Ordinal Regression Question

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Ordinal Regression Question

Vik Rubenfeld
I've done an Ordinal Regression using the following syntax.

PLUM CQIA9all BY CQIA5_1 CQIA5_2 CQIA5_3 CQIA5_4 CQIA5_5 CQIA5_6 CQIA5_7 CQIA6_6 CQIA6_8 CQIA6_13 CQIA6_16 CQIA6_17 CQIA6_19
  /CRITERIA=CIN(95) DELTA(0) LCONVERGE(0) MXITER(100) MXSTEP(5) PCONVERGE(1.0E-6) SINGULAR(1.0E-8)
  /LINK=LOGIT
  /PRINT=FIT PARAMETER SUMMARY TPARALLEL
  /SAVE=PREDCAT.

Results were excellent, with many statistically significant estimates. The test of parallel lines is not significant.

I  have a question regarding the estimates. In this data set, the dependent variable is a purchase-interest-related action, and is coded as:

0 = YES
1 = NO

Favorable attributes (e.g. "I want to go to the store to see the product") therefore would be expected to have negative parameter estimates. And in my results, in most cases, they do.

However, there is one attribute ("smart") which has a small positive parameter estimate of 0.16.  I cross-tabbed "smart" with the presence of the purchase-interest-related action, and as expected, those who consider the product to be "smart" are *more* likely to take the purchase-interest-related action.

So my question is, why does this attribute have a positive, rather than a negative, parameter estimate?

Thanks very much in advance to all for any info.

Best,


-Vik

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Re: Ordinal Regression Question

Bruce Weaver
Administrator
Hi Vik.  I have a couple questions.  

1. If your dependent variable is dichotomous, why are you not using binary logistic regression?

2. How many categories are there for your explanatory variables?

3. How many "events" do you have (with "event" defined as the lower frequency category for your dependent variable)?

Questions 2 and 3 are getting at whether you are over-fitting your model.  A rough rule of thumb suggests you need 15-20 events per parameter if you want to avoid over-fitting (for binary logistic regression).

Re your question about why a coefficient does not have the expected sign, bear in mind that you are looking at partial effects.  I.e., the coefficient for a particular variable depends on what other variables are in the model.  If your library has it, take a look at chapter 13 (Woes of Regression Coefficients) in the Mosteller & Tukey classic, "Data Analysis and Regression: A Second Course in Statistics".  The same point is discussed here:

   http://bulletin.imstat.org/2012/07/terences-stuff-multiple-linear-regression-1/

HTH.

Vik Rubenfeld wrote
I've done an Ordinal Regression using the following syntax.

PLUM CQIA9all BY CQIA5_1 CQIA5_2 CQIA5_3 CQIA5_4 CQIA5_5 CQIA5_6 CQIA5_7 CQIA6_6 CQIA6_8 CQIA6_13 CQIA6_16 CQIA6_17 CQIA6_19
  /CRITERIA=CIN(95) DELTA(0) LCONVERGE(0) MXITER(100) MXSTEP(5) PCONVERGE(1.0E-6) SINGULAR(1.0E-8)
  /LINK=LOGIT
  /PRINT=FIT PARAMETER SUMMARY TPARALLEL
  /SAVE=PREDCAT.

Results were excellent, with many statistically significant estimates. The test of parallel lines is not significant.

I  have a question regarding the estimates. In this data set, the dependent variable is a purchase-interest-related action, and is coded as:

0 = YES
1 = NO

Favorable attributes (e.g. "I want to go to the store to see the product") therefore would be expected to have negative parameter estimates. And in my results, in most cases, they do.

However, there is one attribute ("smart") which has a small positive parameter estimate of 0.16.  I cross-tabbed "smart" with the presence of the purchase-interest-related action, and as expected, those who consider the product to be "smart" are *more* likely to take the purchase-interest-related action.

So my question is, why does this attribute have a positive, rather than a negative, parameter estimate?

Thanks very much in advance to all for any info.

Best,


-Vik

=====================
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
--
Bruce Weaver
bweaver@lakeheadu.ca
http://sites.google.com/a/lakeheadu.ca/bweaver/

"When all else fails, RTFM."

PLEASE NOTE THE FOLLOWING: 
1. My Hotmail account is not monitored regularly. To send me an e-mail, please use the address shown above.
2. The SPSSX Discussion forum on Nabble is no longer linked to the SPSSX-L listserv administered by UGA (https://listserv.uga.edu/).
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Re: Ordinal Regression Question

Vik Rubenfeld
Hi Bruce,

Thanks for your feedback.

> 1. If your dependent variable is dichotomous, why are you not using binary
> logistic regression?

The articles I read didn't state that one could not use a dichotomous dependent variable with ordinal regression. As dichotomous variables may be considered a special case of ordinal variables, I have been using ordinal regression. However, I am happy to use binary logistic regression if that is appropriate.

> 2. How many categories are there for your explanatory variables?

Seven explanatory variables have 5 categories each ("Strongly agree" to "Strongly disagree"). An additional 20 explanatory variables are dichotomous ("Yes" or "No").

> 3. How many "events" do you have (with "event" defined as the lower
> frequency category for your dependent variable)?

The dependent variable is dichotomous ("Yes" or "No").

