If we have a response variable y and three predictor variables x1, x2, and x3 and M1 and M2 are nested within M3 where
M1: y = intercept + b1 *x1 + b2* x2
M2: y = intercept + b3 * x3
M3: y = intercept + b1 *x1 + b2* x2 + b3 * x3
can M1 and M2 be tested even though they are not nested by subtracting the deviances of M1 and M2? I don't think they can be tested and I cannot define the null hypothesis of testing M1 and M2.
In addition is M4 as follows nested in M3? M4 has a fixed parameter value.
M4: y = intercept + 0.3 *x1 + b2* x2
