As the title reads, the results from the linear and first degree polynomial model are different and I am not sure why. Any ideas why this might be?
linear_model <- nlme::lme(mpg ~ vs * gear, random = ~ 1 | ID,
data = mutate(mtcars, ID = dplyr::row_number()))
summary(linear_model)
Value Std.Error DF t-value p-value
(Intercept) 8.378571 4.242762 28 1.9747918 0.0582
vs -3.047802 9.300390 28 -0.3277069 0.7456
gear 2.316964 1.161928 28 1.9940684 0.0560
vs:gear 2.667651 2.423512 28 1.1007375 0.2804
------------------------------------------------------------------------
poly_model <- nlme::lme(mpg ~ vs * poly(gear, 1), random = ~ 1 | ID,
data = mutate(mtcars, ID = dplyr::row_number()))
summary(poly_model)
Value Std.Error DF t-value p-value
(Intercept) 16.922377 0.978208 28 17.299367 0.0000
vs 6.789161 1.512328 28 4.489213 0.0001
poly(gear, 1) 9.517902 4.773107 28 1.994068 0.0560
vs:poly(gear, 1) 10.958495 9.955593 28 1.100738 0.2804
```
?polyindicates that these are orthogonal polynomials. More information: mathoverflow.net/questions/38864/… $\endgroup$