> Questions 2 and 3 are getting at whether you are over-fitting your model.  A
> rough rule of thumb suggests you need 15-20 events per parameter if you want
> to avoid over-fitting (for binary logistic regression).

I am currently using ordinal regression rather than binary logistic regression. However, I am happy to use binary logistic regression if that is appropriate.

Would binary logistic regression indeed be more appropriate in this case, given that the explanatory variables have fewer than than 15-20 events per parameter?

Thanks very much in advance for your advice, and for the link to the excellent article from IMS Bulletin.

Best,


-Vik


On Oct 16, 2012, at 4:33 AM, Bruce Weaver wrote:

> Hi Vik.  I have a couple questions.
>
> 1. If your dependent variable is dichotomous, why are you not using binary
> logistic regression?
>
> 2. How many categories are there for your explanatory variables?
>
> 3. How many "events" do you have (with "event" defined as the lower
> frequency category for your dependent variable)?
>
> Questions 2 and 3 are getting at whether you are over-fitting your model.  A
> rough rule of thumb suggests you need 15-20 events per parameter if you want
> to avoid over-fitting (for binary logistic regression).
>
> Re your question about why a coefficient does not have the expected sign,
> bear in mind that you are looking at partial effects.  I.e., the coefficient
> for a particular variable depends on what other variables are in the model.
> If your library has it, take a look at chapter 13 (Woes of Regression
> Coefficients) in the Mosteller & Tukey classic, "Data Analysis and
> Regression: A Second Course in Statistics".  The same point is discussed
> here:
>
>
> http://bulletin.imstat.org/2012/07/terences-stuff-multiple-linear-regression-1/
>
> HTH.
>
>
> Vik Rubenfeld wrote
>> I've done an Ordinal Regression using the following syntax.
>>
>> PLUM CQIA9all BY CQIA5_1 CQIA5_2 CQIA5_3 CQIA5_4 CQIA5_5 CQIA5_6 CQIA5_7
>> CQIA6_6 CQIA6_8 CQIA6_13 CQIA6_16 CQIA6_17 CQIA6_19
>>  /CRITERIA=CIN(95) DELTA(0) LCONVERGE(0) MXITER(100) MXSTEP(5)
>> PCONVERGE(1.0E-6) SINGULAR(1.0E-8)
>>  /LINK=LOGIT
>>  /PRINT=FIT PARAMETER SUMMARY TPARALLEL
>>  /SAVE=PREDCAT.
>>
>> Results were excellent, with many statistically significant estimates. The
>> test of parallel lines is not significant.
>>
>> I  have a question regarding the estimates. In this data set, the
>> dependent variable is a purchase-interest-related action, and is coded as:
>>
>> 0 = YES
>> 1 = NO
>>
>> Favorable attributes (e.g. "I want to go to the store to see the product")
>> therefore would be expected to have negative parameter estimates. And in
>> my results, in most cases, they do.
>>
>> However, there is one attribute ("smart") which has a small positive
>> parameter estimate of 0.16.  I cross-tabbed "smart" with the presence of
>> the purchase-interest-related action, and as expected, those who consider
>> the product to be "smart" are *more* likely to take the
>> purchase-interest-related action.
>>
>> So my question is, why does this attribute have a positive, rather than a
>> negative, parameter estimate?
>>
>> Thanks very much in advance to all for any info.
>>
>> Best,
>>
>>
>> -Vik
>>
>> =====================
>> To manage your subscription to SPSSX-L, send a message to
>
>> LISTSERV@.UGA
>
>> (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
>
>
>
>
>
> -----
> --
> 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/Ordinal-Regression-Question-tp5715664p5715667.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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Re: Ordinal Regression Question

Bruce Weaver
Administrator
See below.

Vik Rubenfeld wrote
Hi Bruce,

Thanks for your feedback.

> 1. If your dependent variable is dichotomous, why are you not using binary
> logistic regression?

The articles I read didn't state that one could not use a dichotomous dependent variable with ordinal regression. As dichotomous variables may be considered a special case of ordinal variables, I have been using ordinal regression. However, I am happy to use binary logistic regression if that is appropriate.


BW:  I suspect that PLUM and LOGISTIC REGRESSION (and NOMREG and GENLIN using a logit link and binomial error distribution) will give the same result when the dependent variable is dichotomous.  (The only differences might be due to which category is treated as the reference category.)


> 2. How many categories are there for your explanatory variables?

Seven explanatory variables have 5 categories each ("Strongly agree" to "Strongly disagree"). An additional 20 explanatory variables are dichotomous ("Yes" or "No").


BW:  When you treat the 5-category variables as factors, each one eats up 4 degrees of freedom.  And each dichotomous variable eats 1 df.  So with all those variables in the model, you have 41 parameters to estimate (including the constant).  That means you should have about 600 "events" where an event is either a Yes or No response to the DV (whichever has the lower frequency count over all cases).  What is your total N, how many have DV=Yes and DV=No?


> 3. How many "events" do you have (with "event" defined as the lower
> frequency category for your dependent variable)?

The dependent variable is dichotomous ("Yes" or "No").

BW:  What I meant was that if there are fewer YES than NO responses, then an event = a YES response.  Or if there are fewer NO than YES responses, event = a NO response.


> Questions 2 and 3 are getting at whether you are over-fitting your model.  A
> rough rule of thumb suggests you need 15-20 events per parameter if you want
> to avoid over-fitting (for binary logistic regression).

