Question about difference between slopes

[Howard Schuman]

I have two independent logistic regression B values, and would like to
test whether they differ significantly (even at p < .10), as indeed they
do visually with one sloping up and the other down. I wonder if there is
a fairly straightforward way to do this in SPSS, starting from the data
set that includes both. Each line is based on just two points [i.e., two
ages], which are the same for both lines, but with different dependent
variables (attitudes). Advice much appreciated.   -Howard Schuman

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[Ryan]

Howard,

You should be able to test for a significant difference in slopes by
fitting a multivariate model through the GENLIN procedure offered in
SPSS.

You'll need to structure your data set as follows:

ID   Y_Indic   Age   Y
1        1         24     0
1        2         24     1
2        1         33     1
2        2         33     0
3        1         28     0
3        2         28     1
4        1         16     1
4        2         16     1
.
.

Once you've structured your data set as described above, you can fit
the model using the following code:

GENLIN Y (REFERENCE=FIRST) BY Y_Indic (ORDER=ASCENDING) WITH Age
  /MODEL Y_Indic Age Y_Indic*Age INTERCEPT=YES
 DISTRIBUTION=BINOMIAL LINK=LOGIT
  /REPEATED SUBJECT=ID WITHINSUBJECT=Y_Indic SORT=YES
CORRTYPE=EXCHANGEABLE ADJUSTCORR=YES
  /PRINT CPS DESCRIPTIVES MODELINFO FIT SUMMARY SOLUTION.

The test associated with the Y_Indic*Age term will tell you if the
slopes are significantly different.

This code is specifically designed to handle the data set I described.
Deviations from the presumed data set structure may require another
approach.

Ryan

On Thu, Aug 5, 2010 at 3:19 PM, howard schuman <[hidden email]> wrote:

> I have two independent logistic regression B values, and would like to
> test whether they differ significantly (even at p < .10), as indeed they
> do visually with one sloping up and the other down. I wonder if there is
> a fairly straightforward way to do this in SPSS, starting from the data
> set that includes both. Each line is based on just two points [i.e., two
> ages], which are the same for both lines, but with different dependent
> variables (attitudes). Advice much appreciated.   -Howard Schuman
>
> =====================
> 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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[Ryan]

All,

I have woken up to a couple of private emails with comments and
questions. Let me be entirely clear in this post why a standard binary
logistic regression is NOT appropriate in the design I have
envisioned. I am assuming that EACH person was measured on BOTH
dichotomous items. Hence you see two records for each subject ID in
the dummy data set I posted previously. This introduces repeated
measures, and one usually wants to account for correlation resulting
from repeated measures. Treating observations as independent as one
would do when fitting a standard binary logistic regression is usually
an incorrect assumption. The multivariate model GEE I presented in the
previous post accounts for the correlation introduced by repeated
measures.

Now, if my assumption that EACH person was measured on BOTH
dichotomous outcomes is NOT correct, then we clearly no longer have
repeated measures. I must admit that if this were true, I'd have some
concerns about the prospect of testing for differences in age slopes
across different samples on different outcomes.

Back to the GEE I suggested in the previous post (assuming repeated
measures)...I was also contacted by another person who suggested that
one DV be coded as 0/1 while the other coded as 1/2. I would NOT do
this. Simply code your DV, "Y," in 0s and 1s, as suggested in my
original post. There is absolutely no need to change the coding
scheme.

If a data set is structured in wide format such as:

ID   Age   DV1   DV2
1     19      0         1
2     20      1         0
3     22      1         1
.
.
.

then an easy way to restructure the data set into long (aka vertical)
format, as is required by the GENLIN procedure for this design, is to
employ the VARSTOCASES function.

Finally, if someone has a comment or question about my posts or
another post in this thread, please post back to the entire list and
not my private email.

