[R] Behavior of ordered factors in glm

[Duncan Murdoch]

On 05/01/2008 7:16 PM, David Winsemius wrote:
> David Winsemius <dwinsemius at comcast.net> wrote in
> news:Xns9A1CC05755274dNOTwinscomcast at 80.91.229.13: 
> 
>> I have a variable which is roughly age categories in decades. In the
>> original data, it came in coded:
>>> str(xxx)
>> 'data.frame':   58271 obs. of  29 variables:
>>  $ issuecat   : Factor w/ 5 levels "0 - 39","40 - 49",..: 1 1  1
>>  1... 
>> snip
>>
>> I then defined issuecat as ordered:
>>> xxx$issuecat<-as.ordered(xxx$issuecat)
>> When I include issuecat in a glm model, the result makes me think I 
>> have asked R for a linear+quadratic+cubic+quartic polynomial fit.
>> The results are not terribly surprising under that interpretation,
>> but I was hoping for only a linear term (which I was taught to
>> call a "test of trend"), at least as a starting point.
>>
>>> age.mdl<-glm(actual~issuecat,data=xxx,family="poisson")
>>> summary(age.mdl)
>> Call:
>> glm(formula = actual ~ issuecat, family = "poisson", data = xxx)
>>
>> Deviance Residuals: 
>>     Min       1Q   Median       3Q      Max  
>> -0.3190  -0.2262  -0.1649  -0.1221   5.4776  
>>
>> Coefficients:
>>             Estimate Std. Error z value Pr(>|z|)    
>> (Intercept) -4.31321    0.04865 -88.665   <2e-16 ***
>> issuecat.L   2.12717    0.13328  15.960   <2e-16 ***
>> issuecat.Q  -0.06568    0.11842  -0.555    0.579    
>> issuecat.C   0.08838    0.09737   0.908    0.364    
>> issuecat^4  -0.02701    0.07786  -0.347    0.729 
>>
>> This also means my advice to a another poster this morning may have 
>> been misleading. I have tried puzzling out what I don't understand
>> by looking at indices or searching in MASSv2, the Blue Book,
>> Thompson's application of R to Agresti's text, and the FAQ, so far
>> without success. What I would like to achieve is having the lowest
>> age category be a reference category (with the intercept being the
>> log-rate) and each succeeding age category  be incremented by 1. The
>> linear estimate would be the log(risk-ratio) for increasing ages. I
>> don't want the higher order polynomial estimates. Am I hoping for
>> too much? 
>>
> 
> I acheived what I needed by:
> 
>> xxx$agecat<-as.numeric(xxx$issuecat)
>> xxx$agecat<-xxx$agecat-1
> 
> The results look quite sensible:
>> exp.mdl<-glm(actual~gendercat+agecat+smokecat, data=xxx, 
> family="poisson", offset=expected)
>> summary(exp.mdl)
> 
> Call:
> glm(formula = actual ~ gendercat + agecat + smokecat, family = 
> "poisson", 
>     data = xxx, offset = expected)
> 
> Deviance Residuals: 
>     Min       1Q   Median       3Q      Max  
> -0.5596  -0.2327  -0.1671  -0.1199   5.2386  
> 
> Coefficients:
>                 Estimate Std. Error z value Pr(>|z|)    
> (Intercept)     -5.89410    0.11009 -53.539  < 2e-16 ***
> gendercatMale    0.29660    0.06426   4.615 3.92e-06 ***
> agecat           0.66143    0.02958  22.360  < 2e-16 ***
> smokecatSmoker   0.22178    0.07870   2.818  0.00483 ** 
> smokecatUnknown  0.02378    0.08607   0.276  0.78233
> 
> I remain curious about how to correctly control ordered factors, or I 
> should just simply avoid them.

If you're using a factor, R generally assumes you mean each level is a 
different category, so you get levels-1 parameters.  If you don't want 
this, you shouldn't use a factor:  convert to a numeric scale, just as 
you did.

Duncan Murdoch