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Ordinal predictor: Can be treated Continuous?

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E. Bernardo

Ordinal predictor: Can be treated Continuous?

Hi all,

One of the independent variables in my logistic regression is "education of mother" which is ordinal with values 1 to 4 (1 being elementary and 4 being postgraduate). Can I consider it as continuous rather than categorical so that my interpretation of the exp(B) for example would be the log odds for Y=1 (my dependent) is higher when the mother has more eduation?

Eins

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Christopher Stride

Re: Ordinal predictor: Can be treated Continuous?

Hi Eins
If you do, and retain the coding 1,2,3,4, then you will be making the
assumption that the difference in standard of education between each
category is somehow equal. I would personally recommend considering it
as a categorical variable and enter 3 dummy vars to represent the 4 cats
(in fact, since you are running logistic regression, you can define the
variable as categorical and SPSS automatically does this dummy coding
for you)
cheers
Chris

Eins Bernardo wrote:

> Hi all,
> One of the independent variables in my logistic regression is
> "education of mother" which is ordinal with values 1 to 4 (1 being
> elementary and 4 being postgraduate). Can I consider it as continuous
> rather than categorical so that my interpretation of the exp(B) for
> example would be the log odds for Y=1 (my dependent) is higher when
> the mother has more eduation?
> Eins
>
>
> ------------------------------------------------------------------------
> Fast, Ad-free, Unlimited Storage - Yahoo! Mail allows you to have it
> all. <http://ph.mail.yahoo.com>

E. Bernardo

Re: Ordinal predictor: Can be treated Continuous?

In reply to this post by E. Bernardo

Thank you, Chris.

I follow your suggestion because it is logical of course. I have a couple of follow-up questions based on the logistic regression output below. My question is about the mother's education (Mo_ed). The codes used are 1, 2, 3 and 4 where 4 was selected as its reference category. How to interpret these part of the output? For example,what does it mean when category 4 is nonsignificant(p=.152); what is meant when category 2 is significant (p=.024)?

Variables in the Equation
		B	S.E.	Wald	df	Sig.	Exp(B)
Step 1^a	Acad_Perf	.412	.130	10.002	1	.002	1.510
	Inc	.104	.018	32.608	1	.000	1.110
	Mo_Ed			5.281	3	.152
	Mo_Ed(1)	-.496	.643	.596	1	.440	.609
	Mo_Ed(2)	-.605	.268	5.100	1	.024	.546
	Mo_Ed(3)	-.239	.178	1.794	1	.180	.788
	Constant	-.417	.203	4.214	1	.040	.659
a. Variable(s) entered on step 1: Acad_Perf, Inc, Mo_Ed.

Best,.

Eins

--- On Tue, 6/16/09, Dr C B Stride <[hidden email]> wrote:

From: Dr C B Stride <[hidden email]>
Subject: Re: Ordinal predictor: Can be treated Continuous?
To: "Eins Bernardo" <[hidden email]>
Cc: [hidden email]
Date: Tuesday, 16 June, 2009, 10:15 AM

Hi Eins
If you do, and retain the coding 1,2,3,4, then you will be making the assumption that the difference in standard of education between each category is somehow equal. I would personally recommend considering it as a categorical variable and enter 3 dummy vars to represent the 4 cats (in fact, since you are running logistic regression, you can define the variable as categorical and SPSS automatically does this dummy coding for you)
cheers
Chris

Eins Bernardo wrote:
> Hi all,
> One of the independent variables in my logistic regression is "education of mother" which is ordinal with values 1 to 4 (1 being elementary and 4 being postgraduate). Can I consider it as continuous rather than categorical so that my interpretation of the exp(B) for example would be the log odds for Y=1 (my dependent) is higher when the mother has more eduation?
> Eins
>
>
> ------------------------------------------------------------------------
> Fast, Ad-free, Unlimited Storage - Yahoo! Mail allows you to have it all. <http://ph.mail.yahoo.com>

-- Dr Chris Stride, C. Stat, Statistician, Institute of Work Psychology, University of Sheffield
Telephone: 0114 2223262
Fax: 0114 2727206

“Figure It Out”
Statistical Consultancy and Training Service for Social Scientists

Visit www..figureitout.org.uk for details of my consultancy services and forthcoming training courses in June 2009

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Christopher Stride

Re: Ordinal predictor: Can be treated Continuous?

Hi Eins
Mo-ED represents the overall effect of Mother's education, which is
non-significant; not category 4. (Category 4 is the reference category,
which is hence not dummy coded)

However there is a statistically significant difference at the p < 0.05
level between category 2 and category 4. The coefficients of each of the
three dummy vars refer to the difference in the outcome vs that of the
reference category; it appears that all 3 cats are less likely to be in
outcome group Y = 1 than thoe with mother's with high education, since
all coeffs are negative. Such differences are usually expressed in terms
of the odds ratios for comparative categories, using the Exp(B) statistic.

I'd hazard a guess from your results though, that you have fairly small
numbers in category 1, and possibly category 4.
cheers
Chris

Eins Bernardo wrote:

> Thank you, Chris.
> I follow your suggestion because it is logical of course. I have a
> couple of follow-up questions based on the logistic regression output
> below. My question is about the mother's education (Mo_ed). The codes
> used are 1, 2, 3 and 4 where 4 was selected as its reference category.
> How to interpret these part of the output? For example,what does it
> mean when category 4 is nonsignificant(p=.152); what is meant when
> category 2 is significant (p=.024)?
>
> *Variables in the Equation*
>
>
>
>
>
> B
>
>
>
> S.E.
>
>
>
> Wald
>
>
>
> df
>
>
>
> Sig.
>
>
>
> Exp(B)
>
> Step 1^a
>
>
>
> Acad_Perf
>
>
>
> .412
>
>
>
> .130
>
>
>
> 10.002
>
>
>
> 1
>
>
>
> .002
>
>
>
> 1.510
>
> Inc
>
>
>
> .104
>
>
>
> .018
>
>
>
> 32.608
>
>
>
> 1
>
>
>
> .000
>
>
>
> 1.110
>
> Mo_Ed
>
>
>
>
>
>
>
> 5.281
>
>
>
> 3
>
>
>
> .152
>
>
>
> Mo_Ed(1)
>
>
>
> -.496
>
>
>
> .643
>
>
>
> .596
>
>
>
> 1
>
>
>
> .440
>
>
>
> .609
>
> Mo_Ed(2)
>
>
>
> -.605
>
>
>
> .268
>
>
>
> 5.100
>
>
>
> 1
>
>
>
> .024
>
>
>
> .546
>
> Mo_Ed(3)
>
>
>
> -.239
>
>
>
> .178
>
>
>
> 1.794
>
>
>
> 1
>
>
>
> .180
>
>
>
> .788
>
> Constant
>
>
>
> -.417
>
>
>
> .203
>
>
>
> 4.214
>
>
>
> 1
>
>
>
> .040
>
>
>
> .659
>
> a. Variable(s) entered on step 1: Acad_Perf, Inc, Mo_Ed.
>
> Best,.
> Eins
>
>
> --- On *Tue, 6/16/09, Dr C B Stride /<[hidden email]>/* wrote:
>
>
> From: Dr C B Stride <[hidden email]>
> Subject: Re: Ordinal predictor: Can be treated Continuous?
> To: "Eins Bernardo" <[hidden email]>
> Cc: [hidden email]
> Date: Tuesday, 16 June, 2009, 10:15 AM
>
> Hi Eins
> If you do, and retain the coding 1,2,3,4, then you will be making
> the assumption that the difference in standard of education
> between each category is somehow equal. I would personally
> recommend considering it as a categorical variable and enter 3
> dummy vars to represent the 4 cats (in fact, since you are running
> logistic regression, you can define the variable as categorical
> and SPSS automatically does this dummy coding for you)
> cheers
> Chris
>
> Eins Bernardo wrote:
> > Hi all,
> > One of the independent variables in my logistic regression is
> "education of mother" which is ordinal with values 1 to 4 (1 being
> elementary and 4 being postgraduate). Can I consider it as
> continuous rather than categorical so that my interpretation of
> the exp(B) for example would be the log odds for Y=1 (my
> dependent) is higher when the mother has more eduation?
> > Eins
> >
> >
> >
> ------------------------------------------------------------------------
> > Fast, Ad-free, Unlimited Storage - Yahoo! Mail allows you to
> have it all. <http://ph.mail.yahoo.com <http://ph.mail.yahoo.com/>>
>
> -- Dr Chris Stride, C. Stat, Statistician, Institute of Work
> Psychology, University of Sheffield
> Telephone: 0114 2223262
> Fax: 0114 2727206
>
> â€œFigure It Outâ€�
> Statistical Consultancy and Training Service for Social Scientists
>
> Visit www..figureitout.org.uk for details of my consultancy
> services and forthcoming training courses in June 2009
>
>
>
>
>
> ------------------------------------------------------------------------
> Adding more friends is quick and easy.
> <http://sg.rd.yahoo.com/ph/mail/trueswitch/mailtagline/*https://secure5.trueswitch.com/yahoo-intl/?country=ph&language=en>
> Import them over to Yahoo! Mail today!

Art Kendall

Re: Ordinal predictor: Can be treated Continuous?

In reply to this post by E. Bernardo

see CATREG where you can see the effects of different measurement assumptions.

Art Kendall
Social Research Consultants
Eins Bernardo wrote:

Hi all,

One of the independent variables in my logistic regression is "education of mother" which is ordinal with values 1 to 4 (1 being elementary and 4 being postgraduate). Can I consider it as continuous rather than categorical so that my interpretation of the exp(B) for example would be the log odds for Y=1 (my dependent) is higher when the mother has more eduation?

Eins

Fast, Ad-free, Unlimited Storage - Yahoo! Mail allows you to have it all.

Art Kendall
Social Research Consultants

E. Bernardo

Re: Ordinal predictor: Can be treated Continuous?

In reply to this post by E. Bernardo

I confused because the overall effect of Mo_ed is nonsignificant(p>.05) while there is at least one pair of categories (category 2 and 4) is significantly different(p<.05).

On the other hand, the effect of Mo_ed on the dependent is significant(p<.05) when it is treated continuous/interval.

Can you please enlighthen me on this issue.

