Dear all,
I am trying to wrap my head around interpreting the coefficients of my Cox model. Perhaps I have the wrong variable set-up. Let me first introduce the data that I am working with and the model that I have estimated.
Basically, I am working with a dataset about an auction where products get sold. I’m tracking how long it takes for a product to change hands (like when it gets sold). When a product is put up for sale, people can bid on it, and eventually, it might get sold. The time-to-event, defined as the duration between the auction start and product sale, is typically very short, often just a few minutes. I have this intra-day auction data spanning a period of several years.
The products that get sold can be divided into two groups: ‘gold’ and ‘not-gold’. Furthermore, each product belongs to one of the following five product types: ‘Electronics’, ‘Clothing’, ‘Food’, ‘Automobiles’ and ‘Health’.
I want to examine how the presence of 'gold' products within a product group affects the selling time for a product (e.g. I want to see the effect on gold and non-gold products while controlling for other factors). In this regard, I have created a daily variable called ‘Gold_proportion’ that measures the percentage of the products in a certain product group that are ‘gold’.
I have estimated the following (cox) regression equation:
Time-to-eventi,t = Goldi + High_riski + High_riski x Goldi + Pricei,t + Clothingi + Foodi + Automobilesi + Healthi + Goldi x (Clothingi + Foodi + Automobilesi + Healthi) + Gold_proportioni + Gold_proportioni x Goldi + Mondayi,t + Tuesdayi,t + Wednesdayi,t + Thursdayi,t + Fridayi,t + Saturdayi,t.
Note that I did not include a dummy for the Electronics product group (so this acts as the reference group). Similarly, I have not included a dummy for Sunday.
Questions:
Any help would be greatly appreciated.
I am trying to wrap my head around interpreting the coefficients of my Cox model. Perhaps I have the wrong variable set-up. Let me first introduce the data that I am working with and the model that I have estimated.
Basically, I am working with a dataset about an auction where products get sold. I’m tracking how long it takes for a product to change hands (like when it gets sold). When a product is put up for sale, people can bid on it, and eventually, it might get sold. The time-to-event, defined as the duration between the auction start and product sale, is typically very short, often just a few minutes. I have this intra-day auction data spanning a period of several years.
The products that get sold can be divided into two groups: ‘gold’ and ‘not-gold’. Furthermore, each product belongs to one of the following five product types: ‘Electronics’, ‘Clothing’, ‘Food’, ‘Automobiles’ and ‘Health’.
I want to examine how the presence of 'gold' products within a product group affects the selling time for a product (e.g. I want to see the effect on gold and non-gold products while controlling for other factors). In this regard, I have created a daily variable called ‘Gold_proportion’ that measures the percentage of the products in a certain product group that are ‘gold’.
I have estimated the following (cox) regression equation:
Time-to-eventi,t = Goldi + High_riski + High_riski x Goldi + Pricei,t + Clothingi + Foodi + Automobilesi + Healthi + Goldi x (Clothingi + Foodi + Automobilesi + Healthi) + Gold_proportioni + Gold_proportioni x Goldi + Mondayi,t + Tuesdayi,t + Wednesdayi,t + Thursdayi,t + Fridayi,t + Saturdayi,t.
Note that I did not include a dummy for the Electronics product group (so this acts as the reference group). Similarly, I have not included a dummy for Sunday.
Questions:
- How do I interpret the coefficients? Since included many different dummy variables, as well as many interactions with the Goldi variable, this confuses me. For instance, what would be the interpretation of Gold_proportioni and Gold_proportioni x Goldi? And what would be the interpretation of Goldi and Goldi x Clothingi?
- In order to examine the effect of the presence of 'gold' products within a product group, is it necessary to include the Gold x Product type dummies? Or would the individual Product type dummies be sufficient? How would this change the interpretation of Gold_proportioni and Gold_proportioni x Goldi?
- Similarly, does it make sense to include the Gold x Risk category dummies? Or does it make more sense to examine this effect in a separate regression?
Any help would be greatly appreciated.
