On Mon, 14 Mar 2011, Jen wrote:
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))
The scaling of your regressors is extremely bad. data_in3 is in the
hundreds of thousands. This computationally challenging, to put it mildly.
I would recommend to either scale data_in by some constant (here 10 or 100
is enough) or to use an orthogonal coding of the polynomial. Both can be
achieved easily using the poly() function:
- Your model would be: ldata_out ~ poly(data_in, 3, raw = TRUE)
- With scaled regressors: ldata_out ~ poly(data_in/100, 3, raw = TRUE)
- With orthogonal coding: ldata_out ~ poly(data_in/100, 3)
All models conceptually lead to the same fitted values and the same
maximal likelihood. Numerically, however, the first model only achieves
suboptimal values depending on the starting values. The latter two models
seem to yield more sensible results and be close to the actual maximum.
Note that the coefficients change of course due to the different codings
of the regressors. This needs to be taken into account if you want to
compare the slopes.
In summary, I would probably use
cubicz <- tobit(ldata_out ~ poly(data_in/100, 3, raw = TRUE),
left = log(15-0.01))
which is very robust to the choice of starting values.
hth,
Z
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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