Nominal Depndent with Ordinal Independent

[dr_msantu]

I have
1) a dependent ordinal variable with 4 groups (low inadequate, high inadequate, adequate and excess)
2) a nominal dependent variable with 2 groups (normal and abnormal)
3) sample size 87
4) one cell value less than 5.
I am using SPSS 20. Can anyone tell what test I should do - parametric/non-parametric ? If Parametric whether I have to do Exact Fisher test or not ?

[Bruce Weaver]

You've identified both variables as dependent (points 1 and 2 below).  Given that Group is often an explanatory variable, I guess you meant to say group is the independent variable.  If so, you could use the linear-by-linear chi-square test in the output from CROSSTABS.  For more info, see this note by Dave Howell:

  http://www.uvm.edu/~dhowell/methods7/Supplements/OrdinalChiSq.html

HTH.

dr_msantu wrote

I have
1) a dependent ordinal variable with 4 groups (low inadequate, high inadequate, adequate and excess)
2) a nominal dependent variable with 2 groups (normal and abnormal)
3) sample size 87
4) one cell value less than 5.
I am using SPSS 20. Can anyone tell what test I should do - parametric/non-parametric ? If Parametric whether I have to do Exact Fisher test or not ?

[dr_msantu]

Sorry for my typing mistake. Actually I have an independent variable with 4 categories (low inadequate, high inadequate, adequate and excess).

I have another independent variable with 4 categories (underweight, normal weight, overweight and obese).

I used chi-square followed by binary logistic regression with these variables. I want to know how can I detect multicollinearity between these two categorical independent variable?

[Art Kendall]

What is the construct behind the first independent variable, i.e., the one with (low inadequate, high inadequate, adequate and excess) as values.

Your situation is still unclear.

Are you trying to to predict one or more other variables from these? Or are you just interested in the relation of these two ordinal and even possibly interval level variables?
What are those variables?  What are the values they can have? 

multicollinearity is usually a consideration when using variables as independent in a general linear model like regression.
On 4/1/2013 10:24 AM, dr_msantu [via SPSSX Discussion] wrote:

Sorry for my typing mistake. Actually I have an independent variable with 4 categories (low inadequate, high inadequate, adequate and excess).

I have another independent variable with 4 categories (underweight, normal weight, overweight and obese).

I used chi-square followed by binary logistic regression with these variables. I want to know how can I detect multicollinearity between these two categorical independent variable?

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[Bruce Weaver]

Art asks about the first independent variable. For the second, it appears you are using BMI categories.  If you have the actual BMI, why not just analyze it as a continuous variable?  After all, the cut-points used to form categories are somewhat arbitrary, and using categories throws away information and uses up degrees of freedom.  

But, to address the question about assessing multicollinearity when one has indicator variables for categorical variables, you could take a look at the generalized variance inflation factor (GVIF).  E.g., see section 3.1 in the notes found here:

   http://rbakker.myweb.uga.edu/week10.7014.2008.pdf

HTH.

Art Kendall wrote

What is the construct behind the first independent variable,
      i.e., the one with (low inadequate, high inadequate, adequate and
      excess) as values.
     
      Your situation is still unclear.
     
      Are you trying to to predict one or more other variables from
      these? Or are you just interested in the relation of these two
      ordinal and even possibly interval level variables?
      What are those variables?  What are the values they can have? 
     
      multicollinearity is usually a consideration when using variables
      as independent in a general linear model like regression.
      Art Kendall
Social Research Consultants
      On 4/1/2013 10:24 AM, dr_msantu [via SPSSX Discussion] wrote:
   
     Sorry for my typing mistake. Actually I have an
      independent variable with 4 categories (low inadequate, high
      inadequate, adequate and excess).
     
     
      I have another independent variable with 4 categories
      (underweight, normal weight, overweight and obese).
     
     
      I used chi-square followed by binary logistic regression with
      these variables. I want to know how can I detect multicollinearity
      between these two categorical independent variable?
     
