A predictor that "becomes" categorical when larger than a cutoff I have a dataset where a predictor can have 2 states - if it's in state 1, then the value is always the same. If it's in state 2, then the value is continuous and changes. An example to this can be number of cigarettes smoked per day. If the person is a non-smoker, the value is always 0. If the person is a smoker, the value can be 0 or higher. In my model, I have 2 predictor variables - NoSmoke and Cig. Until recently, I thought this was the correct approach (based on another SO post that I can no longer find). However, I was recently told by a statistician that this approach is problematic - partly because the 2 predictors are independent, and partly because they're correlated.
When I run the model and plot the predictions, things seem to be working out. Is there an issue with this modeling approach? And if so - what's the correct way to analyze this, while preserving the continuous predictor values?
toy example with simulated data:
library(plyr)
library(dplyr)
library(tidyr)
library(ggplot2)

df1 <- data.frame(NoSmoke = "NoSmoke", Cig = rep(0, 100), Response = rnorm(100, 20, 5))
df2 <- data.frame(NoSmoke = "Smoke", Cig = rpois(100, 2)) %>%
        mutate(Response = 5 + 2 * Cig + rnorm(100, 20, 5))
df <- rbind(df1, df2)

mod <- lm(Response ~ NoSmoke + Cig, data = df)

new <- data.frame(NoSmoke = c("NoSmoke", rep("Smoke", 7)), Cig = c(0, 0:6))
preds <- as.data.frame(predict(mod, newdata = new, interval = "confidence"))

new$Pred <- preds$fit
new$Lower <- preds$lwr
new$Upper <- preds$upr

ggplot(df) +
    geom_point(aes(x = Cig, y = Response, colour = NoSmoke), position = position_dodge(width = 0.2)) +
    geom_point(data = new, aes(x = Cig, y = Pred, fill = NoSmoke), size = 2, shape = 21, colour = "black", 
        position = position_dodge(width = 0.2)) +
    geom_errorbar(data = new, aes(x = Cig, ymin = Lower, ymax = Upper, colour = NoSmoke), 
        position = position_dodge(width = 0.2)) 

EDIT
I left this out of the question for simplicity, but following some of the answers/comments - my actual continuous variable is actually continuous, as opposed to the number of cigarettes in the example (apologies, I was trying for simplicity). In terms of correlation between the NoSmoke and the Cig variables - in my analysis, I standardize Cig, so that the standardized value for the Smoke=="Smoke" cases is standardized as normal, and the standardized value for the Smoke=="NoSmoke" is zero. This allows the model to be Response = Intercept + beta_cig*Cig for the smokers and Response = Intercept + beta_nosmoke for the non-smokers. The correlation between the NoSmoke and the CigS is low - ~0.4 in the example, and <0.1 in my real data.
Here's the toy example with the standardization:
df <- df %>%
        group_by(NoSmoke) %>%
        mutate(CigS = (Cig - mean(Cig)) / sd(Cig)) %>%
        ungroup() %>%
        mutate(CigS = ifelse(NoSmoke == "NoSmoke", 0, CigS)) 
                NoSmoke = factor(NoSmoke, levels = c("Smoke", "NoSmoke")))
cor(as.numeric(df$NoSmoke), df$CigS)

mod <- lm(Response ~ NoSmoke + CigS, data = df)

new <- data.frame(NoSmoke = c("NoSmoke", rep("Smoke", 7)), Cig = c(0, 0:6)) %>%
        left_join(unique(select(df, NoSmoke, Cig, CigS)))
preds <- as.data.frame(predict(mod, newdata = new, interval = "confidence"))

new$Pred <- preds$fit
new$Lower <- preds$lwr
new$Upper <- preds$upr

ggplot(df) +
    geom_point(aes(x = Cig, y = Response, colour = NoSmoke), position = position_dodge(width = 0.2)) +
    geom_point(data = new, aes(x = Cig, y = Pred, fill = NoSmoke), size = 2, shape = 21, colour = "black", 
        position = position_dodge(width = 0.2)) +
    geom_errorbar(data = new, aes(x = Cig, ymin = Lower, ymax = Upper, colour = NoSmoke), 
        position = position_dodge(width = 0.2)) 


Other answers are right but I think we should take in account that by including or not including the binary variable we are adjusting different models with underlying different assumptions.
Dropping the binary variable and only using the continuous variable means assuming that the effects of smoking are continuous at 0. That is, the effect of smoking very little (approaching zero) approaches the effect of not smoking.
You can see that in your example this assumption is false, because the expected response for a non smoker is 20 but the expected response for a smoker of 0 cigarettes is 25. Therefore for this example the model can match better the underlying problem when both predictors are included.
From actual data we might not know how the response behaves near zero. For some  problems the knowledge on the problem may give some clue: for example, some contaminants are known not to have any safe dose, so we can suppose that very little exposure is going to produce a different response than no exposure at all and using both predictors may be useful. Other phenomena can behave differently.
In case of no prior knowledge, you can test if the categorical predictor is significant, just as with any other predictor. Here we are working in the opposite way, and finding reasons to discard it as not significant may suggest that the response is continuous at zero smoking and that may be an interesting result in itself.
Additionally, if your actual problem involves more variables, by discarding the categorical predictor you are assuming that the effects of those other variables are the same for smokers and non smokers, but by including the categorical predictor and its interactions with other variables you are actually adjusting two different models for smokers and non smokers. If you have an enough large dataset to adjust such a model without overfitting, it can give interesting results.