Eins

- On Tue, 6/16/09, Dr C B Stride <[hidden email]> wrote:

From: Dr C B Stride <[hidden email]>
Subject: Re: Ordinal predictor: Can be treated Continuous?
To: "Eins Bernardo" <[hidden email]>
Cc: [hidden email]
Date: Tuesday, 16 June, 2009, 11:17 AM

Hi Eins
Mo-ED represents the overall effect of Mother's education, which is
non-significant; not category 4. (Category 4 is the reference category,
which is hence not dummy coded)

However there is a statistically significant difference at the p < 0.05
level between category 2 and category 4. The coefficients of each of the
three dummy vars refer to the difference in the outcome vs that of the
reference category; it appears that all 3 cats are less likely to be in
outcome group Y = 1 than thoe with mother's with high education, since
all coeffs are negative. Such differences are usually expressed in terms
of the odds ratios for comparative categories, using the Exp(B) statistic.

I'd hazard a guess from your results though, that you have fairly small
numbers in category 1, and possibly category 4.
cheers
Chris

Eins Bernardo wrote:

> Thank you, Chris.
> I follow your suggestion because it is logical of course. I have a
> couple of follow-up questions based on the logistic regression output
> below. My question is about the mother's education (Mo_ed). The codes
> used are 1, 2, 3 and 4 where 4 was selected as its reference category.
> How to interpret these part of the output? For example,what does it
> mean when category 4 is nonsignificant(p=.152); what is meant when
> category 2 is significant (p=.024)?
>
> *Variables in the Equation*
>
>
>
>
>
> B
>
>
>
> S.E.
>
>
>
> Wald
>
>
>
> df
>
>
>
> Sig.
>
>
>
> Exp(B)
>
> Step 1^a
>
>
>
> Acad_Perf
>
>
>
> .412
>
>
>
> .130
>
>
>
> 10.002
>
>
>
> 1
>
>
>
> .002
>
>
>
> 1.510
>
> Inc
>
>
>
> .104
>
>
>
> .018
>
>
>
> 32.608
>
>
>
> 1
>
>
>
> .000
>
>
>
> 1.110
>
> Mo_Ed
>
>
>
>
>
>
>
> 5.281
>
>
>
> 3
>
>
>
> .152
>
>
>
> Mo_Ed(1)
>
>
>
> -.496
>
>
>
> .643
>
>
>
> .596
>
>
>
> 1
>
>
>
> .440
>
>
>
> .609
>
> Mo_Ed(2)
>
>
>
> -.605
>
>
>
> .268
>
>
>
> 5.100
>
>
>
> 1
>
>
>
> .024
>
>
>
> .546
>
> Mo_Ed(3)
>
>
>
> -.239
>
>
>
> .178
>
>
>
> 1.794
>
>
>
> 1
>
>
>
> .180
>
>
>
> .788
>
> Constant
>
>
>
> -.417
>
>
>
> .203
>
>
>
> 4.214
>
>
>
> 1
>
>
>
> .040
>
>
>
> .659
>
> a. Variable(s) entered on step 1: Acad_Perf, Inc, Mo_Ed.
>
> Best,.
> Eins
>
>
> --- On *Tue, 6/16/09, Dr C B Stride /<c.b.stride@...>/* wrote:
>
>
>    From: Dr C B Stride <c.b.stride@...>
>    Subject: Re: Ordinal predictor: Can be treated Continuous?
>    To: "Eins Bernardo" <einsbernardo@...>
>    Cc: SPSSX-L@...
>    Date: Tuesday, 16 June, 2009, 10:15 AM
>
>    Hi Eins
>    If you do, and retain the coding 1,2,3,4, then you will be making
>    the assumption that the difference in standard of education
>    between each category is somehow equal. I would personally
>    recommend considering it as a categorical variable and enter 3
>    dummy vars to represent the 4 cats (in fact, since you are running
>    logistic regression, you can define the variable as categorical
>    and SPSS automatically does this dummy coding for you)
>    cheers
>    Chris
>
>    Eins Bernardo wrote:
>    > Hi all,
>    > One of the independent variables in my logistic regression is
>    "education of mother" which is ordinal with values 1 to 4 (1 being
>    elementary and 4 being postgraduate). Can I consider it as
>    continuous rather than categorical so that my interpretation of
>    the exp(B) for example would be the log odds for Y=1 (my
>    dependent) is higher when the mother has more eduation?
>    > Eins
>    >
>    >
>    >
>    ------------------------------------------------------------------------
>    > Fast, Ad-free, Unlimited Storage - Yahoo! Mail allows you to
>    have it all. <http://ph.mail.yahoo.com <http://ph.mail.yahoo.com/>>
>
>    -- Dr Chris Stride, C. Stat, Statistician, Institute of Work
>    Psychology, University of Sheffield
>    Telephone: 0114 2223262
>    Fax: 0114 2727206
>
>    “Figure It Out”
>    Statistical Consultancy and Training Service for Social Scientists
>
>    Visit www..figureitout.org.uk for details of my consultancy
>    services and forthcoming training courses in June 2009
>
>
>
>
>
> ------------------------------------------------------------------------
> Adding more friends is quick and easy.
> <http://sg.rd.yahoo.com/ph/mail/trueswitch/mailtagline/*https://secure5.trueswitch.com/yahoo-intl/?country=ph&language=en>
> Import them over to Yahoo! Mail today!

--
Dr Chris Stride, C. Stat,
Statistician, Institute of Work Psychology, University of Sheffield
Telephone: 0114 2223262
Fax: 0114 2727206

�Figure It Out�
Statistical Consultancy and Training Service for Social Scientists

Visit www.figureitout.org.uk for details of my consultancy services and forthcoming training courses in June 2009

Importing contacts has never been easier.
Bring your friends over to Yahoo! Mail today!

Allan Lundy, PhD

Re: Ordinal predictor: It CAN be treated AS Continuous

In reply to this post by Christopher Stride

Hi, All who are interested,

I'd like to weigh in on this issue. True, technically Chris is correct. However, it makes surprisingly little difference to the stats. If you can reasonably assume that the data underlying the ordinal measure is actually continuous, which is certainly the case here, then it can be shown empirically that the ordinal measure will correlate very highly with the "true" data. I have a couple of Excel spreadsheets programmed to randomly generate numbers on a "true" scale that vary between 1 and 10 points apart, then correlate them with the ordinal equivalent. Correlations are almost always r= .95 or higher, and typically above r= .98. In other words, the ordinal measure is a much more accurate reflection of the presumed true underlying scale than most measures in the social sciences. If anyone would like copies of my explanation and Excel files, please contact me directly.

Of course, treating an ordinal measure as continuous is not perfect, but I would argue that it is not very unconservative and is more informative than treating the values as not on a scale at all, which is what dummy variables do.
Allan

At 06:15 AM 6/16/2009, Dr C B Stride wrote:

Hi Eins
If you do, and retain the coding 1,2,3,4, then you will be making the
assumption that the difference in standard of education between each
category is somehow equal. I would personally recommend considering it
as a categorical variable and enter 3 dummy vars to represent the 4 cats
(in fact, since you are running logistic regression, you can define the
variable as categorical and SPSS automatically does this dummy coding
for you)
cheers
Chris

Eins Bernardo wrote:

Hi all,
One of the independent variables in my logistic regression is
"education of mother" which is ordinal with values 1 to 4 (1 being
elementary and 4 being postgraduate). Can I consider it as continuous
rather than categorical so that my interpretation of the exp(B) for
example would be the log odds for Y=1 (my dependent) is higher when
the mother has more eduation?
Eins

------------------------------------------------------------------------
Fast, Ad-free, Unlimited Storage - Yahoo! Mail allows you to have it
all. < http://ph.mail.yahoo.com>

--
Dr Chris Stride, C. Stat,
Statistician, Institute of Work Psychology, University of Sheffield
Telephone: 0114 2223262
Fax: 0114 2727206

Figure It Out
Statistical Consultancy and Training Service for Social Scientists

Visit www.figureitout.org.uk for details of my consultancy services and forthcoming training courses in June 2009

=====================
To manage your subscription to SPSSX-L, send a message to
[hidden email] (not to SPSSX-L), with no body text except the
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For a list of commands to manage subscriptions, send the command
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Allan Lundy, PhD
Research Consultant      [hidden email]

Business & Cell (any time): 215 820-8100
Home: Voice and fax (8am - 10pm, 7 days/week): 215 885-5313
Address: 108 Cliff Terrace, Wyncote, PA 19095
Visit my Web site at   www.dissertationconsulting.net
===================== 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

Christopher Stride

Re: Ordinal predictor: It CAN be treated AS Continuous

Interesting... and I can see the argument for this approach where you
have, for instance, likert scale response codings to questionnaire items.

However, I would consider Eins' highest education level variable an
example of the type of ordinal variable where differences between
vategories could be verey small or very large;

Also, whilst correlations between the true underlying and ordinal
versions of a var may be very high, that isn't actually the only issue
when using the ordinal var as a predictor.

Take the following example: ordinal variable predicting continuous
outcome. ordinal var edqual coded 1 = no ed,2 = a-level, 3 = B.Sc ,4 =
Phd. Gives a good looking linear fit.
But actually, the 'true' spacing between categories, in terms of
educational competence, would be 1,8,9,10
Now, if you plot with those numbers on the X-axis, the relationship
looks a lot more curvilinear!

cheers
Chris

Allan Lundy, PhD wrote:

>
> Hi, All who are interested,
>
> I'd like to weigh in on this issue. True, technically Chris is
> correct. However, it makes surprisingly little difference to the
> stats. If you can reasonably assume that the data underlying the
> ordinal measure is actually continuous, which is certainly the case
> here, then it can be shown empirically that the ordinal measure will
> correlate very highly with the "true" data. I have a couple of Excel
> spreadsheets programmed to randomly generate numbers on a "true" scale
> that vary between 1 and 10 points apart, then correlate them with the
> ordinal equivalent. Correlations are almost always r= .95 or higher,
> and typically above r= .98. In other words, the ordinal measure is a
> much more accurate reflection of the presumed true underlying scale
> than most measures in the social sciences. If anyone would like copies
> of my explanation and Excel files, please contact me directly.
>
> Of course, treating an ordinal measure as continuous is not perfect,
> but I would argue that it is not very unconservative and is more
> informative than treating the values as not on a scale at all, which
> is what dummy variables do.
> Allan
>
>
>
> At 06:15 AM 6/16/2009, Dr C B Stride wrote:
>> Hi Eins
>> If you do, and retain the coding 1,2,3,4, then you will be making the
>> assumption that the difference in standard of education between each
>> category is somehow equal. I would personally recommend considering it
>> as a categorical variable and enter 3 dummy vars to represent the 4 cats
>> (in fact, since you are running logistic regression, you can define the
>> variable as categorical and SPSS automatically does this dummy coding
>> for you)
>> cheers
>> Chris
>>
>> Eins Bernardo wrote:
>>> Hi all,
>>> One of the independent variables in my logistic regression is
>>> "education of mother" which is ordinal with values 1 to 4 (1 being
>>> elementary and 4 being postgraduate). Can I consider it as continuous
>>> rather than categorical so that my interpretation of the exp(B) for
>>> example would be the log odds for Y=1 (my dependent) is higher when
>>> the mother has more eduation?
>>> Eins
>>>
>>>
>>> ------------------------------------------------------------------------
>>> Fast, Ad-free, Unlimited Storage - Yahoo! Mail allows you to have it
>>> all. < http://ph.mail.yahoo.com <http://ph.mail.yahoo.com/>>
>>
>> --
>> Dr Chris Stride, C. Stat,
>> Statistician, Institute of Work Psychology, University of Sheffield
>> Telephone: 0114 2223262
>> Fax: 0114 2727206
>>
>> “Figure It Out”
>> Statistical Consultancy and Training Service for Social Scientists
>>
>> Visit www.figureitout.org.uk <http://www.figureitout.org.uk/> for
>> details of my consultancy services and forthcoming training courses
>> in June 2009
>>
>> =====================
>> 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
>
> */Allan Lundy, PhD/*
> *Research Consultant* [hidden email]
>
> *Business & Cell (any time): 215 820-8100*
> Home: Voice and fax (8am - 10pm, 7 days/week): 215 885-5313
> Address: 108 Cliff Terrace, Wyncote, PA 19095
> Visit my Web site at www.dissertationconsulting.net
> <http://www.dissertationconsulting.net/>===================== 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
>

Gerard M. Keogh

Re: Ordinal predictor: It CAN be treated AS Continuous

AND -
re education you can recode levels to years in fulltime education giving
primary = 9, secondary = 14, 3rd level = 18, 4th level = 22 etc.
and the curvature will be worse again.

Is this discussion not an aguument for proportional odds regression - not
sure but probably available in SPSS as an add-on?
Alternative - use the polr method in R.

Gerard

Dr C B Stride
<c.b.stride@sheff
ield.ac.uk> To
Sent by: [hidden email]
"SPSSX(r) cc
Discussion"
<SPSSX-L@LISTSERV Subject
.UGA.EDU> Re: Ordinal predictor: It CAN be
treated AS Continuous

16/06/2009 14:59

Please respond to
c.b.stride@sheffi
eld.ac.uk

Interesting... and I can see the argument for this approach where you
have, for instance, likert scale response codings to questionnaire items.

However, I would consider Eins' highest education level variable an
example of the type of ordinal variable where differences between
vategories could be verey small or very large;

Also, whilst correlations between the true underlying and ordinal
versions of a var may be very high, that isn't actually the only issue
when using the ordinal var as a predictor.

Take the following example: ordinal variable predicting continuous
outcome. ordinal var edqual coded 1 = no ed,2 = a-level, 3 = B.Sc ,4 =
Phd. Gives a good looking linear fit.
But actually, the 'true' spacing between categories, in terms of
educational competence, would be 1,8,9,10
Now, if you plot with those numbers on the X-axis, the relationship
looks a lot more curvilinear!

cheers
Chris

Allan Lundy, PhD wrote:

------------------------------------------------------------------------

>>> Fast, Ad-free, Unlimited Storage - Yahoo! Mail allows you to have it
>>> all. < http://ph.mail.yahoo.com <http://ph.mail.yahoo.com/>>
>>
>> --
>> Dr Chris Stride, C. Stat,
>> Statistician, Institute of Work Psychology, University of Sheffield
>> Telephone: 0114 2223262
>> Fax: 0114 2727206
>>
>> “Figure It Out”
>> Statistical Consultancy and Training Service for Social Scientists
>>
>> Visit www.figureitout.org.uk <http://www.figureitout.org.uk/> for
>> details of my consultancy services and forthcoming training courses
>> in June 2009
>>
>> =====================
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>> [hidden email] (not to SPSSX-L), with no body text except the
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>
> */Allan Lundy, PhD/*
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>
> *Business & Cell (any time): 215 820-8100*
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> <http://www.dissertationconsulting.net/>===================== To
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>

--
Dr Chris Stride, C. Stat,
Statistician, Institute of Work Psychology, University of Sheffield
Telephone: 0114 2223262
Fax: 0114 2727206

“Figure It Out”
Statistical Consultancy and Training Service for Social Scientists

Visit www.figureitout.org.uk for details of my consultancy services and
forthcoming training courses in June 2009

=====================
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Is le haghaidh an duine nó an eintitis ar a bhfuil sí dírithe, agus le haghaidh an duine nó an eintitis sin amháin, a bheartaítear an fhaisnéis a tarchuireadh agus féadfaidh sé go bhfuil ábhar faoi rún agus/nó faoi phribhléid inti. Toirmisctear aon athbhreithniú, atarchur nó leathadh a dhéanamh ar an bhfaisnéis seo, aon úsáid eile a bhaint aisti nó aon ghníomh a dhéanamh ar a hiontaoibh, ag daoine nó ag eintitis seachas an faighteoir beartaithe. Má fuair tú é seo trí dhearmad, téigh i dteagmháil leis an seoltóir, le do thoil, agus scrios an t-ábhar as aon ríomhaire. Is é beartas na Roinne Dlí agus Cirt, Comhionannais agus Athchóirithe Dlí, agus na nOifígí agus na nGníomhaireachtaí a úsáideann seirbhísí TF na Roinne, seoladh ábhair cholúil a dhícheadú.
Más rud é go measann tú gur ábhar colúil atá san ábhar atá sa teachtaireacht seo is ceart duit dul i dteagmháil leis an seoltóir láithreach agus le mailminder[ag]justice.ie chomh maith.
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Kooij, A.J. van der

Re: Ordinal predictor: It CAN be treated AS Continuous

Use CATREG (Analyze, Regression, Optimal Scaling), choose ordinal scaling level. Look at transformation plot; if it looks close to linear you might as well treat the variable as interval.

Regards,
Anita van der Kooij
Data Theory Group
Leiden University

-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Gerard M. Keogh
Sent: 16 June 2009 16:36
To: [hidden email]
Subject: Re: Ordinal predictor: It CAN be treated AS Continuous

AND -
re education you can recode levels to years in fulltime education giving primary = 9, secondary = 14, 3rd level = 18, 4th level = 22 etc.
and the curvature will be worse again.

Is this discussion not an aguument for proportional odds regression - not sure but probably available in SPSS as an add-on?
Alternative - use the polr method in R.

Gerard

Dr C B Stride
<c.b.stride@sheff
ield.ac.uk> To
Sent by: [hidden email]
"SPSSX(r) cc
Discussion"
<SPSSX-L@LISTSERV Subject
.UGA.EDU> Re: Ordinal predictor: It CAN be
treated AS Continuous

16/06/2009 14:59

Please respond to
c.b.stride@sheffi
eld.ac.uk

Interesting... and I can see the argument for this approach where you have, for instance, likert scale response codings to questionnaire items.

However, I would consider Eins' highest education level variable an example of the type of ordinal variable where differences between vategories could be verey small or very large;

Also, whilst correlations between the true underlying and ordinal versions of a var may be very high, that isn't actually the only issue when using the ordinal var as a predictor.

Take the following example: ordinal variable predicting continuous outcome. ordinal var edqual coded 1 = no ed,2 = a-level, 3 = B.Sc ,4 = Phd. Gives a good looking linear fit.
But actually, the 'true' spacing between categories, in terms of educational competence, would be 1,8,9,10 Now, if you plot with those numbers on the X-axis, the relationship looks a lot more curvilinear!

cheers
Chris

Allan Lundy, PhD wrote:

------------------------------------------------------------------------

>>> Fast, Ad-free, Unlimited Storage - Yahoo! Mail allows you to have it
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>>
>> --
>> Dr Chris Stride, C. Stat,
>> Statistician, Institute of Work Psychology, University of Sheffield
>> Telephone: 0114 2223262
>> Fax: 0114 2727206
>>
>> "Figure It Out"
>> Statistical Consultancy and Training Service for Social Scientists
>>
>> Visit www.figureitout.org.uk <http://www.figureitout.org.uk/> for
>> details of my consultancy services and forthcoming training courses
>> in June 2009
>>
>> =====================
>> 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
>
> */Allan Lundy, PhD/*
> *Research Consultant* [hidden email]
>
> *Business & Cell (any time): 215 820-8100*
> Home: Voice and fax (8am - 10pm, 7 days/week): 215 885-5313
> Address: 108 Cliff Terrace, Wyncote, PA 19095 Visit my Web site at
> www.dissertationconsulting.net
> <http://www.dissertationconsulting.net/>===================== 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
>

--
Dr Chris Stride, C. Stat,
Statistician, Institute of Work Psychology, University of Sheffield
Telephone: 0114 2223262
Fax: 0114 2727206

"Figure It Out"
Statistical Consultancy and Training Service for Social Scientists

Visit www.figureitout.org.uk for details of my consultancy services and forthcoming training courses in June 2009

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

**********************************************************************************
The information transmitted is intended only for the person or entity to which it is addressed and may contain confidential and/or privileged material. Any review, retransmission, dissemination or other use of, or taking of any action in reliance upon, this information by persons or entities other than the intended recipient is prohibited. If you received this in error, please contact the sender and delete the material from any computer. It is the policy of the Department of Justice, Equality and Law Reform and the Agencies and Offices using its IT services to disallow the sending of offensive material.
Should you consider that the material contained in this message is offensive you should contact the sender immediately and also mailminder[at]justice.ie.

