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)) 


Having two features like those described by you is a perfectly normal and valid solution. It also arises in many different scenarios. For example, if you have two features: age and gender, and consider interaction age * gender, the values for it would be 0 for people whose gender was coded as 0 and non-negative otherwise (see also the link mentioned in the comment by EdM).
I cannot comment on what the statistician said because you didn't give us a full quote and context. Maybe they meant some specific scenario, but in general, such features and their interactions are commonly used.