     
     
        If you reply to this email, your
          message will be added to the discussion below:
        http://spssx-discussion.1045642.n5.nabble.com/Nominal-Depndent-with-Ordinal-Independent-tp5718913p5719214.html 
     
     
        To start a new topic under SPSSX Discussion, email
        [hidden email] 
        To unsubscribe from SPSSX Discussion, click
          here .
        NAML

[dr_msantu]

My independent variables are:
1) BMI (Basal Metabolic Index) measured as continuous variable and also grouped into 4 categories: underweight, normal weight, overweight and obese as defined by WHO.
2) Gestational weight gain measured as continuous variable and grouped into 3 categories: inadequate, recommended and excess as defined by Institute of Medicine, 2009.
3) Maternal age measured as continuous variable in years.
4) Socioeconomic status in modified Kupuswamy scale as: lower, upper lower and lower middle.

My dependent variables are:
1) Birth weight (measured as continuous)
2) Birth weight category (low or normal)
3) Birth category (preterm or term)
4) Condition at birth (asphyxiated or normal)
5) Mode of delivery (caesarean or vaginal)
6) Maternal hypertension (present or not)
7) Maternal gestational diabetes (present or not)

I have used binary logistic regression for the above variables. How can I detect multicollinearity among my independent variables or is this at all possible in binary logistic regression.

[Ryan]

Click here for the answer:

 

http://www-01.ibm.com/support/docview.wss?uid=swg21476696

 

Ryan

On Sun, Apr 7, 2013 at 3:50 PM, dr_msantu <[hidden email]> wrote:

My independent variables are:
1) BMI (Basal Metabolic Index) measured as continuous variable and also
grouped into 4 categories: underweight, normal weight, overweight and obese
as defined by WHO.
2) Gestational weight gain measured as continuous variable and grouped into
3 categories: inadequate, recommended and excess as defined by Institute of
Medicine, 2009.
3) Maternal age measured as continuous variable in years.
4) Socioeconomic status in modified Kupuswamy scale as: lower, upper lower
and lower middle.

My dependent variables are:
1) Birth weight (measured as continuous)
2) Birth weight category (low or normal)
3) Birth category (preterm or term)
4) Condition at birth (asphyxiated or normal)
5) Mode of delivery (caesarean or vaginal)
6) Maternal hypertension (present or not)
7) Maternal gestational diabetes (present or not)

I have used binary logistic regression for the above variables. How can I
detect multicollinearity among my independent variables or is this at all
possible in binary logistic regression.




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[John McConnell-2]

Hi

 

I'll be in Cairo this week but checking mail as much as i can subject to the usual interventions; political, technical ... and other

 

Thanks

John

 

[Rich Ulrich]

Ryan gives a good reference for obtaining the multicollinearity stats.
For this set of IVs, it does not look like it should be a problem, so long
as you don't try putting into one analysis both ways of measuring
BMI or weight gain. 

Another problem might be the sample size, which you stated as N=87
in your first post.  A recommended standard for ordinary regression
is to have 10 (or twenty) cases for each d.f.  of predictor.  The similar
standard for for Logistic regression is to have 10 cases for each d.f.
in the *smaller* of the two outcome groups.  You meet that criterion
for whichever outcomes are pretty evenly split; otherwise, not.  And if
you use your categorical predictors as categories -- then, not.

You might "confirm" your LR analyses by seeing that their coefficients
are not too different from those of the similar OLS regression.  The
LR coefficients will become very extreme if the sample happens to
provide 100% separation for some prediction equation.  They will be
distorted to a lesser amount if the separation is near 100% and hinges
on just a couple of cases.  (This is a point that is somewhat subtle, and
is not well-recognized.)