Is le haghaidh an duine nó an eintitis ar a bhfuil sí dírithe, agus le haghaidh an duine nó an eintitis sin amháin, a bheartaítear an fhaisnéis a tarchuireadh agus féadfaidh sé go bhfuil ábhar faoi rún agus/nó faoi phribhléid inti. Toirmisctear aon athbhreithniú, atarchur nó leathadh a dhéanamh ar an bhfaisnéis seo, aon úsáid eile a bhaint aisti nó aon ghníomh a dhéanamh ar a hiontaoibh, ag daoine nó ag eintitis seachas an faighteoir beartaithe. Má fuair tú é seo trí dhearmad, téigh i dteagmháil leis an seoltóir, le do thoil, agus scrios an t-ábhar as aon ríomhaire. Is é beartas na Roinne Dlí agus Cirt, Comhionannais agus Athchóirithe Dlí, agus na nOifígí agus na nGníomhaireachtaí a úsáideann seirbhísí TF na Roinne, seoladh ábhair cholúil a dhícheadú.
Más rud é go measann tú gur ábhar colúil atá san ábhar atá sa teachtaireacht seo is ceart duit dul i dteagmháil leis an seoltóir láithreach agus le mailminder[ag]justice.ie chomh maith.
***********************************************************************************

=====================
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Allan Lundy, PhD

Re: Ordinal predictor: It CAN be treated AS Continuous

In reply to this post by Gerard M. Keogh

First off, note that Chris's example would still correlate at r= .885 with ordinal scores of 1-4, and, though it might look more curved, Gerard's example would correlate at r= .998.

But here's a much more basic consideration. Even if we use the exact number of years of education, this itself treats the difference between 5 years and 8 years as the same as the difference between 1 year of college and 4 years of college. It seems satisfyingly exact to refer to "years of education," but most likely, we are using that as a proxy for something like knowledge, intellectual sophistication, etc. Hence, it may still not be a one-to-one representation of whatever we are using it for. Likewise many other variables in the social sciences, at least. Is a 50-year-old twice something than a 25-year-old? Is the difference between ages 0 and 10 the same as between 25 and 35?

To wax philosophical, I have often had a similar complaint about the way intelligence is measured. IQ scores were developed on the ASSUMPTION that intelligence is normally distributed. Having taught at a wide range of grades and student ability levels, I am convinced that it is not. What we really mean by intelligence is positively skewed, like wealth, and for the same reason: once you have a lot of it, you tend to get more and more of it.

But don't get me started.
Allan

At 10:35 AM 6/16/2009, Gerard M. Keogh wrote:

AND -
re education you can recode levels to years in fulltime education giving
primary = 9, secondary = 14, 3rd level = 18, 4th level = 22 etc.
and the curvature will be worse again.

Is this discussion not an aguument for proportional odds regression - not
sure but probably available in SPSS as an add-on?
Alternative - use the polr method in R.

Gerard

             Dr C B Stride
             <c.b.stride@sheff
             ield.ac.uk>                                                To
             Sent by:                  [hidden email]
             "SPSSX(r)                                                  cc
             Discussion"
             <SPSSX-L@LISTSERV                                     Subject
             .UGA.EDU>                 Re: Ordinal predictor: It CAN be
                                       treated AS Continuous

             16/06/2009 14:59

             Please respond to
             c.b.stride@sheffi
                 eld.ac.uk

Interesting... and I can see the argument for this approach where you
have, for instance, likert scale response codings to questionnaire items.

However, I would consider Eins' highest education level variable an
example of the type of ordinal variable where differences between
vategories could be verey small or very large;

Also, whilst correlations between the true underlying and ordinal
versions of a var may be very high, that isn't actually the only issue
when using the ordinal var as a predictor.

Take the following example: ordinal variable predicting continuous
outcome. ordinal var edqual coded 1 = no ed,2 = a-level, 3 = B.Sc ,4 =
Phd. Gives a good looking linear fit.
But actually, the 'true' spacing between categories, in terms of
educational competence, would be 1,8,9,10
Now, if you plot with those numbers on the X-axis, the relationship
looks a lot more curvilinear!

cheers
Chris

Allan Lundy, PhD wrote:
>
> Hi, All who are interested,
>
> I'd like to weigh in on this issue. True, technically Chris is
> correct. However, it makes surprisingly little difference to the
> stats. If you can reasonably assume that the data underlying the
> ordinal measure is actually continuous, which is certainly the case
> here, then it can be shown empirically that the ordinal measure will
> correlate very highly with the "true" data. I have a couple of Excel
> spreadsheets programmed to randomly generate numbers on a "true" scale
> that vary between 1 and 10 points apart, then correlate them with the
> ordinal equivalent. Correlations are almost always r= .95 or higher,
> and typically above r= .98. In other words, the ordinal measure is a
> much more accurate reflection of the presumed true underlying scale
> than most measures in the social sciences. If anyone would like copies
> of my explanation and Excel files, please contact me directly.
>
> Of course, treating an ordinal measure as continuous is not perfect,
> but I would argue that it is not very unconservative and is more
> informative than treating the values as not on a scale at all, which
> is what dummy variables do.
> Allan
>
>
>
> At 06:15 AM 6/16/2009, Dr C B Stride wrote:
>> Hi Eins
>> If you do, and retain the coding 1,2,3,4, then you will be making the
>> assumption that the difference in standard of education between each
>> category is somehow equal. I would personally recommend considering it
>> as a categorical variable and enter 3 dummy vars to represent the 4 cats
>> (in fact, since you are running logistic regression, you can define the
>> variable as categorical and SPSS automatically does this dummy coding
>> for you)
>> cheers
>> Chris
>>
>> Eins Bernardo wrote:
>>> Hi all,
>>> One of the independent variables in my logistic regression is
>>> "education of mother" which is ordinal with values 1 to 4 (1 being
>>> elementary and 4 being postgraduate). Can I consider it as continuous
>>> rather than categorical so that my interpretation of the exp(B) for
>>> example would be the log odds for Y=1 (my dependent) is higher when
>>> the mother has more eduation?
>>> Eins
>>>

Art Kendall

Re: Ordinal predictor: It CAN be treated AS Continuous

I have attached some PASW (SPSS) syntax that I use to look at discrepancies from perfectly equal intervals.
It changes the intervals in 3 ways. 1) by basic transformations. 2) by increasingly larger intervals 3) by different amounts of fuzz around scores.
Of course careful design of measurement would avoid such a simplistic representation of a construct as using a single "Likert" item.

If you do the plots, go back and edit the output to insert a linear fit.
Open a new instance of SPSS. Copy the syntax below to a syntax file. Click <run>. Click <all>.

You can easily modify this to see other kinds of variations on the size and equality of intervals.

Art Kendall
Social Research ConsultantsINPUT PROGRAM. LOOP id=1 TO 100. COMPUTE x = rnd(rv.uniform(.5,5.5)). compute x_sq = x**2. compute x_cubed = x**3. compute x_sqrt =sqrt(x). compute x_spread1.10 = (x-1)+((x-1)*1.10). compute x_spread1.25 = (x-1)+((x-1)*1.25). compute x_spread1.50 = (x-1)+((x-1)*1.50). compute x_spread2 = (x-1)+((x-1)*2.00). compute x_spread3 = (x-1)+((x-1)*3.00).. compute x_spread4 = (x-1)+((x-1)*4.00). END CASE. END LOOP. END FILE. END INPUT PROGRAM. do repeat fuzz = .01, .02,.05,.10,.25,.50 1.00/ xfuzzed = xfuzzed.01, xfuzzed.02,xfuzzed.05,xfuzzed.10,xfuzzed.25,xfuzzed.50 xfuzzed1. compute xfuzzed = x + rv.uniform(0,fuzz). *compute xfuzzed = x + rv.uniform(0,fuzz*x).
end repeat. FORMATS id (F3.0) X to x_cubed x_spread2 to x_spread4(F3) x_sqrt X_spread1.10 to x_spread1.50 (f6.2). FREQUENCIES VARS= X to xfuzzed1. correlations vars = x_sq to xfuzzed1 with x. crosstabs x_sq to x_spread4 by x. *edit grph in output to put in a linear fit line. * Chart Builder. GGRAPH /GRAPHDATASET NAME="graphdataset" VARIABLES=x x_cubed MISSING=LISTWISE REPORTMISSING=NO /GRAPHSPEC SOURCE=INLINE. BEGIN GPL SOURCE: s=userSource(id("graphdataset")) DATA: x=col(source(s), name("x")) DATA: x_cubed=col(source(s), name("x_cubed")) GUIDE: axis(dim(1), label("x")) GUIDE: axis(dim(2), label("x_cubed")) ELEMENT: point(position(x*x_cubed)) END GPL. * Chart Builder. GGRAPH /GRAPHDATASET NAME="graphdataset" VARIABLES=x xfuzzed1 MISSING=LISTWISE REPORTMISSING=NO /GRAPHSPEC SOURCE=INLINE. BEGIN GPL SOURCE: s=userSource(id("graphdataset")) DATA: x=col(source(s), name("x")) DATA: xfuzzed1=col(source(s), name("xfuzzed1")) GUIDE: axis(dim(1), label("x")) GUIDE: axis(dim(2), label("xfuzzed1")) ELEMENT: point(position(x*xfuzzed1)) END GPL.
Allan Lundy, PhD wrote:

First off, note that Chris's example would still correlate at r= .885 with ordinal scores of 1-4, and, though it might look more curved, Gerard's example would correlate at r= .998.

But here's a much more basic consideration. Even if we use the exact number of years of education, this itself treats the difference between 5 years and 8 years as the same as the difference between 1 year of college and 4 years of college. It seems satisfyingly exact to refer to "years of education," but most likely, we are using that as a proxy for something like knowledge, intellectual sophistication, etc. Hence, it may still not be a one-to-one representation of whatever we are using it for. Likewise many other variables in the social sciences, at least. Is a 50-year-old twice something than a 25-year-old? Is the difference between ages 0 and 10 the same as between 25 and 35?

To wax philosophical, I have often had a similar complaint about the way intelligence is measured. IQ scores were developed on the ASSUMPTION that intelligence is normally distributed. Having taught at a wide range of grades and student ability levels, I am convinced that it is not. What we really mean by intelligence is positively skewed, like wealth, and for the same reason: once you have a lot of it, you tend to get more and more of it.

But don't get me started.
Allan

At 10:35 AM 6/16/2009, Gerard M. Keogh wrote:

AND -
re education you can recode levels to years in fulltime education giving
primary = 9, secondary = 14, 3rd level = 18, 4th level = 22 etc.
and the curvature will be worse again.

Is this discussion not an aguument for proportional odds regression - not
sure but probably available in SPSS as an add-on?
Alternative - use the polr method in R.

