http://spssx-discussion.165.s1.nabble.com/Multinomial-Logistic-Regression-Category-Size-tp3286013p3289461.html
relative risk ratios. Go to the bottom of the page for details.
> Bruce et al.,
>
> I have little doubt that the parameter estimates obtained from a
> generalized logits multinomial regression without any predictors yield
> log(relative risks), and assuming predictors are in the model,
> relative risk ratios. Allow me to provide a couple simple examples
> (without a predictor and with a dichotomous predictor) here to provide
> evidence in support of what I've stated. But before I do, let's make
> sure we all agree on some basic definitions within a logistic
> regression framework:
>
> Risk_A = probability of event A
> Risk_B = probability of event B
> Risk_C = probability of event C
>
> Relative Risk_A_B = Risk A / Risk B
> Relative Risk_A_C = Risk A / Risk C
> Relative Risk_B_C = Risk B / Risk C
>
> Odds_A = probability of event A / probability of not event A
> Odds_B = probability of event B / probability of not event B
> Odds_C = probability of event C / probability of not event C
>
> Odds Ratio_A_B = Odds_A / Odds_B
> Odds Ratio_A_C = Odds_A / Odds_C
> Odds Ratio_B_C = Odds_B / Odds_C
>
> Now, the first example I provide below shows that the parameter
> estimates obtained from the generalized logits multinomial regression
> model with no predictors below are equivalent to log(Relative Risks).
>
> data list list / Y.
> begin data
> 1
> 1
> 1
> 2
> 2
> 2
> 2
> 2
> 2
> 3
> 3
> 3
> 3
> 3
> 3
> 3
> 3
> 3
> end data.
>
> FREQUENCIES VARIABLES=Y
> /ORDER=ANALYSIS.
>
> COMPUTE RR_1_3_raw = 16.666666666666664 / 50.
> COMPUTE RR_2_3_raw = 33.33333333333333 / 50.
> EXECUTE.
>
> NOMREG Y (BASE = LAST ORDER=ASCENDING)
> /MODEL
> /INTERCEPT=INCLUDE
> /PRINT=PARAMETER .
>
> COMPUTE RR_1_3 = exp(-1.0986122886681096).
> COMPUTE RR_2_3 = exp(-0.4054651081081645).
> EXECUTE.
>
> It should be clear from the example above that the parameter estimates
> can certainly be interpreted as log(Relative Risks). Those calculated
> from CROSSTABS using the definitional formulas are exactly the same as
> those output from NOMREG. Now, let's add a dichotomous predictor to
> the model to see what happens. I provide further comments after this
> code.
>
> data list list / Y X.
> begin data
> 1 1
> 1 1
> 1 0
> 2 1
> 2 1
> 2 1
> 2 0
> 2 1
> 2 1
> 3 1
> 3 1
> 3 0
> 3 1
> 3 1
> 3 1
> 3 0
> 3 1
> 3 1
> end data.
>
> CROSSTABS
> /TABLES=Y BY X
> /FORMAT=AVALUE TABLES
> /CELLS=COUNT ROW COLUMN
> /COUNT ROUND CELL.
>
> COMPUTE RR_1_3_X0_Raw = (25 / 50) .
> COMPUTE RR_1_3_X1_Raw = (14.285714285714285 / 50).
> COMPUTE RRR_1_3_Raw = RR_1_3_X1_Raw / RR_1_3_X0_Raw.
> EXECUTE.
>
> COMPUTE RR_2_3_X0_Raw = (25 / 50) .
> COMPUTE RR_2_3_X1_Raw = (35.714285714285715 / 50).
> COMPUTE RRR_2_3_Raw = RR_2_3_X1_Raw / RR_2_3_X0_Raw.
> EXECUTE.
>
> NOMREG Y (BASE = LAST ORDER=ASCENDING) WITH X
> /MODEL X
> /INTERCEPT=INCLUDE
> /PRINT=PARAMETER .