I am currently using ordinal regression rather than binary logistic regression. However, I am happy to use binary logistic regression if that is appropriate.

Would binary logistic regression indeed be more appropriate in this case, given that the explanatory variables have fewer than than 15-20 events per parameter?

BW:  As noted above, you'll get the same results.


Thanks very much in advance for your advice, and for the link to the excellent article from IMS Bulletin.

Best,


-Vik

BW:  Here's another one you might find interesting:

http://os1.amc.nl/mediawiki/images/Babyak_-_overfitting.pdf

HTH.


On Oct 16, 2012, at 4:33 AM, Bruce Weaver wrote:

> Hi Vik.  I have a couple questions.
>
> 1. If your dependent variable is dichotomous, why are you not using binary
> logistic regression?
>
> 2. How many categories are there for your explanatory variables?
>
> 3. How many "events" do you have (with "event" defined as the lower
> frequency category for your dependent variable)?
>
> Questions 2 and 3 are getting at whether you are over-fitting your model.  A
> rough rule of thumb suggests you need 15-20 events per parameter if you want
> to avoid over-fitting (for binary logistic regression).
>
> Re your question about why a coefficient does not have the expected sign,
> bear in mind that you are looking at partial effects.  I.e., the coefficient
> for a particular variable depends on what other variables are in the model.
> If your library has it, take a look at chapter 13 (Woes of Regression
> Coefficients) in the Mosteller & Tukey classic, "Data Analysis and
> Regression: A Second Course in Statistics".  The same point is discussed
> here:
>
>
> http://bulletin.imstat.org/2012/07/terences-stuff-multiple-linear-regression-1/
>
> HTH.
>
>
> Vik Rubenfeld wrote
>> I've done an Ordinal Regression using the following syntax.
>>
>> PLUM CQIA9all BY CQIA5_1 CQIA5_2 CQIA5_3 CQIA5_4 CQIA5_5 CQIA5_6 CQIA5_7
>> CQIA6_6 CQIA6_8 CQIA6_13 CQIA6_16 CQIA6_17 CQIA6_19
>>  /CRITERIA=CIN(95) DELTA(0) LCONVERGE(0) MXITER(100) MXSTEP(5)
>> PCONVERGE(1.0E-6) SINGULAR(1.0E-8)
>>  /LINK=LOGIT
>>  /PRINT=FIT PARAMETER SUMMARY TPARALLEL
>>  /SAVE=PREDCAT.
>>
>> Results were excellent, with many statistically significant estimates. The
>> test of parallel lines is not significant.
>>
>> I  have a question regarding the estimates. In this data set, the
>> dependent variable is a purchase-interest-related action, and is coded as:
>>
>> 0 = YES
>> 1 = NO
>>
>> Favorable attributes (e.g. "I want to go to the store to see the product")
>> therefore would be expected to have negative parameter estimates. And in
>> my results, in most cases, they do.
>>
>> However, there is one attribute ("smart") which has a small positive
>> parameter estimate of 0.16.  I cross-tabbed "smart" with the presence of
>> the purchase-interest-related action, and as expected, those who consider
>> the product to be "smart" are *more* likely to take the
>> purchase-interest-related action.
>>
>> So my question is, why does this attribute have a positive, rather than a
>> negative, parameter estimate?
>>
>> Thanks very much in advance to all for any info.
>>
>> Best,
>>
>>
>> -Vik
>>
>> =====================
>> To manage your subscription to SPSSX-L, send a message to
>
>> LISTSERV@.UGA
>
>> (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
>
>
>
>
>
> -----
> --
> 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/Ordinal-Regression-Question-tp5715664p5715667.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

=====================
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
--
Bruce Weaver
bweaver@lakeheadu.ca
http://sites.google.com/a/lakeheadu.ca/bweaver/

"When all else fails, RTFM."

PLEASE NOTE THE FOLLOWING: 
1. My Hotmail account is not monitored regularly. To send me an e-mail, please use the address shown above.
2. The SPSSX Discussion forum on Nabble is no longer linked to the SPSSX-L listserv administered by UGA (https://listserv.uga.edu/).
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Re: Ordinal Regression Question

Vik Rubenfeld
Hi Bruce,

> BW:  When you treat the 5-category variables as factors, each one eats up
> 4 degrees of freedom.  And each dichotomous variable eats 1 df.  So with
> all those variables in the model, you have 41 parameters to estimate
> (including the constant).  That means you should have about 600 "events"
> where an event is either a Yes or No response to the DV (whichever has the
> lower frequency count over all cases).  What is your total N, how many
> have DV=Yes and DV=No?


For my training data set, total N = 4640 observations. DV=YES for 2173 observations, and DV=NO for 2467 observations. So, there are fewer YES responses in the DV. It may be helpful for me to note that after reviewing initial results I reduced the total explanatory variables to 13 (7 with 5 categories, and 6 dichotomous).

I really appreciate your advice and look forward to hearing your thoughts.

