Hi there! I am attempting an ANCOVA test on SPSS, with categorical covariates. Most references recommend entering a categorical variable as a covariate after dummy-coding it. However, I am not able to understand the error that happens if (1) the categorical covariate has two levels, for example, gender, or, (2) has more than two levels, for example, age group (say, 5 levels).
I will sincerely appreciate any help to understand the magnitude of the errors, that is, do the ANCOVA results that get generated (SPSS), become completely wrong, or there's likely to be a marginal impact? I will grateful if you could point me to any reference that discusses these issues.
Thank you for your time!
Diptiman Banerji , havin 6 age groups is a "suboptimal" design. Age is a numeric/metric variable, there should (except in very rare and very special cases) be no need to discretize this into groups. Usually, discretizing metric variables is a bad idea.
You would ideally model the response depending on some function of age. If there is no sensible function known (or nothing sensible you could assume), there is still the possibility to use over-parametrized functions like splines that can follow virtually any pattern.
Hello Diptiman,
If the categorical variable has only two levels, then there is no need to recode it so long as each level as a unique numeric value (e.g., 1, 2 or 0, 1). If it has more than two levels, then you need to recode it into k - 1 dummy variates, where k is the number of levels of the categorical variable. Strictly speaking, the sum of explained variation (SS values) associated with the set of dummy variates in the ancova informs you as to the explanatory power for that categorical variable.
There's no error in this process. Though, it's quite possible that someone might misrepresent the information in the results (always a threat in presenting statistical information).
Here's a good starting point for understanding what goes on in recasting nominal variables for linear models: https://stats.idre.ucla.edu/spss/faq/coding-systems-for-categorical-variables-in-regression-analysis-2/
Good luck with your work.
I don't understand how an ANCOVA has a categorical covariate. I know all these models are located under the umbrella of GLM.
What I mean is when a model has only categorical "covariates" then it is not called ANCOVA but factorial ANOVA. It seems that correct naming will pre-remedy potential problems.
If you dummy code (0 and 1) a dichotomous variable, your coefficient will be the difference in the means between the two categories. For your age variable, I suggest you recode it so that each category is given the score for the midpoint of the original range (e.g. 25 for 20 to 30) and the treat that as continuous.
Dear @David Morse, thank you so much for your very clear explanation. Grateful! I had read your answers to the ANCOVA questions that were asked earlier, and they were a lot of help as well.
To clarify my question further, supposing I have 6 age groups, and they are coded as 1,2,3,4,5 and 6. What would be the extent of the error if I entered a categorical variable that has been coded this way as a covariate?
For example, if the test becomes more conservative this way, and I still get a significant effect of the IV on the DV, then I can just do the test to see the results. However, if the test becomes unreliable, then there's no point.
Dear Mehmet Sinan Iyisoy
Thank you for your comment. I will have to dig deeper to know about this further :-)
Dear David Morse
Thank you so much for your very clear explanation. Grateful! I had read your answers to the ANCOVA questions that were asked earlier, and they were a lot of help as well.
To clarify my question further, supposing I have 6 age groups, and they are coded as 1,2,3,4,5 and 6. What would be the extent of the error if I entered a categorical variable that has been coded this way as a covariate?
For example, if the test becomes more conservative this way, and I still get a significant effect of the IV on the DV, then I can just do the test to see the results. However, if the test becomes unreliable, then there's no point.
Dear Prof. David L Morgan,
Thank you for your answer, and for the very implementable solution! The idea of recoding each category with a score for the midpoint of the original range is so neat! Grateful!
Diptiman Banerji , havin 6 age groups is a "suboptimal" design. Age is a numeric/metric variable, there should (except in very rare and very special cases) be no need to discretize this into groups. Usually, discretizing metric variables is a bad idea.
You would ideally model the response depending on some function of age. If there is no sensible function known (or nothing sensible you could assume), there is still the possibility to use over-parametrized functions like splines that can follow virtually any pattern.
Diptiman Banerji, do you have people's actual ages, or only the age groups they belong to? If the latter, what are the cut-points between the age groups?
Regarding the the UNIANOVA command in SPSS (Analyze > General Linear Model > Univariate), categorical explanatory variables are referred to as "fixed factors", and quantitative explanatory variables are called "covariates". Be sure to put things in the appropriate boxes when using the GUI to generate a draft of your command syntax. If you wish to include fixed factor x covariate product terms, you'll have to add the manually the the /DESIGN sub-command after "pasting" the command syntax.
Dear Dr. Jochen Wilhelm, thank you for taking the time to help clarify my thoughts. I agree that discretizing age data into groups is sub-optimal, but, in my survey (as in most of the management research), I have captured age-groups only (as a socially acceptable norm). I appreciate your perspective and will definitely reconsider this choice from now on. Warm regards.
Dear Prof. Bruce Weaver, Thank you for taking the time to revert to my question. My age groups were 18-27, 28-37, 38-47, 48-57, 57+ (five, actually). Appreciate the clarification that you have given about categorical explanatory variables and quantitative explanatory variables, it was a big help :-). Warm regards,
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