Ryan

On Fri, Aug 6, 2010 at 5:44 PM, Ryan Black <[hidden email]> wrote:

> Howard,
>
> You should be able to test for a significant difference in slopes by
> fitting a multivariate model through the GENLIN procedure offered in
> SPSS.
>
> You'll need to structure your data set as follows:
>
> ID   Y_Indic   Age   Y
> 1        1         24     0
> 1        2         24     1
> 2        1         33     1
> 2        2         33     0
> 3        1         28     0
> 3        2         28     1
> 4        1         16     1
> 4        2         16     1
> .
> .
>
> Once you've structured your data set as described above, you can fit
> the model using the following code:
>
> GENLIN Y (REFERENCE=FIRST) BY Y_Indic (ORDER=ASCENDING) WITH Age
>  /MODEL Y_Indic Age Y_Indic*Age INTERCEPT=YES
>  DISTRIBUTION=BINOMIAL LINK=LOGIT
>  /REPEATED SUBJECT=ID WITHINSUBJECT=Y_Indic SORT=YES
> CORRTYPE=EXCHANGEABLE ADJUSTCORR=YES
>  /PRINT CPS DESCRIPTIVES MODELINFO FIT SUMMARY SOLUTION.
>
> The test associated with the Y_Indic*Age term will tell you if the
> slopes are significantly different.
>
> This code is specifically designed to handle the data set I described.
> Deviations from the presumed data set structure may require another
> approach.
>
> Ryan
>
> On Thu, Aug 5, 2010 at 3:19 PM, howard schuman <[hidden email]> wrote:
>> I have two independent logistic regression B values, and would like to
>> test whether they differ significantly (even at p < .10), as indeed they
>> do visually with one sloping up and the other down. I wonder if there is
>> a fairly straightforward way to do this in SPSS, starting from the data
>> set that includes both. Each line is based on just two points [i.e., two
>> ages], which are the same for both lines, but with different dependent
>> variables (attitudes). Advice much appreciated.   -Howard Schuman
>>
>> =====================
>> 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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[Ryan]

One more point--I failed to define the variables in the vertical data
set I proposed, which might be causing some confusion. I will do that
now.

ID = Subject ID
Y_Indic = Response Indicator (1=first dependent variable and 2=second
dependent variable)
Age = Age of Subject (in years)
Y = Actual Response

So, using the data set structure I posted previously:

ID   Y_Indic   Age   Y
1        1         24     0
1        2         24     1
2        1         33     1
2        2         33     0
3        1         28     0
3        2         28     1
4        1         16     1
4        2         16     1
.
.

we see that Subject 1 (ID=1) is 24 years old, and scored a "0" on the
first dependent variable and a "1" on the second dependent variable.
Subject 2 (ID=2) is 33 years old, and scored a "1" on the first
dependent variable and a "0" on the second dependent variable.

HTH,

Ryan

On Sat, Aug 7, 2010 at 8:22 AM, Ryan Black <[hidden email]> wrote:

> All,
>
> I have woken up to a couple of private emails with comments and
> questions. Let me be entirely clear in this post why a standard binary
> logistic regression is NOT appropriate in the design I have
> envisioned. I am assuming that EACH person was measured on BOTH
> dichotomous items. Hence you see two records for each subject ID in
> the dummy data set I posted previously. This introduces repeated
> measures, and one usually wants to account for correlation resulting
> from repeated measures. Treating observations as independent as one
