The terms sex*weight
and sex:weight
have different meanings. The first one (*) is a shorthand for sex + weight + sex:weight
, that is, for including each parameter AND the interaction. sex:weight
only adds the interaction term. Therefore the resulting models differ.
As far as I know, models should always include the lower level terms which are involved in interactions. Otherwise, the interaction can not be interpreted (easily), see for instance here: https://stats.stackexchange.com/q/11009/133735
#model including both parameters and their interaction with "*"
m1 <- lm(Sepal.Length ~ Petal.Width * Petal.Length, data = iris)
coef(m1)
(Intercept) Petal.Width Petal.Length Petal.Width:Petal.Length
4.5771709 -1.2393154 0.4416762 0.1885887
#model including both pars and interaction (all terms spelled out)
m2 <- lm(Sepal.Length ~ Petal.Width + Petal.Length + Petal.Width:Petal.Length, data = iris)
coef(m2)
(Intercept) Petal.Width Petal.Length Petal.Width:Petal.Length
4.5771709 -1.2393154 0.4416762 0.1885887
#model only including the interaction
m3 <- lm(Sepal.Length ~ Petal.Width:Petal.Length, data = iris)
coef(m3)
(Intercept) Petal.Width:Petal.Length
4.9704818 0.1506457
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