--
Rich Ulrich

> Date: Sun, 7 Apr 2013 12:50:14 -0700

> From: [hidden email]
> Subject: Re: Nominal Depndent with Ordinal Independent
> To: [hidden email]
>
> My independent variables are:
> 1) BMI (Basal Metabolic Index) measured as continuous variable and also
> grouped into 4 categories: underweight, normal weight, overweight and obese
> as defined by WHO.
> 2) Gestational weight gain measured as continuous variable and grouped into
> 3 categories: inadequate, recommended and excess as defined by Institute of
> Medicine, 2009.
> 3) Maternal age measured as continuous variable in years.
> 4) Socioeconomic status in modified Kupuswamy scale as: lower, upper lower
> and lower middle.
>
> My dependent variables are:
> 1) Birth weight (measured as continuous)
> 2) Birth weight category (low or normal)
> 3) Birth category (preterm or term)
> 4) Condition at birth (asphyxiated or normal)
> 5) Mode of delivery (caesarean or vaginal)
> 6) Maternal hypertension (present or not)
> 7) Maternal gestational diabetes (present or not)
>
> I have used binary logistic regression for the above variables. How can I
> detect multicollinearity among my independent variables or is this at all
> possible in binary logistic regression.
>
> ...

[Bruce Weaver]

Here's a nice readable article that speaks to Rich's point about "over-fitting" your models.  

  http://people.duke.edu/~mababyak/papers/babyakregression.pdf

For logistic regression, that 10 events-per variable (EPV) is a bare minimum in the simulations by Peduzzi et al (cited in the article above).  IIRC, Babyak (and Frank Harrell) suggest that 15 or 20 EPV is better.

Re linear regression, here are some comments from Dave Howell's popular textbook.  

  http://www.angelfire.com/wv/bwhomedir/notes/linreg_rule_of_thumb.txt

HTH.

Rich Ulrich-2 wrote

Ryan gives a good reference for obtaining the multicollinearity stats.
For this set of IVs, it does not look like it should be a problem, so long
as you don't try putting into one analysis both ways of measuring
BMI or weight gain.  

Another problem might be the sample size, which you stated as N=87
in your first post.  A recommended standard for ordinary regression
is to have 10 (or twenty) cases for each d.f.  of predictor.  The similar
standard for for Logistic regression is to have 10 cases for each d.f.
in the *smaller* of the two outcome groups.  You meet that criterion
for whichever outcomes are pretty evenly split; otherwise, not.  And if
you use your categorical predictors as categories -- then, not.

You might "confirm" your LR analyses by seeing that their coefficients
are not too different from those of the similar OLS regression.  The
LR coefficients will become very extreme if the sample happens to
provide 100% separation for some prediction equation.  They will be
distorted to a lesser amount if the separation is near 100% and hinges
on just a couple of cases.  (This is a point that is somewhat subtle, and
is not well-recognized.)

--
Rich Ulrich

> Date: Sun, 7 Apr 2013 12:50:14 -0700
> From: [hidden email]
> Subject: Re: Nominal Depndent with Ordinal Independent
> To: [hidden email]
>
> My independent variables are:
> 1) BMI (Basal Metabolic Index) measured as continuous variable and also
> grouped into 4 categories: underweight, normal weight, overweight and obese
> as defined by WHO.
> 2) Gestational weight gain measured as continuous variable and grouped into
> 3 categories: inadequate, recommended and excess as defined by Institute of
> Medicine, 2009.
> 3) Maternal age measured as continuous variable in years.
> 4) Socioeconomic status in modified Kupuswamy scale as: lower, upper lower
> and lower middle.
>
> My dependent variables are:
> 1) Birth weight (measured as continuous)
> 2) Birth weight category (low or normal)
> 3) Birth category (preterm or term)
> 4) Condition at birth (asphyxiated or normal)
> 5) Mode of delivery (caesarean or vaginal)
> 6) Maternal hypertension (present or not)
> 7) Maternal gestational diabetes (present or not)
>
> I have used binary logistic regression for the above variables. How can I
> detect multicollinearity among my independent variables or is this at all
> possible in binary logistic regression.
>
> ...

[John McConnell-2]

Hi

 

I'll be in Cairo this week but checking mail as much as i can

 

Thanks

John

 

[Tierney, Mary Lou]

I am out of the office 4/8-16/13.  I will respond to email when I return to the office.