Gerard

             Dr C B Stride
             <c.b.stride@sheff
             ield.ac.uk>                                                To
             Sent by:                  [hidden email]
             "SPSSX(r)                                                  cc
             Discussion"
             <SPSSX-L@LISTSERV                                     Subject
             .UGA.EDU>                 Re: Ordinal predictor: It CAN be
                                       treated AS Continuous

             16/06/2009 14:59

             Please respond to
             c.b.stride@sheffi
                 eld.ac.uk

Interesting... and I can see the argument for this approach where you
have, for instance, likert scale response codings to questionnaire items.

However, I would consider Eins' highest education level variable an
example of the type of ordinal variable where differences between
vategories could be verey small or very large;

Also, whilst correlations between the true underlying and ordinal
versions of a var may be very high, that isn't actually the only issue
when using the ordinal var as a predictor.

Take the following example: ordinal variable predicting continuous
outcome. ordinal var edqual coded 1 = no ed,2 = a-level, 3 = B.Sc ,4 =
Phd. Gives a good looking linear fit.
But actually, the 'true' spacing between categories, in terms of
educational competence, would be 1,8,9,10
Now, if you plot with those numbers on the X-axis, the relationship
looks a lot more curvilinear!

cheers
Chris

Allan Lundy, PhD wrote:
>
> Hi, All who are interested,
>
> I'd like to weigh in on this issue. True, technically Chris is
> correct. However, it makes surprisingly little difference to the
> stats. If you can reasonably assume that the data underlying the
> ordinal measure is actually continuous, which is certainly the case
> here, then it can be shown empirically that the ordinal measure will
> correlate very highly with the "true" data. I have a couple of Excel
> spreadsheets programmed to randomly generate numbers on a "true" scale
> that vary between 1 and 10 points apart, then correlate them with the
> ordinal equivalent. Correlations are almost always r= .95 or higher,
> and typically above r= .98. In other words, the ordinal measure is a
> much more accurate reflection of the presumed true underlying scale
> than most measures in the social sciences. If anyone would like copies
> of my explanation and Excel files, please contact me directly.
>
> Of course, treating an ordinal measure as continuous is not perfect,
> but I would argue that it is not very unconservative and is more
> informative than treating the values as not on a scale at all, which
> is what dummy variables do.
> Allan
>
>
>
> At 06:15 AM 6/16/2009, Dr C B Stride wrote:
>> Hi Eins
>> If you do, and retain the coding 1,2,3,4, then you will be making the
>> assumption that the difference in standard of education between each
>> category is somehow equal. I would personally recommend considering it
>> as a categorical variable and enter 3 dummy vars to represent the 4 cats
>> (in fact, since you are running logistic regression, you can define the
>> variable as categorical and SPSS automatically does this dummy coding
>> for you)
>> cheers
>> Chris
>>
>> Eins Bernardo wrote:
>>> Hi all,
>>> One of the independent variables in my logistic regression is
>>> "education of mother" which is ordinal with values 1 to 4 (1 being
>>> elementary and 4 being postgraduate). Can I consider it as continuous
>>> rather than categorical so that my interpretation of the exp(B) for
>>> example would be the log odds for Y=1 (my dependent) is higher when
>>> the mother has more eduation?
>>> Eins
>>>

Allan Lundy, PhD
Research Consultant      [hidden email]

Business & Cell (any time): 215 820-8100
Home: Voice and fax (8am - 10pm, 7 days/week): 215 885-5313
Address: 108 Cliff Terrace, Wyncote, PA 19095
Visit my Web site at   www.dissertationconsulting.net
===================== 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

Art Kendall
Social Research Consultants

Juanito Talili

Re: Ordinal predictor: It CAN be treated AS Continuous

In reply to this post by Allan Lundy, PhD

Art wrote:

>>I have attached some PASW (SPSS) syntax that I use to look at discrepancies from >>perfectly equal intervals.

Just a clarification. Do you mean discrepancies of the Likert/ordinal Scale from perfectly equal intervals? What do you mean by perfectly equal intervals?

>>It changes the intervals in 3 ways. 1) by basic transformations. 2) by increasingly larger intervals 3) by different amounts of fuzz around scores.
Of course careful design of measurement would avoid such a simplistic representation of a construct as using a single "Likert" item.

If you do the plots, go back and edit the output to insert a linear fit.
Open a new instance of SPSS. Copy the syntax below to a syntax file. Click <run>. Click <all>.

I run your syntax. If I understand correctly, the X variable in the SPSS outputs serves as the variable with 5-point likert responses Questions:

1. Why do you introduce the following terms in your simulation: Square of X, Cube of X, Square root of X, Spread, and fuzzed?

2. The variables in the spss outputs with spread and "fuzzed" are new to me. What are the spread and "fuzzed? What are the relevance of the "spread" and "fuzzed" variables with the ordinal variable? Why are spread and 'fuzzed" variables introduce in the simulation? Can you please cite reference(s) about these things?

The simulation is very interesting to me. However, I need to understand why these were done that way.

Thank you for your time, ART.

Juanito

--- On Tue, 6/16/09, Art Kendall <[hidden email]> wrote:

From: Art Kendall <[hidden email]>
Subject: Re: Ordinal predictor: It CAN be treated AS Continuous
To: [hidden email]
Date: Tuesday, 16 June, 2009, 4:36 PM

I have attached some PASW (SPSS) syntax that I use to look at discrepancies from perfectly equal intervals.
It changes the intervals in 3 ways. 1) by basic transformations. 2) by increasingly larger intervals 3) by different amounts of fuzz around scores.
Of course careful design of measurement would avoid such a simplistic representation of a construct as using a single "Likert" item.

If you do the plots, go back and edit the output to insert a linear fit.
Open a new instance of SPSS. Copy the syntax below to a syntax file. Click <run>. Click <all>.

You can easily modify this to see other kinds of variations on the size and equality of intervals.

Art Kendall
Social Research ConsultantsINPUT PROGRAM. LOOP id=1 TO 100. COMPUTE x = rnd(rv.uniform(.5,5.5)). compute x_sq = x**2. compute x_cubed = x**3. compute x_sqrt =sqrt(x). compute x_spread1.10 = (x-1)+((x-1)*1.10). compute x_spread1.25 = (x-1)+((x-1)*1.25). compute x_spread1.50 = (x-1)+((x-1)*1.50). compute x_spread2    = (x-1)+((x-1)*2.00). compute x_spread3    = (x-1)+((x-1)*3.00).. compute x_spread4    = (x-1)+((x-1)*4.00). END CASE. END LOOP. END FILE. END INPUT PROGRAM. do repeat fuzz = .01, .02,.05,.10,.25,.50 1.00/ xfuzzed = xfuzzed.01, xfuzzed.02,xfuzzed.05,xfuzzed.10,xfuzzed.25,xfuzzed.50 xfuzzed1. compute xfuzzed = x + rv.uniform(0,fuzz). *compute xfuzzed = x + rv.uniform(0,fuzz*x).
end repeat. FORMATS id (F3.0) X to x_cubed x_spread2 to x_spread4(F3) x_sqrt X_spread1.10 to x_spread1.50 (f6.2). FREQUENCIES VARS= X to xfuzzed1. correlations vars = x_sq to xfuzzed1 with x. crosstabs x_sq to x_spread4 by x. *edit grph in output to put in a linear fit line. * Chart Builder. GGRAPH /GRAPHDATASET NAME="graphdataset" VARIABLES=x x_cubed MISSING=LISTWISE REPORTMISSING=NO /GRAPHSPEC SOURCE=INLINE. BEGIN GPL SOURCE: s=userSource(id("graphdataset")) DATA: x=col(source(s), name("x")) DATA: x_cubed=col(source(s), name("x_cubed")) GUIDE: axis(dim(1), label("x")) GUIDE: axis(dim(2), label("x_cubed")) ELEMENT: point(position(x*x_cubed)) END GPL. * Chart Builder. GGRAPH /GRAPHDATASET NAME="graphdataset" VARIABLES=x xfuzzed1 MISSING=LISTWISE REPORTMISSING=NO /GRAPHSPEC SOURCE=INLINE. BEGIN GPL SOURCE: s=userSource(id("graphdataset")) DATA: x=col(source(s), name("x")) DATA: xfuzzed1=col(source(s), name("xfuzzed1")) GUIDE: axis(dim(1), label("x")) GUIDE: axis(dim(2), label("xfuzzed1")) ELEMENT: point(position(x*xfuzzed1)) END GPL.
Allan Lundy, PhD wrote:

First off, note that Chris's example would still correlate at r= .885 with ordinal scores of 1-4, and, though it might look more curved, Gerard's example would correlate at r= .998.

But here's a much more basic consideration. Even if we use the exact number of years of education, this itself treats the difference between 5 years and 8 years as the same as the difference between 1 year of college and 4 years of college. It seems satisfyingly exact to refer to "years of education," but most likely, we are using that as a proxy for something like knowledge, intellectual sophistication, etc. Hence, it may still not be a one-to-one representation of whatever we are using it for. Likewise many other variables in the social sciences, at least. Is a 50-year-old twice something than a 25-year-old? Is the difference between ages 0 and 10 the same as between 25 and 35?

To wax philosophical, I have often had a similar complaint about the way intelligence is measured. IQ scores were developed on the ASSUMPTION that intelligence is normally distributed. Having taught at a wide range of grades and student ability levels, I am convinced that it is not. What we really mean by intelligence is positively skewed, like wealth, and for the same reason: once you have a lot of it, you tend to get more and more of it.

But don't get me started.
Allan

At 10:35 AM 6/16/2009, Gerard M. Keogh wrote:

AND -
re education you can recode levels to years in fulltime education giving
primary = 9, secondary = 14, 3rd level = 18, 4th level = 22 etc.
and the curvature will be worse again.

Is this discussion not an aguument for proportional odds regression - not
sure but probably available in SPSS as an add-on?
Alternative - use the polr method in R.

Gerard

             Dr C B Stride
             <c.b.stride@sheff
             ield.ac.uk>                                                To
             Sent by:                  SPSSX-L@...
             "SPSSX(r)                                                  cc
             Discussion"
             <SPSSX-L@LISTSERV                                     Subject
             .UGA.EDU>                 Re: Ordinal predictor: It CAN be
                                       treated AS Continuous

             16/06/2009 14:59

             Please respond to
             c.b.stride@sheffi
                 eld.ac.uk

Interesting... and I can see the argument for this approach where you
have, for instance, likert scale response codings to questionnaire items.

