# Consequence of ignoring the order of a categorical variable with different levels in logistic regression

As title, I have hesitating whether I should use ordinal logistic regression or not, but I don't think I have time to understand that and to figure out how to work it out in R, can I just ignore it? Will the consequence be serious (i.e. seriously under/over-estimate the effect size)?

Thanks.

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Would you still be interested in knowing how ordinal logistic regression work? It may have serious implications on model interpretation when you ignore the natural ordering of a variable. –  chl Jan 24 '11 at 10:50
Just to be clear, it is the outcome variable that's ordinal? What is the alternative to ordinal logistic regression you're considering? Multinomial logistic regression, or grouping the categories into two groups and using standard logistic regression? –  onestop Jan 24 '11 at 11:13
@onestop, the independent variable is ordinal, but not the outcome variable, outcome variable is whether the patient gets an infection or not –  lokheart Jan 25 '11 at 3:20
Ah, in that case you can definitely ignore ordinal logistic regression, as that's for an ordinal outcome variable. –  onestop Jan 25 '11 at 9:46

If you need to quickly use an ordinal variable as an input, I recommend using it as a factor. The order of the factor is important for the interpretation of the results, but it's rather simple to reorder to the factor (using the factor command). The way the results are reported is the first group in the factor is held constant as the intercept and the coefficients for the subsequent groups are the difference between your reference group (the first item in the factor) and the other group. For example, if you three races coded, White, Black, and Asian. Since R does things alphabetically by default, Asian will become your reference group if you use "+factor(race)" which means you won't see a coefficient for Asian, but you will see a coefficient for Black and for White. These coefficients will be for the Difference between White and Asian and the Difference between Black and Asian.

An easy way to think of this is each level in the factor is treated as a binary variable. Each variable is assigned a coefficient, but the input is binary, meaning if your observation is Asian, Asian=1, Black=0, White=0, so it doesn't matter what the coefficients are for Black or White if your observation is Asian because any coefficient multiplied by zero will still be zero. Thus they're all mutually exclusive.

This also works for ordinal things, such as high, medium and low income. Depending on what your independent variable is and how the data was collected this may be completely suitable for your needs. It is important to note that this does not work well for hierarchical variables. If your input(s) are hierarchical in nature, I highly recommend using a nested mixed random effects model (lme4 package).

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for "nested mixed random effects model", do you mean multi-level modelling? if I don't use this for hierarchical variable (my variable are some kind of risk index that higher the number, more risk the patient has, does it suit your case?) –  lokheart Jan 25 '11 at 10:29
Yes, nested models are hierarchical in nature. In the case of a variable representing degree (i.e. degree of risk), you do not need a hierarchical model. Depending on how the risk index you're using is divided, you may even want to consider grouping the levels on the index (i.e. if it's 1-9 consider grouping as high [7-9], medium [4-6], and low [1-3]) as this may allow you to better represent the dominance effect where those in the reference group represent a substantially different outcome than those in the comparisons. –  Adam Feb 8 '11 at 4:42