Best,


-Vik


On Oct 16, 2012, at 12:02 PM, Bruce Weaver wrote:

> See below.
>
>
> Vik Rubenfeld wrote
>> Hi Bruce,
>>
>> Thanks for your feedback.
>>
>>> 1. If your dependent variable is dichotomous, why are you not using
>>> binary
>>> logistic regression?
>>
>> The articles I read didn't state that one could not use a dichotomous
>> dependent variable with ordinal regression. As dichotomous variables may
>> be considered a special case of ordinal variables, I have been using
>> ordinal regression. However, I am happy to use binary logistic regression
>> if that is appropriate.
>>
>>
>> BW:  I suspect that PLUM and LOGISTIC REGRESSION (and NOMREG and GENLIN
>> using a logit link and binomial error distribution) will give the same
>> result when the dependent variable is dichotomous.  (The only differences
>> might be due to which category is treated as the reference category.)
>>
>>
>>> 2. How many categories are there for your explanatory variables?
>>
>> Seven explanatory variables have 5 categories each ("Strongly agree" to
>> "Strongly disagree"). An additional 20 explanatory variables are
>> dichotomous ("Yes" or "No").
>>
>>
>> BW:  When you treat the 5-category variables as factors, each one eats up
>> 4 degrees of freedom.  And each dichotomous variable eats 1 df.  So with
>> all those variables in the model, you have 41 parameters to estimate
>> (including the constant).  That means you should have about 600 "events"
>> where an event is either a Yes or No response to the DV (whichever has the
>> lower frequency count over all cases).  What is your total N, how many
>> have DV=Yes and DV=No?
>>
>>
>>> 3. How many "events" do you have (with "event" defined as the lower
>>> frequency category for your dependent variable)?
>>
>> The dependent variable is dichotomous ("Yes" or "No").
>>
>> BW:  What I meant was that if there are fewer YES than NO responses, then
>> an event = a YES response.  Or if there are fewer NO than YES responses,
>> event = a NO response.
>>
>>
>>> Questions 2 and 3 are getting at whether you are over-fitting your model.
>>> A
>>> rough rule of thumb suggests you need 15-20 events per parameter if you
>>> want
>>> to avoid over-fitting (for binary logistic regression).
>>
>> I am currently using ordinal regression rather than binary logistic
>> regression. However, I am happy to use binary logistic regression if that
>> is appropriate.
>>
>> Would binary logistic regression indeed be more appropriate in this case,
>> given that the explanatory variables have fewer than than 15-20 events per
>> parameter?
>>
>> BW:  As noted above, you'll get the same results.
>>
>>
>> Thanks very much in advance for your advice, and for the link to the
>> excellent article from IMS Bulletin.
>>
>> Best,
>>
>>
>> -Vik
>>
>> BW:  Here's another one you might find interesting:
>>
>> http://os1.amc.nl/mediawiki/images/Babyak_-_overfitting.pdf
>>
>> HTH.
>>
>>
>> On Oct 16, 2012, at 4:33 AM, Bruce Weaver wrote:
>>
>>> Hi Vik.  I have a couple questions.
>>>
>>> 1. If your dependent variable is dichotomous, why are you not using
>>> binary
>>> logistic regression?
>>>
>>> 2. How many categories are there for your explanatory variables?
>>>
>>> 3. How many "events" do you have (with "event" defined as the lower
>>> frequency category for your dependent variable)?
>>>
>>> Questions 2 and 3 are getting at whether you are over-fitting your model.
>>> A
>>> rough rule of thumb suggests you need 15-20 events per parameter if you
>>> want
>>> to avoid over-fitting (for binary logistic regression).
>>>
>>> Re your question about why a coefficient does not have the expected sign,
>>> bear in mind that you are looking at partial effects.  I.e., the
>>> coefficient
>>> for a particular variable depends on what other variables are in the
>>> model.
>>> If your library has it, take a look at chapter 13 (Woes of Regression
>>> Coefficients) in the Mosteller & Tukey classic, "Data Analysis and
>>> Regression: A Second Course in Statistics".  The same point is discussed
>>> here:
>>>
>>>
>>> http://bulletin.imstat.org/2012/07/terences-stuff-multiple-linear-regression-1/
>>>
>>> HTH.
>>>
>>>
>>> Vik Rubenfeld wrote
>>>> I've done an Ordinal Regression using the following syntax.
>>>>
>>>> PLUM CQIA9all BY CQIA5_1 CQIA5_2 CQIA5_3 CQIA5_4 CQIA5_5 CQIA5_6 CQIA5_7
>>>> CQIA6_6 CQIA6_8 CQIA6_13 CQIA6_16 CQIA6_17 CQIA6_19
>>>> /CRITERIA=CIN(95) DELTA(0) LCONVERGE(0) MXITER(100) MXSTEP(5)
>>>> PCONVERGE(1.0E-6) SINGULAR(1.0E-8)
>>>> /LINK=LOGIT
>>>> /PRINT=FIT PARAMETER SUMMARY TPARALLEL
>>>> /SAVE=PREDCAT.
>>>>
>>>> Results were excellent, with many statistically significant estimates.
>>>> The
>>>> test of parallel lines is not significant.
>>>>
>>>> I  have a question regarding the estimates. In this data set, the
>>>> dependent variable is a purchase-interest-related action, and is coded
>>>> as:
>>>>
>>>> 0 = YES
>>>> 1 = NO
>>>>
>>>> Favorable attributes (e.g. "I want to go to the store to see the
>>>> product")
>>>> therefore would be expected to have negative parameter estimates. And in
>>>> my results, in most cases, they do.
>>>>
>>>> However, there is one attribute ("smart") which has a small positive
>>>> parameter estimate of 0.16.  I cross-tabbed "smart" with the presence of
>>>> the purchase-interest-related action, and as expected, those who
>>>> consider
>>>> the product to be "smart" are *more* likely to take the
>>>> purchase-interest-related action.
>>>>
>>>> So my question is, why does this attribute have a positive, rather than
>>>> a
>>>> negative, parameter estimate?
>>>>
>>>> Thanks very much in advance to all for any info.
>>>>
>>>> Best,
>>>>
>>>>
>>>> -Vik
>>>>
>>>> =====================
>>>> To manage your subscription to SPSSX-L, send a message to
>>>
>>>> LISTSERV@.UGA
>>>
>>>> (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
>>>
>>>
>>>
>>>
>>>
>>> -----
>>> --
>>> Bruce Weaver
>>>
>
>> bweaver@
>
>>> 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/Ordinal-Regression-Question-tp5715664p5715667.html
>>> Sent from the SPSSX Discussion mailing list archive at Nabble.com.
>>>
>>> =====================
>>> To manage your subscription to SPSSX-L, send a message to
>>>
>
>> LISTSERV@.UGA
>
>> (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
>>
>> =====================
>> To manage your subscription to SPSSX-L, send a message to
>
>> LISTSERV@.UGA
>
>> (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
>
>
>
>
>
> -----
> --
> 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/Ordinal-Regression-Question-tp5715664p5715680.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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Re: Ordinal Regression Question

