[R] different regression coeffs with different starting point

[Jen]

Hi Bill,
Thanks for your response and I'm sorry -- that was a misleading example of
what I was trying to show. This one should illustrate the point:

require(AER)
data_in = c(0,6,12,18,24,30,36,42,48,54,60,66,72,78)
data_in2 = data_in^2
data_in3 = data_in^3
data_out =
c(139487.00,133333.00,62500.00,58823.00,56338.00,27549.00,4244.00,600.00,112.00,95.00,48.00,31.00,15.00,14.99)
ldata_out = log(data_out)

m1 <- lm(ldata_out ~ data_in + data_in2+data_in3)
cubic <- tobit(ldata_out ~ data_in + data_in2 + data_in3, left=
log(15-0.01),init = coef(m1))
print(cubic)
fitted(cubic)

n= length(data_in)
m2 <- lm(ldata_out[1:(n-1)] ~ data_in[1:(n-1)] +
data_in2[1:(n-1)]+data_in3[1:(n-1)])
cubic2 <- tobit(ldata_out ~ data_in + data_in2 + data_in3, left=
log(15-0.01),init = coef(m2))
print(cubic2)
fitted(cubic2)

The models cubic and cubic2 seem to show that the intercept value in the
model doesn't change from its starting value:

> m1

Call:
lm(formula = ldata_out ~ data_in + data_in2 + data_in3)

Coefficients:
(Intercept)      data_in     data_in2     data_in3  
  1.156e+01    1.004e-01   -7.755e-03    6.464e-05  

> cubic

Call:
tobit(formula = ldata_out ~ data_in + data_in2 + data_in3, left = log(15 - 
    0.01), init = coef(m1))

Coefficients:
(Intercept)      data_in     data_in2     data_in3  
 11.5559540    0.0289083   -0.0040615    0.0000229  

Scale: 3.759 

> m2

Call:
lm(formula = ldata_out[1:(n - 1)] ~ data_in[1:(n - 1)] + data_in2[1:(n - 
    1)] + data_in3[1:(n - 1)])

Coefficients:
        (Intercept)   data_in[1:(n - 1)]  data_in2[1:(n - 1)]  data_in3[1:(n
- 1)]  
          1.150e+01            1.151e-01           -8.381e-03           
7.122e-05  

> cubic2

Call:
tobit(formula = ldata_out ~ data_in + data_in2 + data_in3, left = log(15 - 
    0.01), init = coef(m2))

Coefficients:
(Intercept)      data_in     data_in2     data_in3  
  1.150e+01    3.391e-02   -4.187e-03    2.383e-05  

Scale: 3.759 

Am I missing something here??

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