When using a square transformation inline (i.e. using ~ Parameter^2 in the model formula) is giving different results than when I transform the Parameter first into a different column and use that column in the model ( i.e Parameter2 = Parameter^2 and then using ~ Parameter2 in the formula)
Worst.Perimeter2 = Worst.Perimeter^2
m0x_ <- glm(formula = Diagnosis ~ Worst.Perimeter2, family = binomial,
data = cancerdata)
summary(m0x_)
results:
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -1.090e+01 1.132e+00 -9.634 <2e-16 ***
Worst.Perimeter2 8.974e-04 9.792e-05 9.165 <2e-16 ***
m0x1_ <- glm(formula = Diagnosis ~ Worst.Perimeter^2, family = binomial,
data = cancerdata)
summary(m0x1_)
Results:
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -20.81003 2.22116 -9.369 <2e-16 ***
Worst.Perimeter 0.18931 0.02068 9.156 <2e-16 ***
I would expect them to give the same results for the coefficients but clearly that's not the case. How do I interpret these different results?
^ is a formula operator. You can use it to specify a formula that includes interactions as in this example:
# Formula `(a + b)^2` means `1 + a + b + a*b`
head(model.matrix(~ (mpg + wt)^2, data = mtcars))
#> (Intercept) mpg wt mpg:wt
#> Mazda RX4 1 21.0 2.620 55.020
#> Mazda RX4 Wag 1 21.0 2.875 60.375
#> Datsun 710 1 22.8 2.320 52.896
#> Hornet 4 Drive 1 21.4 3.215 68.801
#> Hornet Sportabout 1 18.7 3.440 64.328
#> Valiant 1 18.1 3.460 62.626
If you want ^ to be interpreted as an arithmetic operator instead, use the I (AsIs) operator as in this example:
head(model.matrix(~ I((mpg + wt)^2), data = mtcars))
#> (Intercept) I((mpg + wt)^2)
#> Mazda RX4 1 557.9044
#> Mazda RX4 Wag 1 570.0156
#> Datsun 710 1 631.0144
#> Hornet 4 Drive 1 605.8982
#> Hornet Sportabout 1 490.1796
#> Valiant 1 464.8336
Created on 2019-04-06 by the reprex package (v0.2.1)