Bruce Weaver
Administrator
Okay, with over 2000 events, you have more than enough to avoid serious over-fitting of the model.

Re your comment on reducing the number of variables after reviewing initial results, notice what Babyak says about that in his article.  IIRC, he uses the term "phantom degrees of freedom", or something along those lines.

HTH.


Vik Rubenfeld wrote
Hi Bruce,

> BW:  When you treat the 5-category variables as factors, each one eats up
> 4 degrees of freedom.  And each dichotomous variable eats 1 df.  So with
> all those variables in the model, you have 41 parameters to estimate
> (including the constant).  That means you should have about 600 "events"
> where an event is either a Yes or No response to the DV (whichever has the
> lower frequency count over all cases).  What is your total N, how many
> have DV=Yes and DV=No?


For my training data set, total N = 4640 observations. DV=YES for 2173 observations, and DV=NO for 2467 observations. So, there are fewer YES responses in the DV. It may be helpful for me to note that after reviewing initial results I reduced the total explanatory variables to 13 (7 with 5 categories, and 6 dichotomous).

I really appreciate your advice and look forward to hearing your thoughts.

Best,


-Vik


On Oct 16, 2012, at 12:02 PM, Bruce Weaver wrote:

> See below.
>
>
> Vik Rubenfeld wrote
>> Hi Bruce,
>>
>> Thanks for your feedback.
>>
>>> 1. If your dependent variable is dichotomous, why are you not using
>>> binary
>>> logistic regression?
>>
>> The articles I read didn't state that one could not use a dichotomous
>> dependent variable with ordinal regression. As dichotomous variables may
>> be considered a special case of ordinal variables, I have been using
>> ordinal regression. However, I am happy to use binary logistic regression
>> if that is appropriate.
>>
>>
>> BW:  I suspect that PLUM and LOGISTIC REGRESSION (and NOMREG and GENLIN
>> using a logit link and binomial error distribution) will give the same
>> result when the dependent variable is dichotomous.  (The only differences
>> might be due to which category is treated as the reference category.)
>>
>>
>>> 2. How many categories are there for your explanatory variables?
>>
>> Seven explanatory variables have 5 categories each ("Strongly agree" to
>> "Strongly disagree"). An additional 20 explanatory variables are
>> dichotomous ("Yes" or "No").
>>
>>
>> BW:  When you treat the 5-category variables as factors, each one eats up
>> 4 degrees of freedom.  And each dichotomous variable eats 1 df.  So with
>> all those variables in the model, you have 41 parameters to estimate
>> (including the constant).  That means you should have about 600 "events"
>> where an event is either a Yes or No response to the DV (whichever has the
>> lower frequency count over all cases).  What is your total N, how many
>> have DV=Yes and DV=No?
>>
>>
>>> 3. How many "events" do you have (with "event" defined as the lower
>>> frequency category for your dependent variable)?
>>
>> The dependent variable is dichotomous ("Yes" or "No").
>>
>> BW:  What I meant was that if there are fewer YES than NO responses, then
>> an event = a YES response.  Or if there are fewer NO than YES responses,
>> event = a NO response.
>>
>>
>>> Questions 2 and 3 are getting at whether you are over-fitting your model.
>>> A
>>> rough rule of thumb suggests you need 15-20 events per parameter if you
>>> want
>>> to avoid over-fitting (for binary logistic regression).
>>
>> I am currently using ordinal regression rather than binary logistic
>> regression. However, I am happy to use binary logistic regression if that
>> is appropriate.
>>
>> Would binary logistic regression indeed be more appropriate in this case,
>> given that the explanatory variables have fewer than than 15-20 events per
>> parameter?
>>
>> BW:  As noted above, you'll get the same results.
>>
>>
>> Thanks very much in advance for your advice, and for the link to the
>> excellent article from IMS Bulletin.
>>
>> Best,
>>
>>
>> -Vik
>>
>> BW:  Here's another one you might find interesting:
>>
>> http://os1.amc.nl/mediawiki/images/Babyak_-_overfitting.pdf
>>
>> HTH.
>>
>>
>> On Oct 16, 2012, at 4:33 AM, Bruce Weaver wrote:
>>
>>> Hi Vik.  I have a couple questions.
>>>
>>> 1. If your dependent variable is dichotomous, why are you not using
>>> binary
>>> logistic regression?
>>>
>>> 2. How many categories are there for your explanatory variables?
>>>