However, I would consider Eins' highest education level variable an
example of the type of ordinal variable where differences between
vategories could be verey small or very large;

Also, whilst correlations between the true underlying and ordinal
versions of a var may be very high, that isn't actually the only issue
when using the ordinal var as a predictor.

Take the following example: ordinal variable predicting continuous
outcome. ordinal var edqual coded 1 = no ed,2 = a-level, 3 = B.Sc ,4 =
Phd. Gives a good looking linear fit.
But actually, the 'true' spacing between categories, in terms of
educational competence, would be 1,8,9,10
Now, if you plot with those numbers on the X-axis, the relationship
looks a lot more curvilinear!

cheers
Chris

Allan Lundy, PhD wrote:

>
> Hi, All who are interested,
>
> I'd like to weigh in on this issue. True, technically Chris is
> correct. However, it makes surprisingly little difference to the
> stats. If you can reasonably assume that the data underlying the
> ordinal measure is actually continuous, which is certainly the case
> here, then it can be shown empirically that the ordinal measure will
> correlate very highly with the "true" data. I have a couple of Excel
> spreadsheets programmed to randomly generate numbers on a "true" scale
> that vary between 1 and 10 points apart, then correlate them with the
> ordinal equivalent. Correlations are almost always r= .95 or higher,
> and typically above r= .98. In other words, the ordinal measure is a
> much more accurate reflection of the presumed true underlying scale
> than most measures in the social sciences. If anyone would like copies
> of my explanation and Excel files, please contact me directly.
>
> Of course, treating an ordinal measure as continuous is not perfect,
> but I would argue that it is not very unconservative and is more
> informative than treating the values as not on a scale at all, which
> is what dummy variables do.
> Allan
>
>
>
> At 06:15 AM 6/16/2009, Dr C B Stride wrote:
>> Hi Eins
>> If you do, and retain the coding 1,2,3,4, then you will be making the
>> assumption that the difference in standard of education between each
>> category is somehow equal. I would personally recommend considering it
>> as a categorical variable and enter 3 dummy vars to represent the 4 cats
>> (in fact, since you are running logistic regression, you can define the
>> variable as categorical and SPSS automatically does this dummy coding
>> for you)
>> cheers
>> Chris
>>
>> Eins Bernardo wrote:
>>> Hi all,
>>> One of the independent variables in my logistic regression is
>>> "education of mother" which is ordinal with values 1 to 4 (1 being
>>> elementary and 4 being postgraduate). Can I consider it as continuous
>>> rather than categorical so that my interpretation of the exp(B) for
>>> example would be the log odds for Y=1 (my dependent) is higher when
>>> the mother has more eduation?
>>> Eins
>>>

Allan Lundy, PhD
Research Consultant      Allan.Lundy@...

Business & Cell (any time): 215 820-8100
Home: Voice and fax (8am - 10pm, 7 days/week): 215 885-5313
Address: 108 Cliff Terrace, Wyncote, PA 19095
Visit my Web site at   www.dissertationconsulting.net
===================== To manage your subscription to SPSSX-L, send a message to LISTSERV@... (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

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Art Kendall

Re: Ordinal predictor: It CAN be treated AS Continuous

In the 1960's there was a lot of work and thought about levels of measurement. Likert items have a response scale of that is ordered categories and the question was whether it made sense to treat the intervals as equal to each other. In other words is the difference between 1 and 2 substantively the same as the difference between 3 and for when considering the underlying construct. [Recall that Likert items are meant to be summed (averaged) into a summative score.]

An common question today is whether it is ok to stick with the conventional use of a single item as interval level, or should we limit ourselves to treating it as strictly ordinal.
[there are two senses of the word ordinal. One is that the variable is a strict ranking of the cases. There are (about) as many values as there are cases (no or few ties). The other is that there are a relatively few values and they are ordered (many ties) but the analyst feels that the sizes of intervals are very discrepant from each other.]
Also the sum of close to interval items, is even closer to interval level.

<on soapbox>
The time to think about the quality of the measurements is before the data is gathered. Reducing continuous constructs to very few values loses a lot of power.
The ultimate reduction is of course is to unnecessarily dichotomize a construct, e.g., to commit the nefarious median split.
<off soapbox>

The availability of CATEGORIES now make it more straight forward to examine the assumptions about level of measurement.

other comments interspersed.

Art Kendall
Social Research Consultants

Juanito Talili wrote:

Art wrote:

>>I have attached some PASW (SPSS) syntax that I use to look at discrepancies from >>perfectly equal intervals.

Just a clarification. Do you mean discrepancies of the Likert/ordinal Scale from perfectly equal intervals? What do you mean by perfectly equal intervals?

>>It changes the intervals in 3 ways. 1) by basic transformations. 2) by increasingly larger intervals 3) by different amounts of fuzz around scores.
Of course careful design of measurement would avoid such a simplistic representation of a construct as using a single "Likert" item.

If you do the plots, go back and edit the output to insert a linear fit.
Open a new instance of SPSS. Copy the syntax below to a syntax file. Click <run>. Click <all>.

I run your syntax. If I understand correctly, the X variable in the SPSS outputs serves as the variable with 5-point likert responses

Although Likert items have 5 points there are response scales other than Strongly Disagree ... Strongly Agree that have 5 legitimate values, e.g., extent scales never or almost never (1) . . . to always or almost always (5).

1. Why do you introduce the following terms in your simulation: Square of X, Cube of X, Square root of X, Spread, and fuzzed?

The underlying question is: How much substantive difference does it make if either x or its transform is the "true" value and the other is the way it is represented in the data?
The interval between 1 and 2 is 1. The interval between 1**2 and 2**2 (1 and 4) is 3. The interval between 4 and 5 is 1. The interval between 4**2 and 5**2 (16 and 25) is 9.
So the size of the intervals is not the same in the two representations.

So the simulation uses different kinds of unequal intervals to look at how much difference it makes to use the alternative representations.

2. The variables in the spss outputs with spread and "fuzzed" are new to me. What are the spread and "fuzzed? What are the relevance of the "spread" and "fuzzed" variables with the ordinal variable? Why are spread and 'fuzzed" variables introduce in the simulation?

the Square of X, Cube of X, Square root of X, Spread are used to demo what systematic changes in the size (spread) of the the intervals do.

"Fuzzed" was used to refer to values that varied by some random process from the integer values they approximated.
The x could be ranking of the "true" value" or conversely it can be thought of as the true interval value.

Can you please cite reference(s) about these things?

Not offhand. The demonstration here is not a formal derivation but is rather meant to provide an intuitive feel.

The simulation is very interesting to me. However, I need to understand why these were done that way.

Thank you for your time, ART.

Juanito

--- On Tue, 6/16/09, Art Kendall [hidden email] wrote:

From: Art Kendall [hidden email]
Subject: Re: Ordinal predictor: It CAN be treated AS Continuous
To: [hidden email]
Date: Tuesday, 16 June, 2009, 4:36 PM

I have attached some PASW (SPSS) syntax that I use to look at discrepancies from perfectly equal intervals.
It changes the intervals in 3 ways. 1) by basic transformations. 2) by increasingly larger intervals 3) by different amounts of fuzz around scores.
Of course careful design of measurement would avoid such a simplistic representation of a construct as using a single "Likert" item.

If you do the plots, go back and edit the output to insert a linear fit.
Open a new instance of SPSS. Copy the syntax below to a syntax file. Click <run>. Click <all>.

You can easily modify this to see other kinds of variations on the size and equality of intervals.

Art Kendall
Social Research ConsultantsINPUT PROGRAM. LOOP id=1 TO 100. COMPUTE x = rnd(rv.uniform(.5,5.5)). compute x_sq = x**2. compute x_cubed = x**3. compute x_sqrt =sqrt(x). compute x_spread1.10 = (x-1)+((x-1)*1.10). compute x_spread1.25 = (x-1)+((x-1)*1.25). compute x_spread1.50 = (x-1)+((x-1)*1.50). compute x_spread2    = (x-1)+((x-1)*2.00). compute x_spread3    = (x-1)+((x-1)*3.00).. compute x_spread4    = (x-1)+((x-1)*4.00). END CASE. END LOOP. END FILE. END INPUT PROGRAM. do repeat fuzz = .01, .02,.05,.10,.25,.50 1.00/ xfuzzed = xfuzzed.01, xfuzzed.02,xfuzzed.05,xfuzzed.10,xfuzzed.25,xfuzzed.50 xfuzzed1. compute xfuzzed = x + rv.uniform(0,fuzz). *compute xfuzzed = x + rv.uniform(0,fuzz*x).
end repeat. FORMATS id (F3.0) X to x_cubed x_spread2 to x_spread4(F3) x_sqrt X_spread1.10 to x_spread1.50 (f6.2). FREQUENCIES VARS= X to xfuzzed1. correlations vars = x_sq to xfuzzed1 with x. crosstabs x_sq to x_spread4 by x. *edit grph in output to put in a linear fit line. * Chart Builder. GGRAPH /GRAPHDATASET NAME="graphdataset" VARIABLES=x x_cubed MISSING=LISTWISE REPORTMISSING=NO /GRAPHSPEC SOURCE=INLINE. BEGIN GPL SOURCE: s=userSource(id("graphdataset")) DATA: x=col(source(s), name("x")) DATA: x_cubed=col(source(s), name("x_cubed")) GUIDE: axis(dim(1), label("x")) GUIDE: axis(dim(2), label("x_cubed")) ELEMENT: point(position(x*x_cubed)) END GPL. * Chart Builder. GGRAPH /GRAPHDATASET NAME="graphdataset" VARIABLES=x xfuzzed1 MISSING=LISTWISE REPORTMISSING=NO /GRAPHSPEC SOURCE=INLINE. BEGIN GPL SOURCE: s=userSource(id("graphdataset")) DATA: x=col(source(s), name("x")) DATA: xfuzzed1=col(source(s), name("xfuzzed1")) GUIDE: axis(dim(1), label("x")) GUIDE: axis(dim(2), label("xfuzzed1")) ELEMENT: point(position(x*xfuzzed1)) END GPL.
Allan Lundy, PhD wrote:

First off, note that Chris's example would still correlate at r= .885 with ordinal scores of 1-4, and, though it might look more curved, Gerard's example would correlate at r= .998.

