GENLIN – Binary logistic model

[Firas Asad]

Hello everyone,

I am trying to examine the effect of people’s annual income (income) on the model of the laptop computer (laptop) they bought within the last year.

I utilised the GENLIN procedure with a binary logistic model whereby the response is the model of the laptop (PC vs. Mac) and the predictor is the annual income (in scale level). The reference category is the (PC). I used the default values of the all other options under the tabs of the GENLIN main window.

My sample size is 329; while 182 people bought a PC, 147 bought a Mac. Regarding the annual income, it ranges from £5300 to £78230 with a mean of £19560.            

In order to get an initial clue, I run the t-test and it showed that there is a significant difference in the mean annual income between the two groups of buyers. Those who bought Macs were with higher income than those who bought PCs.    

Moving on to the next step, I run the GNLIN procedure. The results were quite strange and confusing for me. The odds ratio (exp(B)) associated with the income variable is (1.00) and with significant Wald Chi-square (p-value = 0.00) . According to my understanding, this means there is no any impact of the income on the odds of buying a specific computer type. This contradicts the t-test results.        

I tried two things as an attempt to get this issue sorted out. First, I categorised the originally continuous income variable into 5 categories. Re-running the GENLIN gave quite logical and often significant results. The odds ratios that people have bought a Mac increase with the increase of their income. For example, the highest income category is associated with odds ratio of about 134.

Second, I divided the original quantitative income variable by 1000 ( I just thought this may help). Re-running the GENLIN gave slightly better results than the first run (where OR was 1.00) run. The odds ratio of the income variable is now significant with a value of 1.130.   

Now, having stated that, my main and first question is why transforming the income variable from continuous to multi-categorical has substantially altered the results. The second relevant question is why dividing the income by 1000 has slightly changed the results as well.     

I am not sure if the noted issue(s) above is specific to the algorithm of the GENLIN procedure adopted in the SPSS or actually I am just missing something related to the overall philosophical /mathematical methodology of the Generalised Linear Models.

 

Any little help would be highly appreciated.

Regards and many thanks in advance,

Firas

[Bruce Weaver]

Hello Firas.  First, it would be helpful to see your GENLIN syntax.  Second, when you have a continuous predictor variable such as income, Exp(B) gives the odds ratio associated with a one unit increase in that variable.  In other words, you were getting the odds ratio for a one Pound increase in income.  When you divided income by 1000, you got the odds ratio for a 1000 Pound increase in income.  In short, it's up to you to decide what increment in income is sensible to look at.  One pound is clearly too low.  Given that your range of incomes spans nearly 73,000, maybe the odds ratio for a 5000 Pound increase would be sensible.  

Carving continuous variables into categories is usually a bad idea, because you lose power and eat up degrees of freedom.  I think the only reason I would carve income into categories would be to do some preliminary exploratory analyses into whether the relationship is linear in the logit.  If those analyses suggested some non-linear function, then I would include appropriate polynomial terms (when using the continuous variable once again), or maybe look at using a spline.

HTH.

Firas Asad wrote

Hello everyone,

I am trying to examine the effect of
people’s annual income (income) on the model of the laptop computer (laptop) they
bought within the last year.

I utilised the GENLIN procedure with a
binary logistic model whereby the response is the model of the laptop (PC vs. Mac)
and the predictor is the annual income (in scale level). The reference category
is the (PC). I used the default values of the all other options under the tabs
of the GENLIN main window.

My sample size is 329; while 182 people
bought a PC, 147 bought a Mac. Regarding the annual income, it ranges from £5300
to £78230 with a mean of £19560.            

In order to get an initial clue, I
run the t-test and it showed that there is a significant difference in the mean
annual income between the two groups of buyers. Those who bought Macs were with
higher income than those who bought PCs.    

Moving on to the next step, I run the
GNLIN procedure. The results were quite strange and confusing for me. The odds
ratio (exp(B)) associated with the income variable is (1.00) and with
significant Wald Chi-square (p-value = 0.00) . According to my understanding, this
means there is no any impact of the income on the odds of buying a specific
computer type. This contradicts the t-test results.        

I tried two things as an attempt to
get this issue sorted out. First, I categorised the originally continuous
income variable into 5 categories. Re-running the GENLIN gave quite logical and
often significant results. The odds ratios that people have bought a Mac increase
with the increase of their income. For example, the highest income category is
associated with odds ratio of about 134.

Second, I divided the original
quantitative income variable by 1000 ( I just thought this may help).
Re-running the GENLIN gave slightly better results than the first run (where OR
was 1.00) run. The odds ratio of the income variable is now significant with a value
of 1.130.   

Now, having stated that, my main and
first question is why transforming the income variable from continuous to multi-categorical
has substantially altered the results. The second relevant question is why
dividing the income by 1000 has slightly changed the results as well.     

I am not sure if the noted issue(s) above
is specific to the algorithm of the GENLIN procedure adopted in the SPSS or actually
I am just missing something related to the overall philosophical /mathematical methodology
of the Generalised Linear Models.
 
Any little help would be highly appreciated.

Regards and many thanks in advance,

Firas

[MICHAEL J TONER]



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[Firas Asad]

Dear Bruce,

Thank you so much for your quick, clear and helpful reply. 

It works; the model results sound logical now. I will consider your advise regarding re-coding continuous variable into multi-categories in the future analyses. 

