I am trying to apply log-log in a marketing mix model. The dependent variable is sales, among the independent variables, one is holiday, it is dummy variable, the value is either 1(yes), or 0 (no). Another variable is competitor spend, sometimes, the value is 0.
I want to use a log-log model in R. But how can deal with variables like holiday and competitor's spend which have value of 0? I cannot remove these two variables from the model.
I already did a linear regression model in R, can anyone help me with the log-log model? (As suggested by a comment in below, I used log(x+1) in the log-log model, is it correct?)
model <- lm(SALES ~ HOLIDAY + AVERAGE_PRICE + COMPETITOR_MEDIA_SPEND + IMP_TV + IMP_EMAIL + IMP_PAID_SEARCH + IMP_ONLINE_DISPLAY + IMP_PRODUCT_SEARCH, data = mmm) model2 <- lm(log(SALES) ~ log(HOLIDAY+1) + log(AVERAGE_PRICE) + log(COMPETITOR_MEDIA_SPEND+1)+ log(IMP_TV) + log(IMP_EMAIL) + log(IMP_PAID_SEARCH) + log(IMP_ONLINE_DISPLAY) + log(IMP_PRODUCT_SEARCH), data = mmm)