>>> 3. How many "events" do you have (with "event" defined as the lower
>>> frequency category for your dependent variable)?
>>>
>>> Questions 2 and 3 are getting at whether you are over-fitting your model.
>>> A
>>> rough rule of thumb suggests you need 15-20 events per parameter if you
>>> want
>>> to avoid over-fitting (for binary logistic regression).
>>>
>>> Re your question about why a coefficient does not have the expected sign,
>>> bear in mind that you are looking at partial effects.  I.e., the
>>> coefficient
>>> for a particular variable depends on what other variables are in the
>>> model.
>>> If your library has it, take a look at chapter 13 (Woes of Regression
>>> Coefficients) in the Mosteller & Tukey classic, "Data Analysis and
>>> Regression: A Second Course in Statistics".  The same point is discussed
>>> here:
>>>
>>>
>>> http://bulletin.imstat.org/2012/07/terences-stuff-multiple-linear-regression-1/
>>>
>>> HTH.
>>>
>>>
>>> Vik Rubenfeld wrote
>>>> I've done an Ordinal Regression using the following syntax.
>>>>
>>>> PLUM CQIA9all BY CQIA5_1 CQIA5_2 CQIA5_3 CQIA5_4 CQIA5_5 CQIA5_6 CQIA5_7
>>>> CQIA6_6 CQIA6_8 CQIA6_13 CQIA6_16 CQIA6_17 CQIA6_19
>>>> /CRITERIA=CIN(95) DELTA(0) LCONVERGE(0) MXITER(100) MXSTEP(5)
>>>> PCONVERGE(1.0E-6) SINGULAR(1.0E-8)
>>>> /LINK=LOGIT
>>>> /PRINT=FIT PARAMETER SUMMARY TPARALLEL
>>>> /SAVE=PREDCAT.
>>>>
>>>> Results were excellent, with many statistically significant estimates.
>>>> The
>>>> test of parallel lines is not significant.
>>>>
>>>> I  have a question regarding the estimates. In this data set, the
>>>> dependent variable is a purchase-interest-related action, and is coded
>>>> as:
>>>>
>>>> 0 = YES
>>>> 1 = NO
>>>>
>>>> Favorable attributes (e.g. "I want to go to the store to see the
>>>> product")
>>>> therefore would be expected to have negative parameter estimates. And in
>>>> my results, in most cases, they do.
>>>>
>>>> However, there is one attribute ("smart") which has a small positive
>>>> parameter estimate of 0.16.  I cross-tabbed "smart" with the presence of
>>>> the purchase-interest-related action, and as expected, those who
>>>> consider
>>>> the product to be "smart" are *more* likely to take the
>>>> purchase-interest-related action.
>>>>
>>>> So my question is, why does this attribute have a positive, rather than
>>>> a
>>>> negative, parameter estimate?
>>>>
>>>> Thanks very much in advance to all for any info.
>>>>
>>>> Best,
>>>>
>>>>
>>>> -Vik
>>>>
>>>> =====================
>>>> To manage your subscription to SPSSX-L, send a message to
>>>
>>>> LISTSERV@.UGA
>>>
>>>> (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
>>>
>>>
>>>
>>>
>>>
>>> -----
>>> --
>>> Bruce Weaver
>>>
>
>> bweaver@
>
>>> 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/Ordinal-Regression-Question-tp5715664p5715667.html
>>> Sent from the SPSSX Discussion mailing list archive at Nabble.com.
>>>
>>> =====================
>>> To manage your subscription to SPSSX-L, send a message to
>>>
>
>> LISTSERV@.UGA
>
>> (not to SPSSX-L), with no body text except the
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>>
>> =====================
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>
>> LISTSERV@.UGA
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>> INFO REFCARD
>
>
>
>
>
> -----
> --
> 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/Ordinal-Regression-Question-tp5715664p5715680.html
> Sent from the SPSSX Discussion mailing list archive at Nabble.com.
>
> =====================
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> [hidden email] (not to SPSSX-L), with no body text except the
> command. To leave the list, send the command
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=====================
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--
Bruce Weaver
bweaver@lakeheadu.ca
http://sites.google.com/a/lakeheadu.ca/bweaver/

"When all else fails, RTFM."

PLEASE NOTE THE FOLLOWING: 
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2. The SPSSX Discussion forum on Nabble is no longer linked to the SPSSX-L listserv administered by UGA (https://listserv.uga.edu/).
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Automatic reply: Ordinal Regression Question

MICHAEL J TONER

 

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Re: Ordinal Regression Question

Vik Rubenfeld
In reply to this post by Bruce Weaver
Will do. Thanks very much for sending the link to that article. It was extremely informative and even answered a question I had this morning!