 

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[Bruce Weaver]

I don't think the approach described there is ideal for categorical variables.  This excerpt from John Fox's book (2008, p. 322) explains why.

--- Beginning of excerpt from Fox (2008) ---

The correlations among a set of dummy regressors are affected by the choice of baseline category.  Similarly, the correlations among a set of polynomial regressors in an explanatory variable X are affected by adding a constant to the X values.  Neither of these changes alters the fit of the model to the data, however, so neither is fundamental.  It is indeed always possible to select an orthogonal basis for dummy-regressor or polynomial-regressor subspace (although such a basis does not employ dummy variables or simple powers of X).  What is at issue is the subspace itself and not the arbitrarily chosen basis for it.

We are not concerned, therefore, with the "artificial" collinearity among dummy regressors or polynomial regressors in the same set.  We are instead interested in the relationships between the subspaces generated to represent the effects of different explanatory variables.

--- End of excerpt from Fox (2008) ---

He then goes on to discuss the generalized variance inflation factor (GVIF), which does handle dummy- and polynomial-regressors appropriately.  Earlier in the thread, I pointed to section 3.1 in the notes found here for a brief description of GVIF:

   http://rbakker.myweb.uga.edu/week10.7014.2008.pdf

HTH.

Subscribe SAS-L Anonymous-2 wrote

Click here for the answer:

http://www-01.ibm.com/support/docview.wss?uid=swg21476696

Ryan


On Sun, Apr 7, 2013 at 3:50 PM, dr_msantu <[hidden email]> wrote:

> My independent variables are:
> 1) BMI (Basal Metabolic Index) measured as continuous variable and also
> grouped into 4 categories: underweight, normal weight, overweight and obese
> as defined by WHO.
> 2) Gestational weight gain measured as continuous variable and grouped into
> 3 categories: inadequate, recommended and excess as defined by Institute of
> Medicine, 2009.
> 3) Maternal age measured as continuous variable in years.
> 4) Socioeconomic status in modified Kupuswamy scale as: lower, upper lower
> and lower middle.
>
> My dependent variables are:
> 1) Birth weight (measured as continuous)
> 2) Birth weight category (low or normal)
> 3) Birth category (preterm or term)
> 4) Condition at birth (asphyxiated or normal)
> 5) Mode of delivery (caesarean or vaginal)
> 6) Maternal hypertension (present or not)
> 7) Maternal gestational diabetes (present or not)
>
> I have used binary logistic regression for the above variables. How can I
> detect multicollinearity among my independent variables or is this at all
> possible in binary logistic regression.
>
>
>
>
> --
> View this message in context:
> http://spssx-discussion.1045642.n5.nabble.com/Nominal-Depndent-with-Ordinal-Independent-tp5718913p5719310.html
> Sent from the SPSSX Discussion mailing list archive at Nabble.com.
>
> =====================
> 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
>

[Ryan]

Bruce,

 

I don't recall the OP stating that categorical predictors were included. I guess I missed it. Nonetheless, the excerpt is interesting.

 

Best,

 

Ryan

On Mon, Apr 8, 2013 at 9:00 AM, Bruce Weaver <[hidden email]> wrote:

I don't think the approach described there is ideal for categorical
variables.  This excerpt from John Fox's book (2008, p. 322) explains why.

--- Beginning of excerpt from Fox (2008) ---

The correlations among a set of dummy regressors are affected by the choice
of baseline category.  Similarly, the correlations among a set of polynomial
regressors in an explanatory variable X are affected by adding a constant to
the X values.  Neither of these changes alters the fit of the model to the
data, however, so neither is fundamental.  It is indeed always possible to
select an orthogonal basis for dummy-regressor or polynomial-regressor
subspace (although such a basis does not employ dummy variables or simple
powers of X).  What is at issue is the subspace itself and not the
arbitrarily chosen basis for it.

