Too many categorical predictors in multinomial logistic regression I am not familiar with multi-class prediction so I apologize in advance if this questions seem very basic.
Here is my dataset: So within the dataset, I am trying to predict which fare product is picked by the customer, in which choice is the dependent variable

Columns 6:14 are prices of each option, and the last column shows which option the customer decides to take in the end.
The dataset has about ~160000 rows, so I am not sure for days to departure, week (day of week), and group (week number in a year), if I should encode them as factors or numerical variables. My fear is that if I encode week and group as factors, this will result in me having too many predictors and an incredibly long run time if I try to use multinom regression in caret. Does anyone have any suggestions as to how I should encode them? Thank you for the help in advance :(

Some thoughts:

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*Another consideration is that these variables are ordered, so if you convert them to factors you will lose the ordering information, which may be important.

*The week and group are cyclic, so for the week variable, 6 is probably more similar to 0 than to 3, and for the group variable, 52 is probably more like 1 than 26. This is not captured by a single variable and one way to encode these is to create two variables for each, using sine and cosine encodings. For example, for group:

*

*Normalise the group to the range $[-\pi, \pi]$ to give $group_{norm}$.

*Create two new variables: $group\_sin = sin(group_{norm})$, $group\_cos = cos(group_{norm})$ and use these instead of the original group.