Best,


-Vik

On Oct 16, 2012, at 3:44 PM, Bruce Weaver wrote:

> Okay, with over 2000 events, you have more than enough to avoid serious
> over-fitting of the model.
>
> Re your comment on reducing the number of variables after reviewing initial
> results, notice what Babyak says about that in his article.  IIRC, he uses
> the term "phantom degrees of freedom", or something along those lines.
>
> HTH.
>
>
>
> Vik Rubenfeld wrote
>> Hi Bruce,
>>
>>> BW:  When you treat the 5-category variables as factors, each one eats up
>>> 4 degrees of freedom.  And each dichotomous variable eats 1 df.  So with
>>> all those variables in the model, you have 41 parameters to estimate
>>> (including the constant).  That means you should have about 600 "events"
>>> where an event is either a Yes or No response to the DV (whichever has
>>> the
>>> lower frequency count over all cases).  What is your total N, how many
>>> have DV=Yes and DV=No?
>>
>>
>> For my training data set, total N = 4640 observations. DV=YES for 2173
>> observations, and DV=NO for 2467 observations. So, there are fewer YES
>> responses in the DV. It may be helpful for me to note that after reviewing
>> initial results I reduced the total explanatory variables to 13 (7 with 5
>> categories, and 6 dichotomous).
>>
>> I really appreciate your advice and look forward to hearing your thoughts.
>>
>> Best,
>>
>>
>> -Vik
>>
>>
>> On Oct 16, 2012, at 12:02 PM, Bruce Weaver wrote:
>>
>>> See below.
>>>
>>>
>>> Vik Rubenfeld wrote
>>>> Hi Bruce,
>>>>
>>>> Thanks for your feedback.
>>>>
>>>>> 1. If your dependent variable is dichotomous, why are you not using
>>>>> binary
>>>>> logistic regression?
>>>>
>>>> The articles I read didn't state that one could not use a dichotomous
>>>> dependent variable with ordinal regression. As dichotomous variables may
>>>> be considered a special case of ordinal variables, I have been using
>>>> ordinal regression. However, I am happy to use binary logistic
>>>> regression
>>>> if that is appropriate.
>>>>
>>>>
>>>> BW:  I suspect that PLUM and LOGISTIC REGRESSION (and NOMREG and GENLIN
>>>> using a logit link and binomial error distribution) will give the same
>>>> result when the dependent variable is dichotomous.  (The only
>>>> differences
>>>> might be due to which category is treated as the reference category.)
>>>>
>>>>
>>>>> 2. How many categories are there for your explanatory variables?
>>>>
>>>> Seven explanatory variables have 5 categories each ("Strongly agree" to
>>>> "Strongly disagree"). An additional 20 explanatory variables are
>>>> dichotomous ("Yes" or "No").
>>>>
>>>>
>>>> BW:  When you treat the 5-category variables as factors, each one eats
>>>> up
>>>> 4 degrees of freedom.  And each dichotomous variable eats 1 df.  So with
>>>> all those variables in the model, you have 41 parameters to estimate
>>>> (including the constant).  That means you should have about 600 "events"
>>>> where an event is either a Yes or No response to the DV (whichever has
>>>> the
>>>> lower frequency count over all cases).  What is your total N, how many
>>>> have DV=Yes and DV=No?
>>>>
>>>>
>>>>> 3. How many "events" do you have (with "event" defined as the lower
>>>>> frequency category for your dependent variable)?
>>>>
>>>> The dependent variable is dichotomous ("Yes" or "No").
>>>>
>>>> BW:  What I meant was that if there are fewer YES than NO responses,
>>>> then
>>>> an event = a YES response.  Or if there are fewer NO than YES responses,
>>>> event = a NO response.
>>>>
>>>>
>>>>> Questions 2 and 3 are getting at whether you are over-fitting your
>>>>> model.
>>>>> A
>>>>> rough rule of thumb suggests you need 15-20 events per parameter if you
>>>>> want
>>>>> to avoid over-fitting (for binary logistic regression).
>>>>
>>>> I am currently using ordinal regression rather than binary logistic
>>>> regression. However, I am happy to use binary logistic regression if
>>>> that
>>>> is appropriate.
>>>>
>>>> Would binary logistic regression indeed be more appropriate in this
>>>> case,
>>>> given that the explanatory variables have fewer than than 15-20 events
>>>> per
>>>> parameter?
>>>>
>>>> BW:  As noted above, you'll get the same results.
>>>>
>>>>
>>>> Thanks very much in advance for your advice, and for the link to the
>>>> excellent article from IMS Bulletin.
>>>>
>>>> Best,
>>>>
>>>>
>>>> -Vik
>>>>
>>>> BW:  Here's another one you might find interesting:
>>>>
>>>> http://os1.amc.nl/mediawiki/images/Babyak_-_overfitting.pdf
>>>>
>>>> HTH.
>>>>
>>>>
>>>> On Oct 16, 2012, at 4:33 AM, Bruce Weaver wrote:
>>>>
>>>>> Hi Vik.  I have a couple questions.
>>>>>
>>>>> 1. If your dependent variable is dichotomous, why are you not using
>>>>> binary
>>>>> logistic regression?
>>>>>