Kind regards,

Firas

On Nov 1, 2012, at 21:34, Bruce Weaver <[hidden email]> wrote:

Hello Firas.  First, it would be helpful to see your GENLIN syntax.  Second,
when you have a continuous predictor variable such as income, Exp(B) gives
the odds ratio associated with a one unit increase in that variable.  In
other words, you were getting the odds ratio for a one Pound increase in
income.  When you divided income by 1000, you got the odds ratio for a 1000
Pound increase in income.  In short, it's up to you to decide what increment
in income is sensible to look at.  One pound is clearly too low.  Given that
your range of incomes spans nearly 73,000, maybe the odds ratio for a 5000
Pound increase would be sensible.

Carving continuous variables into categories is usually a bad idea, because
you lose power and eat up degrees of freedom.  I think the only reason I
would carve income into categories would be to do some preliminary
exploratory analyses into whether the relationship is linear in the logit.
If those analyses suggested some non-linear function, then I would include
appropriate polynomial terms (when using the continuous variable once
again), or maybe look at using a spline.

HTH.

Hello everyone,

I am trying to examine the effect of

people’s annual income (income) on the model of the laptop computer

(laptop) they

bought within the last year.

I utilised the GENLIN procedure with a

binary logistic model whereby the response is the model of the laptop (PC

vs. Mac)

and the predictor is the annual income (in scale level). The reference

category

is the (PC). I used the default values of the all other options under the

tabs

of the GENLIN main window.

My sample size is 329; while 182 people

bought a PC, 147 bought a Mac. Regarding the annual income, it ranges from

£5300

to £78230 with a mean of £19560.           Â

In order to get an initial clue, I

run the t-test and it showed that there is a significant difference in the

mean

annual income between the two groups of buyers. Those who bought Macs were

with

higher income than those who bought PCs. Â Â Â

Moving on to the next step, I run the

GNLIN procedure. The results were quite strange and confusing for me. The

odds

ratio (exp(B)) associated with the income variable is (1.00) and with

significant Wald Chi-square (p-value = 0.00) . According to my

understanding, this

means there is no any impact of the income on the odds of buying a

specific

computer type. This contradicts the t-test results. Â Â Â Â Â Â Â

I tried two things as an attempt to

get this issue sorted out. First, I categorised the originally continuous

income variable into 5 categories. Re-running the GENLIN gave quite

logical and

often significant results. The odds ratios that people have bought a Mac

increase

with the increase of their income. For example, the highest income

category is

associated with odds ratio of about 134.

Second, I divided the original

quantitative income variable by 1000 ( I just thought this may help).

Re-running the GENLIN gave slightly better results than the first run

(where OR

was 1.00) run. The odds ratio of the income variable is now significant

with a value

of 1.130. Â Â

Now, having stated that, my main and

first question is why transforming the income variable from continuous to

multi-categorical

has substantially altered the results. The second relevant question is why

dividing the income by 1000 has slightly changed the results as well. Â Â Â Â

I am not sure if the noted issue(s) above

is specific to the algorithm of the GENLIN procedure adopted in the SPSS

or actually

I am just missing something related to the overall philosophical

/mathematical methodology

of the Generalised Linear Models.

Â

Any little help would be highly appreciated.

Regards and many thanks in advance,

Firas

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

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To send me an e-mail, please use the address shown above.

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[Fuller, Matthew]

I will be out of the office until November 5th, with limited access to e-mail.

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[Richard Ristow]

At 05:34 PM 11/1/2012, Bruce Weaver wrote:

>The only reason I would carve income into categories would be for
>preliminary analyses into whether the relationship is linear in the
>logit. If those analyses suggested some non-linear function, then I
>would include polynomial terms [in the continuous variable], or
>maybe look at using a spline.

You might, in particular, try a log transformation of income. Those
are often appropriate first, when the outcome is the result of human
perception; and second, when the ratio of largest to smallest
observed values is large (in this case, something over an order of magnitude).

Then, you're looking for the effect of a certain *fractional* change
in income. What scale should you use? I'd consider one where a unit
change in the scale corresponds to a ratio of 1.2, or 20% change in
income -- which is also about the 4th root of a doubling of income.

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[Dittfurth, Monica]

I will be out of the office on Friday, November 2nd. If you have an urgent need or request before I return, please email [hidden email].

 

Thanks,

Monica

 

[Rich Ulrich]

An important thing to emphasize here is that you have read the output wrong.

The "significant Wald Chi-square (p-value = 0.00)" indicates that there *is* a large
effect for the prediction.  So the results do *not* contradict the t-test results.

Why is the OR 1.00?  That was explained by another poster -- It only looks
like "1.00" because of round-off error when your unit of money is 1.0.  It
will be a bigger value if you restate income in 1000s or 5000s, as he suggested.
I don't remember how clear he was about that implication.


--
Rich Ulrich

---

Date: Thu, 1 Nov 2012 13:30:21 -0700
From: [hidden email]
Subject: GENLIN – Binary logistic model
To: [hidden email]

Hello everyone,

[...snip]

Moving on to the next step, I run the GNLIN procedure. The results were quite strange and confusing for me. The odds ratio (exp(B)) associated with the income variable is (1.00) and with significant Wald Chi-square (p-value = 0.00) . According to my understanding, this means there is no any impact of the income on the odds of buying a specific computer type. This contradicts the t-test results.        

[snip rest]