> would do when fitting a standard binary logistic regression is usually
> an incorrect assumption. The multivariate model GEE I presented in the
> previous post accounts for the correlation introduced by repeated
> measures.
>
> Now, if my assumption that EACH person was measured on BOTH
> dichotomous outcomes is NOT correct, then we clearly no longer have
> repeated measures. I must admit that if this were true, I'd have some
> concerns about the prospect of testing for differences in age slopes
> across different samples on different outcomes.
>
> Back to the GEE I suggested in the previous post (assuming repeated
> measures)...I was also contacted by another person who suggested that
> one DV be coded as 0/1 while the other coded as 1/2. I would NOT do
> this. Simply code your DV, "Y," in 0s and 1s, as suggested in my
> original post. There is absolutely no need to change the coding
> scheme.
>
> If a data set is structured in wide format such as:
>
> ID   Age   DV1   DV2
> 1     19      0         1
> 2     20      1         0
> 3     22      1         1
> .
> .
> .
>
> then an easy way to restructure the data set into long (aka vertical)
> format, as is required by the GENLIN procedure for this design, is to
> employ the VARSTOCASES function.
>
> Finally, if someone has a comment or question about my posts or
> another post in this thread, please post back to the entire list and
> not my private email.
>
> Ryan
>
> On Fri, Aug 6, 2010 at 5:44 PM, Ryan Black <[hidden email]> wrote:
>> Howard,
>>
>> You should be able to test for a significant difference in slopes by
>> fitting a multivariate model through the GENLIN procedure offered in
>> SPSS.
>>
>> You'll need to structure your data set as follows:
>>
>> ID   Y_Indic   Age   Y
>> 1        1         24     0
>> 1        2         24     1
>> 2        1         33     1
>> 2        2         33     0
>> 3        1         28     0
>> 3        2         28     1
>> 4        1         16     1
>> 4        2         16     1
>> .
>> .
>>
>> Once you've structured your data set as described above, you can fit
>> the model using the following code:
>>
>> GENLIN Y (REFERENCE=FIRST) BY Y_Indic (ORDER=ASCENDING) WITH Age
>>  /MODEL Y_Indic Age Y_Indic*Age INTERCEPT=YES
>>  DISTRIBUTION=BINOMIAL LINK=LOGIT
>>  /REPEATED SUBJECT=ID WITHINSUBJECT=Y_Indic SORT=YES
>> CORRTYPE=EXCHANGEABLE ADJUSTCORR=YES
>>  /PRINT CPS DESCRIPTIVES MODELINFO FIT SUMMARY SOLUTION.
>>
>> The test associated with the Y_Indic*Age term will tell you if the
>> slopes are significantly different.
>>
>> This code is specifically designed to handle the data set I described.
>> Deviations from the presumed data set structure may require another
>> approach.
>>
>> Ryan
>>
>> On Thu, Aug 5, 2010 at 3:19 PM, howard schuman <[hidden email]> wrote:
>>> I have two independent logistic regression B values, and would like to
>>> test whether they differ significantly (even at p < .10), as indeed they
>>> do visually with one sloping up and the other down. I wonder if there is
>>> a fairly straightforward way to do this in SPSS, starting from the data
>>> set that includes both. Each line is based on just two points [i.e., two
>>> ages], which are the same for both lines, but with different dependent
>>> variables (attitudes). Advice much appreciated.   -Howard Schuman
>>>
>>> =====================
>>> 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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[Howard Schuman]