>>>>> 2. How many categories are there for your explanatory variables?
>>>>>
>>>>> 3. How many "events" do you have (with "event" defined as the lower
>>>>> frequency category for your dependent variable)?
>>>>>
>>>>> Questions 2 and 3 are getting at whether you are over-fitting your
>>>>> model.
>>>>> A
>>>>> rough rule of thumb suggests you need 15-20 events per parameter if you
>>>>> want
>>>>> to avoid over-fitting (for binary logistic regression).
>>>>>
>>>>> Re your question about why a coefficient does not have the expected
>>>>> sign,
>>>>> bear in mind that you are looking at partial effects.  I.e., the
>>>>> coefficient
>>>>> for a particular variable depends on what other variables are in the
>>>>> model.
>>>>> If your library has it, take a look at chapter 13 (Woes of Regression
>>>>> Coefficients) in the Mosteller & Tukey classic, "Data Analysis and
>>>>> Regression: A Second Course in Statistics".  The same point is
>>>>> discussed
>>>>> here:
>>>>>
>>>>>
>>>>> http://bulletin.imstat.org/2012/07/terences-stuff-multiple-linear-regression-1/
>>>>>
>>>>> HTH.
>>>>>
>>>>>
>>>>> Vik Rubenfeld wrote
>>>>>> I've done an Ordinal Regression using the following syntax.
>>>>>>
>>>>>> PLUM CQIA9all BY CQIA5_1 CQIA5_2 CQIA5_3 CQIA5_4 CQIA5_5 CQIA5_6
>>>>>> CQIA5_7
>>>>>> CQIA6_6 CQIA6_8 CQIA6_13 CQIA6_16 CQIA6_17 CQIA6_19
>>>>>> /CRITERIA=CIN(95) DELTA(0) LCONVERGE(0) MXITER(100) MXSTEP(5)
>>>>>> PCONVERGE(1.0E-6) SINGULAR(1.0E-8)
>>>>>> /LINK=LOGIT
>>>>>> /PRINT=FIT PARAMETER SUMMARY TPARALLEL
>>>>>> /SAVE=PREDCAT.
>>>>>>
>>>>>> Results were excellent, with many statistically significant estimates.
>>>>>> The
>>>>>> test of parallel lines is not significant.
>>>>>>
>>>>>> I  have a question regarding the estimates. In this data set, the
>>>>>> dependent variable is a purchase-interest-related action, and is coded
>>>>>> as:
>>>>>>
>>>>>> 0 = YES
>>>>>> 1 = NO
>>>>>>
>>>>>> Favorable attributes (e.g. "I want to go to the store to see the
>>>>>> product")
>>>>>> therefore would be expected to have negative parameter estimates. And
>>>>>> in
>>>>>> my results, in most cases, they do.
>>>>>>
>>>>>> However, there is one attribute ("smart") which has a small positive
>>>>>> parameter estimate of 0.16.  I cross-tabbed "smart" with the presence
>>>>>> of
>>>>>> the purchase-interest-related action, and as expected, those who
>>>>>> consider
>>>>>> the product to be "smart" are *more* likely to take the
>>>>>> purchase-interest-related action.
>>>>>>
>>>>>> So my question is, why does this attribute have a positive, rather
>>>>>> than
>>>>>> a
>>>>>> negative, parameter estimate?
>>>>>>
>>>>>> Thanks very much in advance to all for any info.
>>>>>>
>>>>>> Best,
>>>>>>
>>>>>>
>>>>>> -Vik
>>>>>>
>>>>>> =====================
>>>>>> To manage your subscription to SPSSX-L, send a message to
>>>>>
>>>>>> LISTSERV@.UGA
>>>>>
>>>>>> (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
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>> -----
>>>>> --
>>>>> Bruce Weaver
>>>>>
>>>
>>>> bweaver@
>>>
>>>>> 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/Ordinal-Regression-Question-tp5715664p5715667.html
>>>>> Sent from the SPSSX Discussion mailing list archive at Nabble.com.
>>>>>
>>>>> =====================
>>>>> To manage your subscription to SPSSX-L, send a message to
>>>>>
>>>
>>>> LISTSERV@.UGA
>>>
>>>> (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
>>>>
>>>> =====================
>>>> To manage your subscription to SPSSX-L, send a message to
>>>
>>>> LISTSERV@.UGA
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>>>> For a list of commands to manage subscriptions, send the command
>>>> INFO REFCARD
>>>
>>>
>>>
>>>
>>>
>>> -----
>>> --
>>> Bruce Weaver
>>>
>
>> bweaver@
>
>>> 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/Ordinal-Regression-Question-tp5715664p5715680.html
>>> Sent from the SPSSX Discussion mailing list archive at Nabble.com.
>>>
>>> =====================
>>> To manage your subscription to SPSSX-L, send a message to
>>>
>
>> LISTSERV@.UGA
>
>> (not to SPSSX-L), with no body text except the
>>> command. To leave the list, send the command
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>>
>> =====================
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>> LISTSERV@.UGA
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>
>
>
>
>
> -----
> --
> 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/Ordinal-Regression-Question-tp5715664p5715685.html
> Sent from the SPSSX Discussion mailing list archive at Nabble.com.
>
> =====================
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> [hidden email] (not to SPSSX-L), with no body text except the
> command. To leave the list, send the command
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