable).
LOGISTIC REGRESSION VARIABLES Male
  /METHOD=ENTER marital
  /CONTRAST (marital)=Indicator
  /PRINT=CI(95)
  /CRITERIA=PIN(0.05) POUT(0.10) ITERATE(20) CUT(0.5).

* Logistic regression with Y = Male, X = Zmarital (as factor variable).
LOGISTIC REGRESSION VARIABLES Male
  /METHOD=ENTER Zmarital
  /CONTRAST (Zmarital)=Indicator
  /PRINT=CI(95)
  /CRITERIA=PIN(0.05) POUT(0.10) ITERATE(20) CUT(0.5).

* Logistic regression with Y = Zmale, X = Zmarital (as factor variable).
LOGISTIC REGRESSION VARIABLES Zmale
  /METHOD=ENTER Zmarital
  /CONTRAST (Zmarital)=Indicator
  /PRINT=CI(95)
  /CRITERIA=PIN(0.05) POUT(0.10) ITERATE(20) CUT(0.5).

I get exactly the same table of coefficients for all 3 of these models (apart from the value labels for the the maritial variable).  Here are my coefficients:

Marital Status        B1        B2        B3
Marital status(1) -0.176 -0.176 -0.176
Marital status(2) -1.530 -1.530 -1.530
Marital status(3) -0.332 -0.332 -0.332
Marital status(4) -0.296 -0.296 -0.296

B1 = coefficient from first model
B2 = coefficient from second model
B3 = coefficient from third model

HTH.

Greg wrote

Correct and thank you for the quick reply. I converted my variables to z-scores and then ran the log regression. (All the predictors are categorical.)

[David Marso]

In what world does the SD or Mean of a categorical variable make any sense?
-------------------------------------------------------------------------------------------------------------

Greg wrote

Correct and thank you for the quick reply. I converted my variables to z-scores and then ran the log regression. (All the predictors are categorical.)

[Bruce Weaver]

Exactly!  It doesn't make any sense.  But as my demo showed, it also doesn't have any effect on the results when you use the LOGISTIC REGRESSION command and treat the variable as categorical.  ;-)

David Marso wrote

In what world does the SD or Mean of a categorical variable make any sense?
-------------------------------------------------------------------------------------------------------------

Greg wrote

Correct and thank you for the quick reply. I converted my variables to z-scores and then ran the log regression. (All the predictors are categorical.)

[Rich Ulrich]

I think you show that whatever two codes there are for the outcome
in a logistic regression, SPSS will accept them and treat them the same.
The only surprise here might be there is no restriction on the codes, not
to (0,1)  or even to something integer. 

Similarly, it seems that it will accept any two (or more?) codes when you specify
    /contrast =
and treat them as the same dummy contrasts every time.

If you want to get something that might be called a standardized OR,
you could "standardize" your dichotomies for dummy variables and
enter them as continuous covariates.  - Maybe I have been missing some
literature, so take this with a grain of salt:  That does not sound like a sensible
thing to do, and if I were a reviewer I would probably demand a strong
justification before accepting it.

--
Rich Ulrich

> Date: Thu, 23 Jun 2016 13:47:10 -0700

> From: [hidden email]
> Subject: Re: standardized odds ratio interpretation
> To: [hidden email]
>
> I don't understand the results you posted, in that case. How did you
> standardize the variables? It would help of you posted your syntax for
> that, as well as syntax to estimate to estimate the two models.
>
> Meanwhile, try the following demonstration.
>
> * Change path below to where you store the sample datasets.
> GET FILE='C:\SPSSdata\survey_sample.sav'.
> COMPUTE Male = sex EQ 1.
> FORMATS Male(F1).
> CROSSTABS sex by Male.
>
> * Get Z-score versions of Male and marital status.
> DESCRIPTIVES Male marital /SAVE.
>
> * Logistic regression with Y = Male, X = marital (as factor variable).
> LOGISTIC REGRESSION VARIABLES Male
> /METHOD=ENTER marital
> /CONTRAST (marital)=Indicator
> /PRINT=CI(95)
> /CRITERIA=PIN(0.05) POUT(0.10) ITERATE(20) CUT(0.5).
>
> * Logistic regression with Y = Male, X = Zmarital (as factor variable).
> LOGISTIC REGRESSION VARIABLES Male
> /METHOD=ENTER Zmarital
> /CONTRAST (Zmarital)=Indicator
> /PRINT=CI(95)
> /CRITERIA=PIN(0.05) POUT(0.10) ITERATE(20) CUT(0.5).
>
> * Logistic regression with Y = Zmale, X = Zmarital (as factor variable).
> LOGISTIC REGRESSION VARIABLES Zmale
> /METHOD=ENTER Zmarital
> /CONTRAST (Zmarital)=Indicator
> /PRINT=CI(95)
> /CRITERIA=PIN(0.05) POUT(0.10) ITERATE(20) CUT(0.5).
>
> I get exactly the same table of coefficients for all 3 of these models
> (apart from the value labels for the the maritial variable). Here are my
> coefficients:
>
> Marital Status B1 B2 B3
> Marital status(1) -0.176 -0.176 -0.176
> Marital status(2) -1.530 -1.530 -1.530
> Marital status(3) -0.332 -0.332 -0.332
> Marital status(4) -0.296 -0.296 -0.296
>
> B1 = coefficient from first model
> B2 = coefficient from second model
> B3 = coefficient from third model
>
> HTH.
>
>
> Greg wrote
> > Correct and thank you for the quick reply. I converted my variables to
> > z-scores and then ran the log regression. (All the predictors are
> > categorical.)
>
>
>
>
>
> -----
> --
> Bruce Weaver
> [hidden email]
> http://sites.google.com/a/lakeheadu.ca/bweaver/
>
> "When all else fails, RTFM."
>
> NOTE: My Hotmail account is not monitored regularly.
> To send me an e-mail, please use the address shown above.
>
> --
> View this message in context: http://spssx-discussion.1045642.n5.nabble.com/standardized-odds-ratio-interpretation-tp5732518p5732522.html
> Sent from the SPSSX Discussion mailing list archive at Nabble.com.
>
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[Art Kendall]

Alas, sometimes we have no control over the quality of the measurement process and we end up with such a coarse measurement of happiness.

[David Marso]

On a scale of 0 to Infinity how would you rate your happiness ?

Friday fun ;-)

Can SPSS handle infinity?  Probably get some sort of overflow ;-)

On Fri, Jun 24, 2016 at 9:36 AM, Art Kendall [via SPSSX Discussion] <[hidden email]> wrote:

Alas, sometimes we have no control over the quality of the measurement process and we end up with such a coarse measurement of happiness.

Art Kendall
Social Research Consultants

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[Greg]

Thank you for the very helpful comment! Turns out the contrasts were all over the place, along with a dummy variable coded differently from what I thought it was.

Upon fixing the above, I was able to get similar results with yours. Again, thank you.

Greg

[Greg]

Thank you everyone for your help and very helpful comments!

Greg