>
> COMPUTE RRR_1_3 = exp(-0.5596157879354635).
> COMPUTE RRR_2_3 = exp(0.35667494393875165).
> EXECUTE.
>
> Again, I calculated the estimates using the probability estimates from
> CROSSTABS. Then I compared those estimates to exponentiated estimates
> from NOMREG. As expected, they [relative risk ratios] are identical.
>
> Ryan
>
> On Wed, Dec 1, 2010 at 10:07 PM, Bruce Weaver <
[hidden email]> wrote:
>> I responded to Ryan off-list to ask if he meant to say that the parameter
>> estimates are interpreted as the change in the log(odds) relative to a
>> reference category. He responded that he did indeed mean log(risk), not
>> log(odds); and we have been having a vigorous back and forth discussion
>> since, exchanging examples and links. Here is one link I sent to Ryan:
>>
>>
http://faculty.chass.ncsu.edu/garson/PA765/logistic.htm#estimates>>
>> And here's one he just sent to me (which I've not read yet--it's bed time
>> here).
>>
>>
http://www.columbia.edu/~so33/SusDev/Lecture_10.pdf>>
>> Just thought I'd post this, in case anyone else was interested. I may have
>> some more to say after reading that last document.
>>
>> Cheers,
>> Bruce
>>
>>
>> R B wrote:
>>>
>>> Stefan,
>>>
>>> What do you mean by the following statement?: "...if the overall model
>>> is significant, I can conclude that there is a significant
>>> relationship between the dependent and independent variable for all
>>> categories of the dependent variable?"
>>>
>>> In the typical multinomial logistic regression assuming a single
>>> continuous predictor, X, the parameter estimates are interpreted as
>>> the change in the log(risk relative to the reference category), given
>>> a one-point increase in X. The parameter estimates do NOT reflect a
>>> change in the log(risk) of observing each category, given a one-point
>>> increase in X. Moreover, it's certainly possible to observe a
>>> non-significant log(relative risk) in the presence an overall
>>> significant model effect.
>>>
>>> Ryan
>>>
>>> On Tue, Nov 30, 2010 at 7:49 AM, s-volk <
[hidden email]>
>>> wrote:
>>>> Dear all,
>>>>
>>>> I ran a multinomial logistic regression analysis with one continuous
>>>> independent variable. I have a sample size of 68 subjects (psychological
>>>> experiment) which end up split into 5 categories ranging in size from 5
>>>> to
>>>> 24 (dependent variable). The MLR-model has a Nagelkerke R2 of 0.27 and
>>>> Model
>>>> Fit χ2=19.71, p<0.01.
>>>>
>>>> Now here is the problem: A reviewer complains that my results may be
>>>> sample
>>>> specific because one of the 5 categories of the dependent variable
>>>> consists
>>>> of only 5 observations (subjects), i.e. sh/e argues that very few
>>>> participants (five) are responsible for the observed effects. Is this
>>>> valid
>>>> argument? I thought that if the overall model is significant, I can
>>>> conclude
>>>> that there is a significant relationship between the dependent and
>>>> independent variable for all categories of the dependent variable? That
>>>> is,
>>>> the calculations for the overall model are based on all observations (68)
>>>> and not only on the observations in specific categories (e.g., 5)?
>>>>
>>>> I was wondering if someone could provide me with or point me to some
>>>> arguments for reviewers (ideally including some references)?
>>>>
>>>> Many thanks in advance,
>>>> Stefan
>>>>
>>>>
>>>>
>>>>
>>>> --
>>>> View this message in context:
>>>>
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>>>>
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>>
>>
>> -----
>> --
>> Bruce Weaver
>>
[hidden email]
>>
http://sites.google.com/a/lakeheadu.ca/bweaver/>>
>> "When all else fails, RTFM."
>>
>> NOTE: My Hotmail account is not monitored regularly.
>> To send me an e-mail, please use the address shown above.
>>
>> --
>> View this message in context:
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