But here's a much more basic consideration. Even if we use the exact number of years of education, this itself treats the difference between 5 years and 8 years as the same as the difference between 1 year of college and 4 years of college. It seems satisfyingly exact to refer to "years of education," but most likely, we are using that as a proxy for something like knowledge, intellectual sophistication, etc. Hence, it may still not be a one-to-one representation of whatever we are using it for. Likewise many other variables in the social sciences, at least. Is a 50-year-old twice something than a 25-year-old? Is the difference between ages 0 and 10 the same as between 25 and 35?

To wax philosophical, I have often had a similar complaint about the way intelligence is measured. IQ scores were developed on the ASSUMPTION that intelligence is normally distributed. Having taught at a wide range of grades and student ability levels, I am convinced that it is not. What we really mean by intelligence is positively skewed, like wealth, and for the same reason: once you have a lot of it, you tend to get more and more of it.

But don't get me started.
Allan

At 10:35 AM 6/16/2009, Gerard M. Keogh wrote:

AND -
re education you can recode levels to years in fulltime education giving
primary = 9, secondary = 14, 3rd level = 18, 4th level = 22 etc.
and the curvature will be worse again.

Is this discussion not an aguument for proportional odds regression - not
sure but probably available in SPSS as an add-on?
Alternative - use the polr method in R.

Gerard

             Dr C B Stride
             <c.b.stride@sheff
             ield.ac.uk>                                                To
             Sent by:                  SPSSX-L@...
             "SPSSX(r)                                                  cc
             Discussion"
             <SPSSX-L@LISTSERV                                     Subject
             .UGA.EDU>                 Re: Ordinal predictor: It CAN be
                                       treated AS Continuous

             16/06/2009 14:59

             Please respond to
             c.b.stride@sheffi
                 eld.ac.uk

Interesting... and I can see the argument for this approach where you
have, for instance, likert scale response codings to questionnaire items.

However, I would consider Eins' highest education level variable an
example of the type of ordinal variable where differences between
vategories could be verey small or very large;

Also, whilst correlations between the true underlying and ordinal
versions of a var may be very high, that isn't actually the only issue
when using the ordinal var as a predictor.

Take the following example: ordinal variable predicting continuous
outcome. ordinal var edqual coded 1 = no ed,2 = a-level, 3 = B.Sc ,4 =
Phd. Gives a good looking linear fit.
But actually, the 'true' spacing between categories, in terms of
educational competence, would be 1,8,9,10
Now, if you plot with those numbers on the X-axis, the relationship
looks a lot more curvilinear!

cheers
Chris

Allan Lundy, PhD wrote:
>
> Hi, All who are interested,
>
> I'd like to weigh in on this issue. True, technically Chris is
> correct. However, it makes surprisingly little difference to the
> stats. If you can reasonably assume that the data underlying the
> ordinal measure is actually continuous, which is certainly the case
> here, then it can be shown empirically that the ordinal measure will
> correlate very highly with the "true" data. I have a couple of Excel
> spreadsheets programmed to randomly generate numbers on a "true" scale
> that vary between 1 and 10 points apart, then correlate them with the
> ordinal equivalent. Correlations are almost always r= .95 or higher,
> and typically above r= .98. In other words, the ordinal measure is a
> much more accurate reflection of the presumed true underlying scale
> than most measures in the social sciences. If anyone would like copies
> of my explanation and Excel files, please contact me directly.
>
> Of course, treating an ordinal measure as continuous is not perfect,
> but I would argue that it is not very unconservative and is more
> informative than treating the values as not on a scale at all, which
> is what dummy variables do.
> Allan
>
>
>
> At 06:15 AM 6/16/2009, Dr C B Stride wrote:
>> Hi Eins
>> If you do, and retain the coding 1,2,3,4, then you will be making the
>> assumption that the difference in standard of education between each
>> category is somehow equal. I would personally recommend considering it
>> as a categorical variable and enter 3 dummy vars to represent the 4 cats
>> (in fact, since you are running logistic regression, you can define the
>> variable as categorical and SPSS automatically does this dummy coding
>> for you)
>> cheers
>> Chris
>>
>> Eins Bernardo wrote:
>>> Hi all,
>>> One of the independent variables in my logistic regression is
>>> "education of mother" which is ordinal with values 1 to 4 (1 being
>>> elementary and 4 being postgraduate). Can I consider it as continuous
>>> rather than categorical so that my interpretation of the exp(B) for
>>> example would be the log odds for Y=1 (my dependent) is higher when
>>> the mother has more eduation?
>>> Eins
>>>

Allan Lundy, PhD
Research Consultant      Allan.Lundy@...

Business & Cell (any time): 215 820-8100
Home: Voice and fax (8am - 10pm, 7 days/week): 215 885-5313
Address: 108 Cliff Terrace, Wyncote, PA 19095
Visit my Web site at   www.dissertationconsulting.net
===================== To manage your subscription to SPSSX-L, send a message to LISTSERV@... (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

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Art Kendall
Social Research Consultants

Hector Maletta

Re: Ordinal predictor: It CAN be treated AS Continuous

Just my two cents in this interesting thread:

Somebody pointed out that even interval measures are in a sense not strictly interval, since the difference, say, between ages 10 and 15 is not the same as the difference between ages 30 and 35.

I beg to disagree.

I think one has to distinguish between the variable itself (or the underlying continuous construct), and its (behavioral, biological or other) correlates. The question with ordinal scales refers to the variable itself: it asks whether the difference in, say, “patriotism” between responses 1 and 2 is the same as the difference between responses 2 and 3 or between 4 and 5, in a Likert scale. Perhaps passing from 1 to 2 is “easier” than passing from 4 to 5 (the former may require, say, respecting the flag and the latter giving your life for your country). It refers to the length of the “jump” from one category to the next, in terms of the underlying construct exclusively.

Now, in the case of age, when you treat age as an interval variable you measure simply age, time elapsed since birth. You are not asking about biological changes occurred in the interval, or psychological significance of the period, or anything else: just the amount of time elapsed (that is, if you want to measure age as continuous). The consequences of age may be nonlinear; mortality, for instance, is relatively high at age 0, then declines to age 5, stays very low until middle age and then climbs until old age. Therefore, one more year implies different MORTALITY changes at different ages, but it always means the same AGE difference.

On the other hand, you may be interested in age just as a qualitative marker of phases in life, and not as an interval of time since birth (childhood, youth, adulthood, old age). In this case, age is no longer “age in years”, but “life stage”, and may be treated as nominal or ordinal (depending on your analysis); you need not keep the natural (chronological) order: in terms of mortality you may rank the groups in an awkward manner: oldies, infants, adults, youths (or the reverse), and it will still be an ordinal (not interval) variable. As far as you’re concerned, the age groups for mortality-analysis purposes may have been based on ethnicity or gender or region: it doesn’t matter because it is just a subgroup marker (ordinal or nominal). In some cases the marker may represent an interval measure (e.g. groups defined by levels of blood pressure) but it is rather rare because of the multitude of possible values, which would generate too many groups.

Hector

From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Art Kendall
Sent: 17 June 2009 11:18
To: [hidden email]
Subject: Re: Ordinal predictor: It CAN be treated AS Continuous

Art wrote:

>>I have attached some PASW (SPSS) syntax that I use to look at discrepancies from >>perfectly equal intervals.

Just a clarification. Do you mean discrepancies of the Likert/ordinal Scale from perfectly equal intervals? What do you mean by perfectly equal intervals?

If you do the plots, go back and edit the output to insert a linear fit.
Open a new instance of SPSS. Copy the syntax below to a syntax file. Click <run>. Click <all>.

I run your syntax. If I understand correctly, the X variable in the SPSS outputs serves as the variable with 5-point likert responses

1. Why do you introduce the following terms in your simulation: Square of X, Cube of X, Square root of X, Spread, and fuzzed?

Can you please cite reference(s) about these things?

Not offhand. The demonstration here is not a formal derivation but is rather meant to provide an intuitive feel.

The simulation is very interesting to me. However, I need to understand why these were done that way.

Thank you for your time, ART.

Juanito

--- On Tue, 6/16/09, Art Kendall [hidden email] wrote:

From: Art Kendall [hidden email]
Subject: Re: Ordinal predictor: It CAN be treated AS Continuous
To: [hidden email]
Date: Tuesday, 16 June, 2009, 4:36 PM

I have attached some PASW (SPSS) syntax that I use to look at discrepancies from perfectly equal intervals.
It changes the intervals in 3 ways. 1) by basic transformations. 2) by increasingly larger intervals 3) by different amounts of fuzz around scores.
Of course careful design of measurement would avoid such a simplistic representation of a construct as using a single "Likert" item.

If you do the plots, go back and edit the output to insert a linear fit.
Open a new instance of SPSS. Copy the syntax below to a syntax file. Click <run>. Click <all>.

You can easily modify this to see other kinds of variations on the size and equality of intervals.

Art Kendall
Social Research Consultants

INPUT PROGRAM.
LOOP id=1 TO 100.
COMPUTE x = rnd(rv.uniform(.5,5.5)).
compute x_sq = x**2.
compute x_cubed = x**3.
compute x_sqrt =sqrt(x).
compute x_spread1.10 = (x-1)+((x-1)*1.10).
compute x_spread1.25 = (x-1)+((x-1)*1.25).
compute x_spread1.50 = (x-1)+((x-1)*1.50).
compute x_spread2    = (x-1)+((x-1)*2.00).
compute x_spread3    = (x-1)+((x-1)*3.00)..
compute x_spread4    = (x-1)+((x-1)*4.00).
END CASE.
END LOOP.
END FILE.
END INPUT PROGRAM.
do repeat fuzz = .01, .02,.05,.10,.25,.50 1.00/
xfuzzed = xfuzzed.01, xfuzzed.02,xfuzzed.05,xfuzzed.10,xfuzzed.25,xfuzzed.50 xfuzzed1.
compute xfuzzed = x + rv.uniform(0,fuzz).
*compute xfuzzed = x + rv.uniform(0,fuzz*x).
end repeat.
FORMATS id (F3.0) X to x_cubed x_spread2 to x_spread4(F3) x_sqrt X_spread1.10 to x_spread1.50 (f6.2).
FREQUENCIES VARS= X to xfuzzed1.
correlations vars = x_sq to xfuzzed1 with x.
crosstabs x_sq to x_spread4 by x.
*edit grph in output to put in a linear fit line.
* Chart Builder.
GGRAPH
/GRAPHDATASET NAME="graphdataset" VARIABLES=x x_cubed MISSING=LISTWISE REPORTMISSING=NO
/GRAPHSPEC SOURCE=INLINE.
BEGIN GPL
SOURCE: s=userSource(id("graphdataset"))
DATA: x=col(source(s), name("x"))
DATA: x_cubed=col(source(s), name("x_cubed"))
GUIDE: axis(dim(1), label("x"))
GUIDE: axis(dim(2), label("x_cubed"))
ELEMENT: point(position(x*x_cubed))
END GPL.

