Testing for model specification error in fractional regression

[Laiy Kho]

Hello,

I employed fractional regression model proposed by Wooldridge and Papke to estimate the dependent variable (a proportional variable that computes remaining/whole) of my study. The dependent variable falls between 0 and 1 (including 1). I ran the regression using the fracreg command on stata. However, I would like to run Ramsey reset test for model specification errors, as Wooldridge reports the reset test value in his paper. When I entered the command "ovtest" and "linktest", Stata states the following:

. estat ovtest
estat ovtest not valid
r(321);

. linktest
not possible after fracreg
r(131);

How do I test for model specification after fracreg command? What other assumptions must be evaluated after estimating fractional regression. As such, in OLS regression, one would test if assumptions such as homoscedasticity, absence of autocorrelation and normality is violated. Similarly, what other tests should one evaluate after fractional regression?

Appreciate your advice.

[Carlo Lazzaro]

Laiy:
testing for model specification relies more on the fucntional form of the regressand than on -estat ovtest- (BTW: -estat ovtest- and -linktest- are not allowed after -probit-, too).
However, you can reproduce by hand the -linktest- machinery:

. webuse 401k
(Firm-level data on 401k participation)

. fracreg probit prate mrate c.ltotemp##c.ltotemp c.age##c.age i.sole

Iteration 0:   log pseudolikelihood = -1769.6832  
Iteration 1:   log pseudolikelihood = -1675.2763  
Iteration 2:   log pseudolikelihood = -1674.6234  
Iteration 3:   log pseudolikelihood = -1674.6232  
Iteration 4:   log pseudolikelihood = -1674.6232  

Fractional probit regression                            Number of obs =  4,075
                                                        Wald chi2(6)  = 815.88
                                                        Prob > chi2   = 0.0000
Log pseudolikelihood = -1674.6232                       Pseudo R2     = 0.0632

-------------------------------------------------------------------------------------
                    |               Robust
              prate | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
--------------------+----------------------------------------------------------------
              mrate |   .5859715   .0387616    15.12   0.000     .5100002    .6619429
            ltotemp |  -.6102767   .0615052    -9.92   0.000    -.7308246   -.4897288
                    |
c.ltotemp#c.ltotemp |   .0313576    .003975     7.89   0.000     .0235667    .0391484
                    |
                age |   .0273266   .0031926     8.56   0.000     .0210691     .033584
                    |
        c.age#c.age |  -.0003159   .0000875    -3.61   0.000    -.0004874   -.0001443
                    |
               sole |
         Only plan  |   .0683196   .0272091     2.51   0.012     .0149908    .1216484
              _cons |    3.25991   .2323929    14.03   0.000     2.804429    3.715392
-------------------------------------------------------------------------------------

. predict fitted, xb

. g sq_fitted=fitted^2

. fracreg probit prate fitted sq_fitted

Iteration 0:   log pseudolikelihood = -1765.3223  
Iteration 1:   log pseudolikelihood = -1674.8029  
Iteration 2:   log pseudolikelihood = -1673.3908  
Iteration 3:   log pseudolikelihood =   -1673.39  
Iteration 4:   log pseudolikelihood =   -1673.39  

Fractional probit regression                            Number of obs =  4,075
                                                        Wald chi2(2)  = 902.49
                                                        Prob > chi2   = 0.0000
Log pseudolikelihood = -1673.39                         Pseudo R2     = 0.0639

------------------------------------------------------------------------------
             |               Robust
       prate | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
      fitted |   1.470791   .1615294     9.11   0.000     1.154199    1.787382
   sq_fitted |  -.2144589   .0705605    -3.04   0.002    -.3527549   -.0761629
       _cons |  -.2283008   .0867032    -2.63   0.008    -.3982359   -.0583658
------------------------------------------------------------------------------

.

As the -sq_fitted- term reaches statistical significance, the model is misspecified.

[Laiy Kho]

Thank you so much Carlo! That worked. What tests would you recommend to run after estimating fracreg on Stata? I am quite new to this regression model. Are there any particular assumptions I need to look out for?

[Maxence Morlet]

Hi Carlo,

Is there a reason why you only included sq_fitted, and not higher order polynomials? Is this conventional in the Ramsey RESET test?

I am still quite novice regarding RESET tests...

[Carlo Lazzaro]

Maxence:
I simply code by hand the -linktest- procedure.
I used to run -estat ovtest-, but now I prefer -linktest- in its-built of (coded by hand) versions.
I also tested higher order polynomials form time to time. However, I feel uncomfortable with trying to explain what a cubic fitted value may mean in the real world (and I feel the same way with cubic predictors, that I never included in the right-hand side of my regression equation) and, most of the time, if -test- on the cubic fitted values turns out statitsically significant, the squared one behaves the same.
Obviously, deailing with health economic data, my experience suffers from the boundaries/limitations of this research field.