We are not concerned, therefore, with the "artificial" collinearity among
dummy regressors or polynomial regressors in the same set.  We are instead
interested in the relationships between the subspaces generated to represent
the effects of /different/ explanatory variables.

--- End of excerpt from Fox (2008) ---

He then goes on to discuss the generalized variance inflation factor (GVIF),
which does handle dummy- and polynomial-regressors appropriately.  Earlier
in the thread, I pointed to section 3.1 in the notes found here for a brief
description of GVIF:

   http://rbakker.myweb.uga.edu/week10.7014.2008.pdf

HTH.



Subscribe SAS-L Anonymous-2 wrote

> Click here for the answer:
>
> http://www-01.ibm.com/support/docview.wss?uid=swg21476696
>
> Ryan
>
>
> On Sun, Apr 7, 2013 at 3:50 PM, dr_msantu <

> drmsantu00@

> > wrote:
>
>> My independent variables are:
>> 1) BMI (Basal Metabolic Index) measured as continuous variable and also
>> grouped into 4 categories: underweight, normal weight, overweight and
>> obese
>> as defined by WHO.
>> 2) Gestational weight gain measured as continuous variable and grouped
>> into
>> 3 categories: inadequate, recommended and excess as defined by Institute
>> of
>> Medicine, 2009.
>> 3) Maternal age measured as continuous variable in years.
>> 4) Socioeconomic status in modified Kupuswamy scale as: lower, upper
>> lower
>> and lower middle.
>>
>> My dependent variables are:
>> 1) Birth weight (measured as continuous)
>> 2) Birth weight category (low or normal)
>> 3) Birth category (preterm or term)
>> 4) Condition at birth (asphyxiated or normal)
>> 5) Mode of delivery (caesarean or vaginal)
>> 6) Maternal hypertension (present or not)
>> 7) Maternal gestational diabetes (present or not)
>>
>> I have used binary logistic regression for the above variables. How can I
>> detect multicollinearity among my independent variables or is this at all
>> possible in binary logistic regression.
>>
>>
>>
>>
>> --
>> View this message in context:
>> http://spssx-discussion.1045642.n5.nabble.com/Nominal-Depndent-with-Ordinal-Independent-tp5718913p5719310.html
>> Sent from the SPSSX Discussion mailing list archive at Nabble.com.
>>
>> =====================
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>>

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-----
--
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"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.

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[John McConnell-2]

Hi

 

I'll be out of the office until the afternoon of Friday 8th April but checking mail as much as i can

 

Thanks

John

 

[dr_msantu]

My full sample size is 308.

I am still confused regarding the detection of multicollinearity among the variables of my data set. I could not find the wright answer.

Is there any method by which I can adjust age or socioeconomic status (so that I can detect whether BMI or gestational weight gain can affect pregnancy outcome independent of age and socioeconmic status)?

[Cheryl Boglarsky]

I will be out of the office until Monday, April 15, 2013, with no access to email. However, please know that your message is very important to me and I will respond when I return.

 

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Thank you.

 

Sincerely,

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_____________________________________________________

Cheryl A. Boglarsky, Ph.D.

Human Synergistics, Inc.

39819 Plymouth Road

Plymouth, MI 48170

734.459.1030

[hidden email] 

 

 

This message includes legally privileged and confidential information that is intended only for the use of the recipient named above. All readers of this message, other than the intended recipient, are hereby notified that any dissemination, modification, distribution or reproduction of this e-mail is strictly forbidden.

[Kylie]

I am currently attending a course interstate and will return on Monday April 15th. I will respond to your email as soon as possible after my return.

Thank you.

[Ryan]

When reviewing the website I sent you (you are welcome BTW), Rich and Bruce's responses, the regression book from which you were taught, and an extensive literature search on the matter, what answer(s) did you find?

