Let's say I am trying to see if there are speed differences among different types of cars (e.g., jeep, SUV, truck, sports car). I also want to see whether the car store (A, B, C, D, E) has an effect on this. I don't have a specific hypothesis about the car stores, but I assume that certain stores tend to sell certain types of cars (e.g., SUVs at Store A and trucks at Store B).
 
So, I tried to fit a linear mixed effect model with lme4 and nlme. 
I have a question about the difference between these two models: 

nlme: 
```
m1 <- lme(speed ~ car_type + car_store + car_type:car_store, 
          data = data1, random = ~ 1 | car_owner, method = "ML")
```

lme4 equivalent is: 
```
m2 <- lmer(speed ~ car_type * car_store + (1 | car_owner), 
           data = data1, REML = FALSE)
```

Now, my question is, can I have interaction as the main effect in nlme like this:
```
m3 <- lme(speed ~ car_type + car_type:car_store, data = data1, 
          random = ~ 1 | car_owner, method = "ML")
```

So far, I can't find the equivalent of `m3` in lme4. Can anyone help me understand why? 

Also, ideally, I think I can achieve my purpose with `m3`. But is there anything else that I should consider? like perhaps it's better to use lme4 and car_store as main/fixed effect as well?