Ryan,

These were independent samples, as I conceptualize the problem, because
respondents in this survey first recalled or did not recall one of two
memories of national events, and the two were mutually exclusive (e.g.,
one might be World War II and the other might be the Vietnam War). Then
each memory (as a dichotomy: recalled vs. did not recall) was regressed
on age. The problem to be solved is whether the b values from the two
regressions can be said to be different in terms of a p value.
        Howard

Ryan Black wrote:

> All,
>
> I have woken up to a couple of private emails with comments and
> questions. Let me be entirely clear in this post why a standard binary
> logistic regression is NOT appropriate in the design I have
> envisioned. I am assuming that EACH person was measured on BOTH
> dichotomous items. Hence you see two records for each subject ID in
> the dummy data set I posted previously. This introduces repeated
> measures, and one usually wants to account for correlation resulting
> from repeated measures. Treating observations as independent as one
> would do when fitting a standard binary logistic regression is usually
> an incorrect assumption. The multivariate model GEE I presented in the
> previous post accounts for the correlation introduced by repeated
> measures.
>
> Now, if my assumption that EACH person was measured on BOTH
> dichotomous outcomes is NOT correct, then we clearly no longer have
> repeated measures. I must admit that if this were true, I'd have some
> concerns about the prospect of testing for differences in age slopes
> across different samples on different outcomes.
>
> Back to the GEE I suggested in the previous post (assuming repeated
> measures)...I was also contacted by another person who suggested that
> one DV be coded as 0/1 while the other coded as 1/2. I would NOT do
> this. Simply code your DV, "Y," in 0s and 1s, as suggested in my
> original post. There is absolutely no need to change the coding
> scheme.
>
> If a data set is structured in wide format such as:
>
> ID   Age   DV1   DV2
> 1     19      0         1
> 2     20      1         0
> 3     22      1         1
> ..
> ..
> ..
>
> then an easy way to restructure the data set into long (aka vertical)
> format, as is required by the GENLIN procedure for this design, is to
> employ the VARSTOCASES function.
>
> Finally, if someone has a comment or question about my posts or
> another post in this thread, please post back to the entire list and
> not my private email.
>
> Ryan
>
> On Fri, Aug 6, 2010 at 5:44 PM, Ryan Black <[hidden email]> wrote:
>> Howard,
>>
>> You should be able to test for a significant difference in slopes by
>> fitting a multivariate model through the GENLIN procedure offered in
>> SPSS.
>>
>> You'll need to structure your data set as follows:
>>
>> ID   Y_Indic   Age   Y
>> 1        1         24     0
>> 1        2         24     1
>> 2        1         33     1
>> 2        2         33     0
>> 3        1         28     0
>> 3        2         28     1
>> 4        1         16     1
>> 4        2         16     1
>> .
>> .
>>
>> Once you've structured your data set as described above, you can fit
>> the model using the following code:
>>
>> GENLIN Y (REFERENCE=FIRST) BY Y_Indic (ORDER=ASCENDING) WITH Age
>>  /MODEL Y_Indic Age Y_Indic*Age INTERCEPT=YES
>>  DISTRIBUTION=BINOMIAL LINK=LOGIT
>>  /REPEATED SUBJECT=ID WITHINSUBJECT=Y_Indic SORT=YES
>> CORRTYPE=EXCHANGEABLE ADJUSTCORR=YES
>>  /PRINT CPS DESCRIPTIVES MODELINFO FIT SUMMARY SOLUTION.
>>
>> The test associated with the Y_Indic*Age term will tell you if the
>> slopes are significantly different.
>>
>> This code is specifically designed to handle the data set I described.
>> Deviations from the presumed data set structure may require another
>> approach.
>>
>> Ryan
>>
>> On Thu, Aug 5, 2010 at 3:19 PM, howard schuman <[hidden email]> wrote:
>>> I have two independent logistic regression B values, and would like to
>>> test whether they differ significantly (even at p < .10), as indeed they
>>> do visually with one sloping up and the other down. I wonder if there is
>>> a fairly straightforward way to do this in SPSS, starting from the data
>>> set that includes both. Each line is based on just two points [i.e., two
>>> ages], which are the same for both lines, but with different dependent
>>> variables (attitudes). Advice much appreciated.   -Howard Schuman
>>>
>>> =====================
>>> 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
>
>

