# How to interpret logistic regression with days of the week and months of the year as predictors together with continuous and binary predictors?

I am using logistic regression to predict electricity spike prices (price that exceeds a certain threshold).

I directly use the following variables as my independent variables together:

(a) demand/load - a continuous IV
(b) is a binary IV
(c) days of the week
(d) months of the year.

I used the reference category for (c) and (d) and end up sept and tue for the reference. How do I interpret the results using marginal effects for all my predictors?

I am using Stata 9.

I think, first of all, you probably need some more complex model to account for time-dependence of the dependent variable. I think a non-linear mixed model is what you want.

But to answer your question, I would say the easiest way is to look at the odds ratio (OR) for each level of each categorical independent variable and note that that is the OR compared to the reference level (e.g. Tuesday)

Be sure to check whether Stata uses reference cell coding or effect coding or something else. These have different interpretations, and you may want to change the default.

• Sir, I use those categorical IV( days and months) to account for the trend and seasonality of the prices. I will look unto the odds ratio, but, sir, I'm more concerned on the interpretion with regards to the probability(marginal effects/discrete change), Sir Peter. I'm using binary logistic regression for this. Thank you
– Marc
Mar 25 '12 at 17:00
• Hi @Marc. No need for "sir"! :-) Unfortunately, days and months do not fully account for the dependence of the data - the value of the DV on (say) Jan 2 is going to be related to that on Jan 1, beyond the fact that both are January and whatever day of the week each is. You can get the probability of each outcome directly in SAS and R, and probably in Stata as well, but since I don't use Stata, I don't know how in that program Mar 25 '12 at 19:33
• Hi Mr. Flom :) hmm, I've ran the program(Stata) with a year's worth of data with months and days (my data is in hrs). I've seen a multiple linear regression used this dummy variables(days and months) as regressors that account to the trend and seasonality of the prices, so I did use it too with the same notion. Can I ask you're opinion on what I did? Thank you.
– Marc
Mar 25 '12 at 20:12
• Months will account for seasonality, at least partly. But what about the dependence (or think of it as auto-correlation) in the dependent variable? Mar 25 '12 at 23:34