Shortening the formula syntax of a regression model - r

Question

I was wondering if the syntax of the regression model below could be made more concise (shorter) than it currently is?
dat <- read.csv('https://raw.githubusercontent.com/rnorouzian/v/main/bv1.csv')
library(nlme)
model <- lme(achieve ~ 0 + D1 + D2+
D1:time + D2:time+
D1:schcontext + D2:schcontext +
D1:female + D2:female+
D1:I(female*time) + D2:I(female*time)+
D1:I(schcontext*time) + D2:I(schcontext*time), correlation = corSymm(),
random = ~0 + D1:time | schcode/id, data = dat, weights = varIdent(form = ~1|factor(math)),
na.action = na.omit, control = lmeControl(maxIter = 200, msMaxIter = 200, niterEM = 50,
msMaxEval = 400))
coef(summary(model))

Answer 1

Focusing on the fixed-effect component only.
Original formula:
form1 <- ~ 0 + D1 + D2+
D1:time + D2:time+
D1:schcontext + D2:schcontext +
D1:female + D2:female+
D1:I(female*time) + D2:I(female*time)+
D1:I(schcontext*time) + D2:I(schcontext*time)
X1 <- model.matrix(form1, data=dat)
I think this is equivalent
form2 <- ~0 +
D1 + D2 +
(D1+D2):(time + schcontext + female + female:time+schcontext:time)
X2 <- model.matrix(form2, data=dat)
(Unfortunately ~ 0 + (D1 + D2):(1 + time + ...) doesn't work as I would have liked/expected.)
For a start, the model matrix has the right dimensions. Staring at the column names of the model matrices and reordering the columns manually:
X2o <- X2[,c(1:3,6,4,7,5,8,9,11,10,12)]
all.equal(c(X1),c(X2o)) ##TRUE
(For numerical predictors, you don't need I(A*B): A:B is equivalent.)
Actually you can do a little better using the * operator
form3 <- ~0 +
D1 + D2 +
(D1+D2):(time*(schcontext+female))
X3 <- model.matrix(form3, data=dat)
X3o <- X3[,c(1:3,6,4,7,5,8,10,12,9,11)]
all.equal(c(X1),c(X3o)) ## TRUE
Compare formula length:
sapply(list(form1,form2,form3),
function(x) nchar(as.character(x)[[2]]))
## [1] 183 84 54