* Chart Builder.
GGRAPH
/GRAPHDATASET NAME="graphdataset" VARIABLES=x xfuzzed1 MISSING=LISTWISE REPORTMISSING=NO
/GRAPHSPEC SOURCE=INLINE.
BEGIN GPL
SOURCE: s=userSource(id("graphdataset"))
DATA: x=col(source(s), name("x"))
DATA: xfuzzed1=col(source(s), name("xfuzzed1"))
GUIDE: axis(dim(1), label("x"))
GUIDE: axis(dim(2), label("xfuzzed1"))
ELEMENT: point(position(x*xfuzzed1))
END GPL.

Allan Lundy, PhD wrote:

First off, note that Chris's example would still correlate at r= .885 with ordinal scores of 1-4, and, though it might look more curved, Gerard's example would correlate at r= .998.

But here's a much more basic consideration. Even if we use the exact number of years of education, this itself treats the difference between 5 years and 8 years as the same as the difference between 1 year of college and 4 years of college. It seems satisfyingly exact to refer to "years of education," but most likely, we are using that as a proxy for something like knowledge, intellectual sophistication, etc. Hence, it may still not be a one-to-one representation of whatever we are using it for. Likewise many other variables in the social sciences, at least. Is a 50-year-old twice something than a 25-year-old? Is the difference between ages 0 and 10 the same as between 25 and 35?

To wax philosophical, I have often had a similar complaint about the way intelligence is measured. IQ scores were developed on the ASSUMPTION that intelligence is normally distributed. Having taught at a wide range of grades and student ability levels, I am convinced that it is not. What we really mean by intelligence is positively skewed, like wealth, and for the same reason: once you have a lot of it, you tend to get more and more of it.

But don't get me started.
Allan

At 10:35 AM 6/16/2009, Gerard M. Keogh wrote:

AND -
re education you can recode levels to years in fulltime education giving
primary = 9, secondary = 14, 3rd level = 18, 4th level = 22 etc.
and the curvature will be worse again.

Is this discussion not an aguument for proportional odds regression - not
sure but probably available in SPSS as an add-on?
Alternative - use the polr method in R.

Gerard

             Dr C B Stride
             <c.b.stride@sheff
             ield.ac.uk>                                                To
             Sent by:                  SPSSX-L@...
             "SPSSX(r)                                                  cc
             Discussion"
             <SPSSX-L@LISTSERV                                     Subject
             .UGA.EDU>                 Re: Ordinal predictor: It CAN be
                                       treated AS Continuous

             16/06/2009 14:59

             Please respond to
             c.b.stride@sheffi
                 eld.ac.uk

Interesting... and I can see the argument for this approach where you
have, for instance, likert scale response codings to questionnaire items.

However, I would consider Eins' highest education level variable an
example of the type of ordinal variable where differences between
vategories could be verey small or very large;

Also, whilst correlations between the true underlying and ordinal
versions of a var may be very high, that isn't actually the only issue
when using the ordinal var as a predictor.

Take the following example: ordinal variable predicting continuous
outcome. ordinal var edqual coded 1 = no ed,2 = a-level, 3 = B.Sc ,4 =
Phd. Gives a good looking linear fit.
But actually, the 'true' spacing between categories, in terms of
educational competence, would be 1,8,9,10
Now, if you plot with those numbers on the X-axis, the relationship
looks a lot more curvilinear!

cheers
Chris

Allan Lundy, PhD wrote:
>
> Hi, All who are interested,
>
> I'd like to weigh in on this issue. True, technically Chris is
> correct. However, it makes surprisingly little difference to the
> stats. If you can reasonably assume that the data underlying the
> ordinal measure is actually continuous, which is certainly the case
> here, then it can be shown empirically that the ordinal measure will
> correlate very highly with the "true" data. I have a couple of Excel
> spreadsheets programmed to randomly generate numbers on a "true" scale
> that vary between 1 and 10 points apart, then correlate them with the
> ordinal equivalent. Correlations are almost always r= .95 or higher,
> and typically above r= .98. In other words, the ordinal measure is a
> much more accurate reflection of the presumed true underlying scale
> than most measures in the social sciences. If anyone would like copies
> of my explanation and Excel files, please contact me directly.
>
> Of course, treating an ordinal measure as continuous is not perfect,
> but I would argue that it is not very unconservative and is more
> informative than treating the values as not on a scale at all, which
> is what dummy variables do.
> Allan
>
>
>
> At 06:15 AM 6/16/2009, Dr C B Stride wrote:
>> Hi Eins
>> If you do, and retain the coding 1,2,3,4, then you will be making the
>> assumption that the difference in standard of education between each
>> category is somehow equal. I would personally recommend considering it
>> as a categorical variable and enter 3 dummy vars to represent the 4 cats
>> (in fact, since you are running logistic regression, you can define the
>> variable as categorical and SPSS automatically does this dummy coding
>> for you)
>> cheers
>> Chris
>>
>> Eins Bernardo wrote:
>>> Hi all,
>>> One of the independent variables in my logistic regression is
>>> "education of mother" which is ordinal with values 1 to 4 (1 being
>>> elementary and 4 being postgraduate). Can I consider it as continuous
>>> rather than categorical so that my interpretation of the exp(B) for
>>> example would be the log odds for Y=1 (my dependent) is higher when
>>> the mother has more eduation?
>>> Eins
>>>

Allan Lundy, PhD
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Allan Lundy, PhD

Re: Ordinal predictor: It CAN be treated AS Continuous

Both Hector and Art have contributed some nice insights and new info to this important and very common, as yet unresolved, issue. I will certainly have to explore CATEGORIES to see what it can do. And Art is absolutely right about not reducing continuous data to categories -- except -- often it is necessary to avoid obtaining precise data in order to maintain both the actual and perceived anonymity of respondents. I recently worked with a data set of about a quarter-million children in which age, school attended, gender, ethnicity, and disability diagnosis would have easily identified most particular children. So, as my motto has it, "Nothing is ever simple."

Re: Hector's comment on my statement that interval measures are often not strictly interval measures: First, as I stated, they are often not strictly interval measures of what they are used as proxies for, so we are on the same page in the sense that more thought needs to go into whether a given measure is appropriate for its use. However, commonsense adjustments may not do the job; age between 30 and 50 may be used as a correlate of earnings, though there is no particular reason to think that earnings rise smoothly with age even within this range. Second, at least among Western and moderately educated people, I suspect that one (implicit? explicit?) advantage of the Likert scale is that respondents interpret the values as evenly spaced, hence the scale is treated as more or less interval. I don't know if this has been empirically researched or even discussed in the psychometric literature.

Now, back to work....

At 12:28 PM 6/17/2009, Hector Maletta wrote:

Just my two cents in this interesting thread:
Somebody pointed out that even interval measures are in a sense not strictly interval, since the difference, say, between ages 10 and 15 is not the same as the difference between ages 30 and 35.
I beg to disagree.
I think one has to distinguish between the variable itself (or the underlying continuous construct), and its (behavioral, biological or other) correlates. The question with ordinal scales refers to the variable itself: it asks whether the difference in, say, patriotism between responses 1 and 2 is the same as the difference between responses 2 and 3 or between 4 and 5, in a Likert scale. Perhaps passing from 1 to 2 is easier than passing from 4 to 5 (the former may require, say, respecting the flag and the latter giving your life for your country). It refers to the length of the jump from one category to the next, in terms of the underlying construct exclusively.
Now, in the case of age, when you treat age as an interval variable you measure simply age, time elapsed since birth. You are not asking about biological changes occurred in the interval, or psychological significance of the period, or anything else: just the amount of time elapsed (that is, if you want to measure age as continuous). The consequences of age may be nonlinear; mortality, for instance, is relatively high at age 0, then declines to age 5, stays very low until middle age and then climbs until old age. Therefore, one more year implies different MORTALITY changes at different ages, but it always means the same AGE difference.
On the other hand, you may be interested in age just as a qualitative marker of phases in life, and not as an interval of time since birth (childhood, youth, adulthood, old age). In this case, age is no longer age in years, but life stage, and may be treated as nominal or ordinal (depending on your analysis); you need not keep the natural (chronological) order: in terms of mortality you may rank the groups in an awkward manner: oldies, infants, adults, youths (or the reverse), and it will still be an ordinal (not interval) variable. As far as youre concerned, the age groups for mortality-analysis purposes may have been based on ethnicity or gender or region: it doesnt matter because it is just a subgroup marker (ordinal or nominal). In some cases the marker may represent an interval measure (e.g. groups defined by levels of blood pressure) but it is rather rare because of the multitude of possible values, which would generate too many groups.

Hector

From: SPSSX(r) Discussion [[hidden email]] On Behalf Of Art Kendall
Sent: 17 June 2009 11:18
To: [hidden email]
Subject: Re: Ordinal predictor: It CAN be treated AS Continuous

In the 1960's there was a lot of work and thought about levels of measurement. Likert items have a response scale of that is ordered categories and the question was whether it made sense to treat the intervals as equal to each other. In other words is the difference between 1 and 2 substantively the same as the difference between 3 and for when considering the underlying construct. [Recall that Likert items are meant to be summed (averaged) into a summative score.]

An common question today is whether it is ok to stick with the conventional use of a single item as interval level, or should we limit ourselves to treating it as strictly ordinal.
[there are two senses of the word ordinal. One is that the variable is a strict ranking of the cases. There are (about) as many values as there are cases (no or few ties). The other is that there are a relatively few values and they are ordered (many ties) but the analyst feels that the sizes of intervals are very discrepant from each other.]
Also the sum of close to interval items, is even closer to interval level.

<on soapbox>
The time to think about the quality of the measurements is before the data is gathered. Reducing continuous constructs to very few values loses a lot of power.
The ultimate reduction is of course is to unnecessarily dichotomize a construct, e.g., to commit the nefarious median split.
<off soapbox>

The availability of CATEGORIES now make it more straight forward to examine the assumptions about level of measurement.

other comments interspersed.

Art Kendall
Social Research Consultants