Ryan

On Apr 10, 2013, at 4:06 AM, dr_msantu <[hidden email]> wrote:

> My full sample size is 308.
>
> I am still confused regarding the detection of multicollinearity among the
> variables of my data set. I could not find the wright answer.
>
> Is there any method by which I can adjust age or socioeconomic status (so
> that I can detect whether BMI or gestational weight gain can affect
> pregnancy outcome independent of age and socioeconmic status)?
>
>
>
> --
> View this message in context: http://spssx-discussion.1045642.n5.nabble.com/Nominal-Depndent-with-Ordinal-Independent-tp5718913p5719374.html
> Sent from the SPSSX Discussion mailing list archive at Nabble.com.
>
> =====================
> 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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[dr_msantu]

You have correctly identified my problem. I think I should not try to
found "multicollinearity" in logistic regression, rather I should
concentrate on "confounding". I am very much thankful to all of you
for making such thorough discussion regarding "multicollinearity",
which helped me a lot. I have two more questions:

1) Is my sample size (308) is adequate enough for this kind of binary
logistic analysis.

2) I have run the binary logistic regression with BMI
category(ordinal), Gestational weight gain category(ordinal),
age(continuous) and socioeconomic status(ordinal) as independent
variable for my dichotomous dependent variable (such as LBW and NBW).
I used SPSS 20.

I found that age was not significantly associated as p >0.05 and
change of coefficient is minimum (for underweight BMI it cganged to
1.182 from 1.181.

But, when I run with socioeconomic status the change of coefficient is
much more and it is also statistically significant p < 0.05.

From these may I conclude that socioeconomic status is correlated with
BMI and Wgain ?. If the confounding factor is present I could I make
adjustment for this?

On 10/04/2013, Rich Ulrich <[hidden email]> wrote:

> I think you are concerned more with what is usually discussed as
> "confounding" rather than as "multicollinearity."
>
> Originally - and still, sometimes - multicollinearity refers to
> what you get, say, when you use 3 dummy variables to code
> three categories.  Or you include a set of items along with their
> total score.  That is, you have redundancy, and the computer
> algorithms will choke and fail when they try to divide by zero
> (or, allowing for round-off, too near to zero).
>
> The usual extended version of concern with multicollinearity arises
> when there is near-redundancy, and this results in "variance inflation"
> for the predictors.  That is:  if your best predictor is equal parts of A
> and B, scaled the same, then when A and B are too similar, you will
> find that  (0.9*A+ 0.1*B)  is practically the same as (0.1*A+ 0.9*B) ...
> Then, even if A and B separately have small CIs on their coefficients,
> the combined regression will show large CIs on whatever the coefficients
> come out as.  That is the variance inflation.  (One simple solution that
> sometimes works great is to replace predictors [A, B]  with the orthogonal
> pair [(A+B), (A-B)].  YMMV.)
>
> If you want to know whether Age and SES change the partial-associations
> seen for BMI and WGain, the simple answer is the direct one:  Do it.
> Run an analysis of outcome for BMI and WGain;  run another analysis for
> BMI and WGain that controls for the demographics.  Do the coefficients
> change?
>
> If the demographic variables are not correlated with BMI and WGain, there
> will be no change.  If correlated, there may or may not be change.  It is
> possible for the coefficients to the same while the tests become more
> significant.  It is appropriate, in the discussion of results, to comment on
>
> whether there was much reason to expect confounding.  Is either BMI or
> WGain associated with age or SES?  If they are not associated even a little
> bit, then there is confounding possible.  But it does not require a huge
> association for some confounding to show its effect, if that is merely
> shifting
> a p-value from 0.051 to 0.049.
>
> --
> Rich Ulrich
>
>> Date: Wed, 10 Apr 2013 01:06:21 -0700
>> From: [hidden email]
>> Subject: Re: Nominal Depndent with Ordinal Independent
>> To: [hidden email]
>>
>> My full sample size is 308.
>>
>> I am still confused regarding the detection of multicollinearity among
>> the
>> variables of my data set. I could not find the wright answer.
>>
>> Is there any method by which I can adjust age or socioeconomic status (so
>> that I can detect whether BMI or gestational weight gain can affect
>> pregnancy outcome independent of age and socioeconmic status)?
>>
>>
>> ...
>

=====================
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