=====================
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[Ryan]

Howard,

So the subject was not permitted to recall both events? It had to be
one or the other? If so, you are correct that you do not have a
repeated measures design. Here's how I see your data set now:

ID   Memory_Type   Age   Recalled
1        1                   61         0
2        2                   70         1
3        2                   59         1
4        1                   82         0
.

The binary logistic regression equation is simplified to:

logit(y) = b0 + b1*Memory_Type + b2*Age + b3*Memory_Type*Age

where Memory_Type is assumed to be dummy coded. (The LOGISTIC
REGRESSION procedure in SPSS will dummy code for you)

You could easily fit the model employing the LOGISTIC REGRESSION
procedure as follows:

LOGISTIC REGRESSION VARIABLES Y
  /METHOD=ENTER Age Memory_Type Age*Memory_Type
  /CONTRAST (Y_Indic)=Indicator.

The test associated with the interm Memory_Type*Age term will answer
your research question.

From the description you provide, I wonder if respondents from one
memory type are consistently much older than respondents from another
memory type.

Ryan

On Sat, Aug 7, 2010 at 9:35 AM, howard schuman <[hidden email]> wrote:

> Ryan,
>
> These were independent samples, as I conceptualize the problem, because
> respondents in this survey first recalled or did not recall one of two
> memories of national events, and the two were mutually exclusive (e.g.,
> one might be World War II and the other might be the Vietnam War). Then
> each memory (as a dichotomy: recalled vs. did not recall) was regressed
> on age. The problem to be solved is whether the b values from the two
> regressions can be said to be different in terms of a p value.
>       Howard
>
> Ryan Black wrote:
>>
>> All,
>>
>> I have woken up to a couple of private emails with comments and
>> questions. Let me be entirely clear in this post why a standard binary
>> logistic regression is NOT appropriate in the design I have
>> envisioned. I am assuming that EACH person was measured on BOTH
>> dichotomous items. Hence you see two records for each subject ID in
>> the dummy data set I posted previously. This introduces repeated
>> measures, and one usually wants to account for correlation resulting
>> from repeated measures. Treating observations as independent as one
>> would do when fitting a standard binary logistic regression is usually
>> an incorrect assumption. The multivariate model GEE I presented in the
>> previous post accounts for the correlation introduced by repeated
>> measures.
>>
>> Now, if my assumption that EACH person was measured on BOTH
>> dichotomous outcomes is NOT correct, then we clearly no longer have
>> repeated measures. I must admit that if this were true, I'd have some
>> concerns about the prospect of testing for differences in age slopes
>> across different samples on different outcomes.
>>
>> Back to the GEE I suggested in the previous post (assuming repeated
>> measures)...I was also contacted by another person who suggested that
>> one DV be coded as 0/1 while the other coded as 1/2. I would NOT do
>> this. Simply code your DV, "Y," in 0s and 1s, as suggested in my
>> original post. There is absolutely no need to change the coding
>> scheme.
>>
>> If a data set is structured in wide format such as:
>>
>> ID   Age   DV1   DV2
>> 1     19      0         1
>> 2     20      1         0
>> 3     22      1         1
>> ..
>> ..
>> ..
>>
>> then an easy way to restructure the data set into long (aka vertical)
>> format, as is required by the GENLIN procedure for this design, is to
>> employ the VARSTOCASES function.
>>
>> Finally, if someone has a comment or question about my posts or
>> another post in this thread, please post back to the entire list and
>> not my private email.
>>
>> Ryan
>>
>> On Fri, Aug 6, 2010 at 5:44 PM, Ryan Black <[hidden email]>
>> wrote:
>>>
>>> Howard,
>>>
>>> You should be able to test for a significant difference in slopes by
>>> fitting a multivariate model through the GENLIN procedure offered in
>>> SPSS.
>>>
>>> You'll need to structure your data set as follows:
>>>
>>> ID   Y_Indic   Age   Y
>>> 1        1         24     0
>>> 1        2         24     1
>>> 2        1         33     1
>>> 2        2         33     0
>>> 3        1         28     0
>>> 3        2         28     1
>>> 4        1         16     1
>>> 4        2         16     1
>>> .
>>> .
>>>
>>> Once you've structured your data set as described above, you can fit
>>> the model using the following code:
>>>
>>> GENLIN Y (REFERENCE=FIRST) BY Y_Indic (ORDER=ASCENDING) WITH Age
>>>  /MODEL Y_Indic Age Y_Indic*Age INTERCEPT=YES
>>>  DISTRIBUTION=BINOMIAL LINK=LOGIT
>>>  /REPEATED SUBJECT=ID WITHINSUBJECT=Y_Indic SORT=YES
>>> CORRTYPE=EXCHANGEABLE ADJUSTCORR=YES
>>>  /PRINT CPS DESCRIPTIVES MODELINFO FIT SUMMARY SOLUTION.
>>>
>>> The test associated with the Y_Indic*Age term will tell you if the
>>> slopes are significantly different.
>>>
>>> This code is specifically designed to handle the data set I described.
>>> Deviations from the presumed data set structure may require another
>>> approach.
>>>
>>> Ryan
>>>
>>> On Thu, Aug 5, 2010 at 3:19 PM, howard schuman <[hidden email]>
>>> wrote:
>>>>
>>>> I have two independent logistic regression B values, and would like to
>>>> test whether they differ significantly (even at p < .10), as indeed they
>>>> do visually with one sloping up and the other down. I wonder if there is
>>>> a fairly straightforward way to do this in SPSS, starting from the data
>>>> set that includes both. Each line is based on just two points [i.e., two
>>>> ages], which are the same for both lines, but with different dependent
>>>> variables (attitudes). Advice much appreciated.   -Howard Schuman
>>>>
>>>> =====================
>>>> 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
>>
>>
>
> =====================
> 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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[hidden email] (not to SPSSX-L), with no body text except the
command. To leave the list, send the command
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For a list of commands to manage subscriptions, send the command
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[Ryan]

Hi Howard,

Small correction to the LOGISTIC REGRESSION code I posted. You need to
replace "Y_Indic" with "Memory_Type." So, the full code should look
like this:

LOGISTIC REGRESSION VARIABLES Y
  /METHOD=ENTER Age Memory_Type Age*Memory_Type
  /CONTRAST (Memory_Type)=Indicator.

I still have some concerns about this design. Anyway assuming it is
valid, as I mentioned before, the interaction term should answer your
question.

