Why do I get NA coefficients and how does "lm" produce a reference level for interaction

Question

I am trying to understand how R defines reference groups for interaction in a linear model. Consider the following:

df <- structure(list(id = structure(c(1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 
2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 3L, 3L, 4L, 4L, 4L, 4L, 4L, 4L, 
5L, 5L, 5L, 5L, 5L, 5L), .Label = c("1", "2", "3", "4", "5"), class = "factor"), 
    year = structure(c(1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 
    1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 
    2L, 1L, 2L, 1L, 2L), .Label = c("1", "2"), class = "factor"), 
    treatment = structure(c(2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 
    2L, 2L, 2L, 2L, 2L, 2L), .Label = c("0", "1"), class = "factor"), 
    y = c(1.4068142116718, 2.67041187927052, 2.69166439169131, 
    3.56550324537293, 1.60021286173782, 4.26629963353237, 3.85741108250572, 
    5.15740731957689, 4.15629768365669, 6.14875441068499, 3.31277276551286, 
    3.47223277168367, 3.74152201649338, 4.02734382610191, 4.49388620764795, 
    5.6432833241724, 4.76639399631094, 4.16885857079297, 4.96830394378801, 
    5.6286092105837, 6.60521404151111, 5.51371821706176, 3.97244221149279, 
    5.68793413111161, 4.90457233598412, 6.02826151378941, 4.92468415350312, 
    8.23718422822134, 5.87695836962708, 7.47264895892575)), .Names = c("id", 
"year", "treatment", "y"), row.names = c(NA, -30L), class = "data.frame")


lm(y ~ -1 + id + year + year:treatment, df)

#Coefficients:
#             id1               id2               id3               id4  
#          2.6585            3.9933            4.1161            5.3544  
#             id5             year2  year1:treatment1  year2:treatment1  
#          6.1991            0.7149           -0.6317                NA  

R is trying to evaluate the full set of interactions, rather than sequentially discarding the control group. As a result, I get NAthe results.

In addition, R is not consistent with which groups it falls. I would like to evaluate a model with the same omitted group ( year1) in the main effect and interactions. How to make R drop year1and year1:treatment1the previous model?

, (, ). , , , .

Answer 1

R , . NA .

. NA , .

R , . (year1) . R year1 year1:treatment1 ?

, model.matrix . , , "" , treatment, treatment:year.

NA, , , .

---

NA

, contr.treatement . :

levels(df$id)
# [1] "1" "2" "3" "4" "5"

levels(df$year)
# [1] "1" "2"

levels(df$treatment)
# [1] "0" "1"

:

lm(y ~ id + year + treatment, df)

#Coefficients:
#(Intercept)          id2          id3          id4          id5        year2  
#      2.153        1.651        1.773        2.696        3.541        1.094  
# treatment1  
#         NA  

, id1, year1 treatment0 , .

NA. , treatment span{id, year}. treatment:year, .

, , treatment id:

lm(y ~ id + treatment, df)

#    Coefficients:
#(Intercept)          id2          id3          id4          id5   treatment1  
#      2.700        1.651        1.773        2.696        3.541           NA

, treatment . id, treatment treatment:*, * .

, . , , , . , contr.treatment:

df$ID <- df$id
lm(y ~ id + ID, df)

#Coefficients:
#(Intercept)          id2          id3          id4          id5          ID2  
#      2.700        1.651        1.773        2.696        3.541           NA  
#        ID3          ID4          ID5  
#         NA           NA           NA  

, , , id id, -.

---

, NA, id. treatment year , no NA , .

. :

lm(y ~ year:treatment, df)  ## no low-order effects at all

#Coefficients:
#     (Intercept)  treatment0:year1  treatment1:year1  treatment0:year2  
#          5.4523           -1.3976           -1.3466           -0.6826  
#treatment1:year2  
#              NA  

lm(y ~ year + treatment + year:treatment, df)  ## with all low-order effects

#Coefficients:
#     (Intercept)        treatment1             year2  treatment1:year2  
#         4.05471           0.05094           0.71493           0.63170  

, , 2- . NA - .

, , :

lm(y ~ year + year:treatment, df)  ## main effect `treatment` is missing

#Coefficients:
#     (Intercept)             year2  year1:treatment1  year2:treatment1  
#         4.05471           0.71493           0.05094           0.68264  

lm(y ~ treatment + year:treatment, df)  ## main effect `year` is missing

#Coefficients:
#     (Intercept)        treatment1  treatment0:year2  treatment1:year2  
#         4.05471           0.05094           0.71493           1.34663  

, . , treatment, treatement0; year, year1.

---

. , . , Cross Validated.

- . , 0.