R help - Dec 2009 - Tobit model fluid milk consumption

Hi all, 

I'm from Brazil. 

I fit a Tobit model to FLUID MILK CONSUMPTION (DEPENDENT VARIABLE) data
using survreg (attached). 

I am confused about the output interpretation and I would like yours
explanations. 

Thanks, Marcio Roberto Silva
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 1. Tobit regression on the raw data:
   The "scale" is the residual standard deviation, or estimate of
"sigma" in the usual linear models terminology.
   For linear regression with uncensored data, the estimate of scale is
independent of the estimate of the other coefficients, and can be
computed at the end.  For censored data this is not so, the scale and
the coefficients must be estimated together.  During the maximization
step the routine uses log(scale), it forces positive coefficients and
also works better numerically; as a consequence the full
variance/covariance matrix includes both beta and log(scale).

2. Tobit regression on the rescaled data.
  You must have rescaled both x and y, since the estimated residual
variance changed.
  I see multiple disadvantages, and no advantages, to regression on
rescaled data.  I know it is common in some fields, but why?  With
respect to your questions on how to interpret rescaled coefficients, I
don't know how to interpret them either.

 3. The "residual" for a censored observation is not a well defined
quantity.  Hence both the computation and meaning of R^2 are unclear to
me.

Terry Therneau


  Terry Therneau

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Hi all, 
I fit a Tobit model to Fluid milk consumption (dependent variable) data
using survreg.  1) The square root of the dependent variable was used to
correct for 
heteroscedasticity since it provides the best fit. 2) The output before
transformation of numeric variables in scores (by "Make.Z") was:
survreg(formula=Surv(QUALEITERPER, QUALEITEPER>0,type= "left") ~
SALARPER +
IDADE + 
IDADE2 + NUMORAD + CIGAFAI + LOCAL, data = leite, dist = "gaussian") 
Value Std.Error z p
(intercept) 14.20 2.50 5.58 1.34e-08
SALARPER 2.98 0.87 3.41 6.45e-04
IDADE -0.50 0.06 -7.91 2.48e-15
IDADE2 0.006 0.00 7.37 1.76e-13
NUMORAD -0.61 0.25 -2.39 1.69e-02
CIGAFAI-10 2.20 2.04 1.11 2.68e-01
CIGAFAI-NF 4.66 1.18 3.92 8.80e-05
LOCALh 4.13 1.82 2.27 2.35e-02
LOCALi 1.78 1.62 1.09 2.74e-01
LOCALm 3.66 1.93 1.89 5.82e-02
LOCALt 4.66 1.85 2.51 1.20e-02
Log(scale) 2.26 0.03 73.35 0.00e+00 Scale=9.65 Gaussian distribution
Loglik(model)=-2270.8 Loglik (intercept only)=-2335
Chisq=128.5 on 10 degrees of
freedom, p=0
Number of Newton-Raphson Iterations: 4
N=704 (19 observations deleted due to missingness) 
2 - The output after transformation of numeric variables in scores by
"Make.Z(X)" was: survreg(formula=Surv(QUALEITERPERz,
QUALEITEPERz>-1.4977406,type= "left") ~ SALARPERz + 
IDADEz + IDADE2z + NUMORADz + CIGAFAI + LOCAL, data = leite, dist
"gaussian")
 Value Std.Error z p
(intercept) -0.80 0.20 -3.93 8.38e-05
SALARPERz 0.15 0.04 3.41 6.45e-04
IDADEz -1.13 0.14 -7.91 2.48e-15
IDADE2z 1.03 0.14 7.37 1.76e-13
NUMORADz -0.11 0.04 -2.39 1.69e-02
CIGAFAI-10 0.24 0.22 1.11 2.68e-01
CIGAFAI-NF 0.51 0.13 3.92 8.80e-05
LOCALh 0.45 0.20 2.27 2.35e-02
LOCALi 0.19 0.17 1.09 2.74e-01
LOCALm 0.40 0.21 1.89 5.82e-02
LOCALt 0.51 0.20 2.51 1.20e-02
Log(scale) 0.06 0.03 1.95 5.16e-02 Scale=1.06 Gaussian distribution
Loglik(model)=-993.3 Loglik (intercept only)=-1057.6
Chisq=128.5 on 10 degrees of freedom, p=0
Number of Newton-Raphson Iterations: 4
N=704 (19 observations deleted due to
missingness) 
I am confused about the output, because: 1) I do not know how to interpret
the "scale". 2) The scale/log(scale) interferes in the interpretation
of
coefficients or both 
are independents? So, how I interpret the coefficients? Give me one
example. 3) How I interpret the coefficients (after score z
transformation)? Give me one 
example. 4) How I could interpret pseudo R2 if it modifies after score z
transformation? 
Should I take it in consideration? Is there some alternative? Thanks,
Marcio Roberto Silva

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