HTH,

Ryan


On Sat, Aug 7, 2010 at 10:02 AM, Ryan Black <[hidden email]> wrote:

> Howard,
>
> So the subject was not permitted to recall both events? It had to be
> one or the other? If so, you are correct that you do not have a
> repeated measures design. Here's how I see your data set now:
>
> ID   Memory_Type   Age   Recalled
> 1        1                   61         0
> 2        2                   70         1
> 3        2                   59         1
> 4        1                   82         0
> .
>
> The binary logistic regression equation is simplified to:
>
> logit(y) = b0 + b1*Memory_Type + b2*Age + b3*Memory_Type*Age
>
> where Memory_Type is assumed to be dummy coded. (The LOGISTIC
> REGRESSION procedure in SPSS will dummy code for you)
>
> You could easily fit the model employing the LOGISTIC REGRESSION
> procedure as follows:
>
> LOGISTIC REGRESSION VARIABLES Y
>  /METHOD=ENTER Age Memory_Type Age*Memory_Type
>  /CONTRAST (Y_Indic)=Indicator.
>
> The test associated with the interm Memory_Type*Age term will answer
> your research question.
>
> From the description you provide, I wonder if respondents from one
> memory type are consistently much older than respondents from another
> memory type.
>
> Ryan
>
> On Sat, Aug 7, 2010 at 9:35 AM, howard schuman <[hidden email]> wrote:
>> Ryan,
>>
>> These were independent samples, as I conceptualize the problem, because
>> respondents in this survey first recalled or did not recall one of two
>> memories of national events, and the two were mutually exclusive (e.g.,
>> one might be World War II and the other might be the Vietnam War). Then
>> each memory (as a dichotomy: recalled vs. did not recall) was regressed
>> on age. The problem to be solved is whether the b values from the two
>> regressions can be said to be different in terms of a p value.
>>       Howard
>>
>> Ryan Black wrote:
>>>
>>> All,
>>>
>>> I have woken up to a couple of private emails with comments and
>>> questions. Let me be entirely clear in this post why a standard binary
>>> logistic regression is NOT appropriate in the design I have
>>> envisioned. I am assuming that EACH person was measured on BOTH
>>> dichotomous items. Hence you see two records for each subject ID in
>>> the dummy data set I posted previously. This introduces repeated
>>> measures, and one usually wants to account for correlation resulting
>>> from repeated measures. Treating observations as independent as one
>>> would do when fitting a standard binary logistic regression is usually
>>> an incorrect assumption. The multivariate model GEE I presented in the
>>> previous post accounts for the correlation introduced by repeated
>>> measures.
>>>
>>> Now, if my assumption that EACH person was measured on BOTH
>>> dichotomous outcomes is NOT correct, then we clearly no longer have
>>> repeated measures. I must admit that if this were true, I'd have some
>>> concerns about the prospect of testing for differences in age slopes
>>> across different samples on different outcomes.
>>>
>>> Back to the GEE I suggested in the previous post (assuming repeated
>>> measures)...I was also contacted by another person who suggested that
>>> one DV be coded as 0/1 while the other coded as 1/2. I would NOT do
>>> this. Simply code your DV, "Y," in 0s and 1s, as suggested in my
>>> original post. There is absolutely no need to change the coding
>>> scheme.
>>>
>>> If a data set is structured in wide format such as:
>>>
>>> ID   Age   DV1   DV2
>>> 1     19      0         1
>>> 2     20      1         0
>>> 3     22      1         1
>>> ..
>>> ..
>>> ..
>>>
>>> then an easy way to restructure the data set into long (aka vertical)
>>> format, as is required by the GENLIN procedure for this design, is to
>>> employ the VARSTOCASES function.
>>>
>>> Finally, if someone has a comment or question about my posts or
>>> another post in this thread, please post back to the entire list and
>>> not my private email.
>>>
>>> Ryan
>>>
>>> On Fri, Aug 6, 2010 at 5:44 PM, Ryan Black <[hidden email]>
>>> wrote:
>>>>
>>>> Howard,
>>>>
>>>> You should be able to test for a significant difference in slopes by
>>>> fitting a multivariate model through the GENLIN procedure offered in
>>>> SPSS.
>>>>
>>>> You'll need to structure your data set as follows:
>>>>
>>>> ID   Y_Indic   Age   Y
>>>> 1        1         24     0
>>>> 1        2         24     1
>>>> 2        1         33     1
>>>> 2        2         33     0
>>>> 3        1         28     0
>>>> 3        2         28     1
>>>> 4        1         16     1
>>>> 4        2         16     1
>>>> .
>>>> .
>>>>
>>>> Once you've structured your data set as described above, you can fit
>>>> the model using the following code:
>>>>
>>>> GENLIN Y (REFERENCE=FIRST) BY Y_Indic (ORDER=ASCENDING) WITH Age
>>>>  /MODEL Y_Indic Age Y_Indic*Age INTERCEPT=YES
>>>>  DISTRIBUTION=BINOMIAL LINK=LOGIT
>>>>  /REPEATED SUBJECT=ID WITHINSUBJECT=Y_Indic SORT=YES
>>>> CORRTYPE=EXCHANGEABLE ADJUSTCORR=YES
>>>>  /PRINT CPS DESCRIPTIVES MODELINFO FIT SUMMARY SOLUTION.
>>>>
>>>> The test associated with the Y_Indic*Age term will tell you if the
>>>> slopes are significantly different.
>>>>
>>>> This code is specifically designed to handle the data set I described.
>>>> Deviations from the presumed data set structure may require another
>>>> approach.
>>>>
>>>> Ryan
>>>>
>>>> On Thu, Aug 5, 2010 at 3:19 PM, howard schuman <[hidden email]>
>>>> wrote:
>>>>>
>>>>> I have two independent logistic regression B values, and would like to
>>>>> test whether they differ significantly (even at p < .10), as indeed they
>>>>> do visually with one sloping up and the other down. I wonder if there is
>>>>> a fairly straightforward way to do this in SPSS, starting from the data
>>>>> set that includes both. Each line is based on just two points [i.e., two
>>>>> ages], which are the same for both lines, but with different dependent
>>>>> variables (attitudes). Advice much appreciated.   -Howard Schuman
>>>>>
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[Kornbrot, Diana]

