# Dealing with categorical response variables with unequal spacing in regression analysis

Bacteria were measured on surfaces over time after using two different types of cleaning methods (A or B). They were measured using a quantitative method but the results have been reported as categorical:

• No growth (0 colonies),
• scanty growth (0< x<2.5)
• low growth(2.5 < x <12),
• medium growth (12 < x <40) and
• high growth(>40).

I've used the mid-point of each category as a continuous response variable in the following regression model: colonies~Cleaning* Time *Surface

But the response is only semi-quantitative and the steps between the categories are uneven. IS the model still valid using linear regression in R?

Here's a picture of the bacteria (aerobic colony counts) using two different cleaning techniques over time. 4 different surface types.

• It is unclear what you might possibly mean by this model because the results are categories, whereas the formula you write requires the response (colonies) to be numerical. Evidently you have in mind some scheme to associate numbers to each of these ordinal categories. The model depends on what numbers you use, which is why your specification is incomplete. Could you clarify what you're doing? – whuber Sep 2 '18 at 17:37
• I've taken the mid point from each category and substituted this value for each response that is given. I have 120 surfaces that were measured for bacteria after cleaning over 48 hours. I'm interested in finding out if the surface type is important, the cleaning method and whether there is some interaction between time and cleaning method. Is this something that's properly defined? – HCAI Sep 2 '18 at 17:57
• Would some form of ordinal regression answer your scientific question? – mdewey Sep 4 '18 at 16:28
• @mdewey ah that seems plausible. It's a repeated measures experiment, so would you incorporate time as a factor or a continuous variable? – HCAI Sep 5 '18 at 6:46
• I think that must depend on exactly what model you fit. I would suggest trying a few and then if you have a new question asking it as such. Note though that anything seen as asking about how to code in R is liable to be closed as off-topic here and you might prefer the R-sig-mixed-models mailing list for them. – mdewey Sep 5 '18 at 17:20