I am trying to estimate a quite complicated model (many variables with different structures), with a limited dependent variable, which ranges from 0-100% with about 45% of the sample having an observed value of 100%. I am currently drowning in the all the "goodness of fit" measures:

The OLS specification for this model provides the following results:

Residual standard error: 27.29 on 23109 degrees of freedom
  (48652 observations deleted due to missingness)
Multiple R-squared:  0.1073,    Adjusted R-squared:  0.1062 
F-statistic: 102.9 on 27 and 23109 DF,  p-value: < 0.00000000000000022

The tobit specification using AER:tobit for this model provides the following results:

Scale: 52.14 

Gaussian distribution
Number of Newton-Raphson Iterations: 4 
Log-likelihood: -7.76e+04 on 28 Df
Wald-statistic:  3835 on 26 Df, p-value: < 0.000000000000000222 

I have tried to calculate the pseudo R-squared based on the answer in this post as follows:

> fm0 <- update(tobit, . ~ 1)
> 1 - as.vector(logLik(tobit)/logLik(fm0))
[1] 0.5953306

In addition, I read that I cannot compare the coefficients of OLS and Tobit directly, but that I have to something like margEff(tobit), this is however again a function of the censReg package.

Obviously I would also like to tinker with my model a bit. And although I am reasonably familiar with comparing OLS models, I have no clue how to compare tobit models. Let's say I include an interaction term, and the output becomes as follows:

Scale: 51.98 

Gaussian distribution
Number of Newton-Raphson Iterations: 4 
Log-likelihood: -7.753e+04 on 30 Df
Wald-statistic:  3947 on 28 Df, p-value: < 0.000000000000000222 

> fm0 <- update(ES1tobit, . ~ 1)
> 1 - as.vector(logLik(ES1tobit)/logLik(fm0))
[1] 0.5957015


In general, my questions mostly is, what do all these stats mean and how do they relate to each other? More specifically.

  1. How do I compare an OLS model with a Tobit model (as well as possible).
  2. How do I compare a Tobit model with another Tobit model?
  3. This is slightly more of an R related question, but with which package do I get the best information, to compare these out. I am currently constantly switching between AER:tobit and censReg, because I only now how to calculate the pseudo with AER:tobit and only the marginal effects with censReg.

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