Its important that we are all talking about the SAME design, as Ryan emphasises
BETWEEN GROUP DESIGN
Group A either remember, 1, or do not remember, 0, event of type A [same event for everyone], age is noted
Group B either remember, 1, or do not remember, 0, event of type B [same event for everyone], age is noted
Data Structure [long, event type B below event type A]
Id age type recall
Analysis [using dialogue boxes for simplicity]
Regression>binarylogistic
Dependent: recall
Covariates: age type(cat) age*type
Results
Type gives MAIN effect of even type
Age gives main effect of age as slope of regression of logit(recall) on age. Could be FLAT if older better at type A and yunger at type B
Age*type gives difference in slopes of regression of logit(recall) on age for types A & B
Textbook stuff, no controversy
WITHIN GROUP DESIGN
All participants given TWO tasks.  They either remember, 1, or do not remember, 0, event of type A [same event for everyone] AND either remember, 1, or do not remember, 0, event of type B [same event for everyone], age is noted
There are, in my view, THREE different potential analyses to determine differences of effect of age for the two types of memory event
ANALYSIS METHOD 1
Do exactly the same as for between group design and do no worry about the correlation between data for two events
Data is in long form
Id age type recall
1   24  A   1
1   24  B   0
2   37  A   1
2   37  B   1....
Its like independent t-test for related groups. Not uninformative, but not ideal [my guess is that if one does an inappropriate independent t-test on correlated data, one gets same results on 75%+ of occasions]
ANALYSIS METHOD 2
Set up data as for 1 and include id(cat) in model
Results interpretted as in method 1, but participant main effect is partialled out. This is an approximation a true multilevel approach, which is more complex and should be doable in generaliZED linear models.
ANALYSIS METHOD 3
Model interaction explicitly, this is extention of the McNemar method, which I am suggesting here for the first time but may have been suggested by others
Create TWO new variables for each participant
Agree =1, if both recall A and recall B = 1; 0 if both = 0, and missing otherwise
Discord = 1, if A=0, B=1; and 0, if A=1 and B = 0, and missing otherwise
Data structure [wide]
id  age recA    recB    agree   discord
1   24     1          0       missing    0
2   37     1          1         1       missing
Then SEPARATE logistic regressions for agree and discord, both with age as a single covariate
Effect on agree gives main effect of age on both types of memory combined
Effect on discord gives effect of age on discrepancy between A & B. This is not the SAME as difference in slope for memory types, b ut if effect is significant I would be confident about taking the numeric difference in slope seriously.
Note that total frequencies of discord = 1 and discord =2 can be used to determine the association between memory types collapsed over age.

Such problems may be better discussed in the works of Agresti, previously noted. Do not know what he would think of method 3

Best

Diana

---

Professor Diana Kornbrot
email:  d.e.kornbrot@...    
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