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This is a really simple problem I am having, yet for the life of me I can't find a solution searching around. In theory I can simply recode the data, but that is an extreme solution I would rather not use if I don't have to.

I am simply trying to do a logistic regression with an ordered factor as my predictor. For a toy data set, consider:

  radiation leukemia other total
1         0       13   378   391
2       1-9        5   200   205
3     10-49        5   151   156
4     50-99        3    47    50
5   100-199        4    31    35
6       200       18    33    51

I want to execute the following:

glm(cbind(leukemia,other)~radiation,data=leuk,family=binomial("logit"))

That is, leukemia are the "successes" and other are the "failures". Basically, trying to predict dose-response relationship between radiation and the proportional mortality rates for leukemia. However, this model is oversaturated:

Call:  glm(formula = cbind(leukemia, other) ~ radiation, family = binomial("logit"), 
    data = leuk)

Coefficients:
     (Intercept)      radiation1-9    radiation10-49  radiation100-199  
         -3.3699           -0.3189           -0.0379            1.3223  
    radiation200    radiation50-99  
          2.7638            0.6184  

Degrees of Freedom: 5 Total (i.e. Null);  0 Residual
Null Deviance:      54.35 
Residual Deviance: -3.331e-15   AIC: 33.67

I don't want each level of radiation as a factor to be its own predictor variable; that makes no sense, especially when you only have a small number of data points (note, this isn't actually the real data I am using, this is just a toy example that is similar). In any case, how do I force R to simply consider the factor radiation as a single variable with multiple levels? For example, if I do the following:

x<-c(0,1,2,3,4,5)
glm(cbind(leukemia,other)~x,data=leuk,family=binomial("logit"))

Call:  glm(formula = cbind(leukemia, other) ~ x, family = binomial("logit"), 
    data = leuk)

Coefficients:
(Intercept)            x  
    -3.9116       0.5731  

Degrees of Freedom: 5 Total (i.e. Null);  4 Residual
Null Deviance:      54.35 
Residual Deviance: 10.18        AIC: 35.84

This is more in line with what I want. But I am nervous about using that x variable in the regression for fear of changing the interpretation of the results. Similarly, I'd prefer to avoid an irritating system of dummy variables.

How do I go about doing this? Or is there a better workaround altogether for studying this type of relationship that I am not considering?

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    $\begingroup$ how about glm(cbind(leukemia,other)~as.numeric(x),data=leuk,family=binomial("logit")) (oops, not significantly different from your second solution)? Or consider the ordinal package. $\endgroup$
    – Ben Bolker
    Commented Oct 1, 2014 at 22:19
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    $\begingroup$ What sort of modeling procedure do you want to use for an orginal predictor. None of the "standard" linear models use ordinal values any differently than categorical values. You need to include additional assumptions, like do you think the effects of the radiation 1-9 are 2x greater than 0? Is there a linear relationship (or other complicated relationship) between the levels? Are some point you are going to have to map them to numerical values based on additional modeling assumptions. $\endgroup$
    – MrFlick
    Commented Oct 1, 2014 at 22:22
  • $\begingroup$ @MrFlick That's not correct. Ordered factors are modeled using polynomial contrasts by default. $\endgroup$
    – Roland
    Commented Oct 2, 2014 at 13:01
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    $\begingroup$ possible duplicate of Continuous dependent variable with ordinal independent variable, Coding for an ordered covariate, & Logistic regression and ordinal independent variables. $\endgroup$
    – Scortchi ♦
    Commented Oct 2, 2014 at 14:23
  • $\begingroup$ @Roland: True enough (in R) but that amounts to no more than an alternative coding scheme for a categorical predictor - unless you want to fit only the linear & quadratic, say, contrasts of an ordinal predictor with more than three levels; in which case the considerations raised by MrFlick again become relevant. $\endgroup$
    – Scortchi ♦
    Commented Oct 2, 2014 at 14:34

1 Answer 1

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It is already considered as a single (factor) variable with multiple levels where radiation 0 is the reference level. If you want to treat radiation as a numeric variable you need to first have or create one (e.g. mean radiation or so).

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