12:03 p.m.
Dear all,
I could find the formula explaining how to calculate McFadden R-squared in
the gretl user's guide.
I tried to replicate it in Probit model but I fail to get the same value. Is
anything wrong with my calculation as follows.
Thanks
Yi-Nung Yang
<script>
nulldata 10
set seed 89675430
series u=normal()
series y=(u>0)
series x = uniform()
probit y const x
scalar lnL=$lnl
probit y const
scalar lnL0=$lnl
# McFadden R-squared as in Greene's Econometric Analysis
scalar McR2= 1-lnL/lnL0
</script>
12:24 p.m.
On Mon, 19 Apr 2010, yinung at Gmail wrote:
I could find the formula explaining how to calculate McFadden
R-squared in
the gretl user's guide.
I tried to replicate it in Probit model but I fail to get the same value. Is
anything wrong with my calculation as follows.
We use the formula you use below -- except that we don't bother
running the probit with constant only, we use the short-cut
calculation of the restricted loglikelihood. This may differ
slightly from what you get if you actually estimate the
constant-only model, but only to machine precision.
I have added a couple of lines to your script below:
<script>
nulldata 10
set seed 89675430
series u=normal()
series y=(u>0)
series x = uniform()
probit y const x
scalar lnL=$lnl
scalar McR2_gretl = $rsq # added
probit y const
scalar lnL0=$lnl
# McFadden R-squared as in Greene's Econometric Analysis
scalar McR2= 1-lnL/lnL0
scalar test = McR2_gretl - McR2 # added
</script>
If I run your script as modified I get a "test" value of
1.665e-16, which doesn't seem like a problem. What are you seeing?
Allin
12:51 p.m.
Thanks, Allin
2010/4/19 Allin Cottrell <cottrell(a)wfu.edu>
If I run your script as modified I get a "test" value of
1.665e-16, which doesn't seem like a problem. What are you seeing?
Allin
_______________________________________________
This is what I got (the script is attached in the bottom of this mail). The
difference is quiet large. test = -0.108229
I use gretl for windows build date 2010-03-26
Yi-Nung Yang
>>>>>>>>>>>>>>>>
gretl version 1.8.7cvs
Current session: 2010-04-19 01:46
? nulldata 10
periodicity: 1, maxobs: 10
observations range: 1-10
? set seed 89675430
Pseudo-random number generator seeded with 89675430
? series u=normal()
Generated series u (ID 2)
? series y=(u>0)
Generated series y (ID 3)
? series x = uniform()
Generated series x (ID 4)
? probit y const x
Convergence achieved after 5 iterations
Model 1: Probit, using observations 1-10
Dependent variable: y
coefficient std. error z slope
-------------------------------------------------------
const -1.17560 0.906894 -1.296
x 2.31663 2.00475 1.156 0.889540
Mean dependent var 0.400000 S.D. dependent var 0.383980
McFadden R-squared 0.108229 Adjusted R-squared -0.188942
Log-likelihood -6.001721 Akaike criterion 16.00344
Schwarz criterion 16.60861 Hannan-Quinn 15.33957
Number of cases 'correctly predicted' = 7 (70.0%)
f(beta'x) at mean of independent vars = 0.384
Likelihood ratio test: Chi-square(1) = 1.45679 [0.2274]
Predicted
0 1
Actual 0 5 1
1 2 2
? scalar lnL=$lnl
Generated scalar lnL = -6.00172
? probit y const
Convergence achieved after 4 iterations
Model 2: Probit, using observations 1-10
Dependent variable: y
coefficient std. error z slope
-----------------------------------------------------
const -0.253347 0.400990 -0.6318
Mean dependent var 0.400000 S.D. dependent var 0.386343
McFadden R-squared 0.000000 Adjusted R-squared -0.148586
Log-likelihood -6.730117 Akaike criterion 15.46023
Schwarz criterion 15.76282 Hannan-Quinn 15.12830
Number of cases 'correctly predicted' = 6 (60.0%)
f(beta'x) at mean of independent vars = 0.386
Predicted
0 1
Actual 0 6 0
1 4 0
? scalar lnL0=$lnl
Generated scalar lnL0 = -6.73012
# McFadden R-squared as in Greene's Econometric Analysis
? scalar McR2= 1-lnL/lnL0
Generated scalar McR2 = 0.108229
? scalar McR2_gretl = $rsq # added
Generated scalar McR2_gretl = 1.11022e-016
? scalar test = McR2_gretl - McR2 # added
Generated scalar test = -0.108229
<script>
nulldata 10
set seed 89675430
series u=normal()
series y=(u>0)
series x = uniform()
probit y const x
scalar lnL=$lnl
probit y const
scalar lnL0=$lnl
# McFadden R-squared as in Greene's Econometric Analysis
scalar McR2= 1-lnL/lnL0
scalar McR2_gretl = $rsq # added
scalar test = McR2_gretl - McR2 # added
</script>
1:06 p.m.
On Mon, 19 Apr 2010, yinung at Gmail wrote:
Thanks, Allin
2010/4/19 Allin Cottrell <cottrell(a)wfu.edu>
>
> If I run your script as modified I get a "test" value of
> 1.665e-16, which doesn't seem like a problem. What are you seeing?
>
> Allin
> _______________________________________________
>
This is what I got (the script is attached in the bottom of this mail). The
difference is quiet large. test = -0.108229
[snip]
<script>
nulldata 10
set seed 89675430
series u=normal()
series y=(u>0)
series x = uniform()
probit y const x
scalar lnL=$lnl
probit y const
scalar lnL0=$lnl
# McFadden R-squared as in Greene's Econometric Analysis
scalar McR2= 1-lnL/lnL0
scalar McR2_gretl = $rsq # added
scalar test = McR2_gretl - McR2 # added
</script>
You need to save "McR2_gretl" before estimating the constant-only
model, as in the version I showed.
Allin
1:10 p.m.
yinung at Gmail schrieb:
This is what I got (the script is attached in the bottom of this mail).
The difference is quiet large. test = -0.108229
I use gretl for windows build date 2010-03-26
It seems to me you're asking in your script for the wrong $rsq (you're
asking one model too late, so to speak)
<script>
nulldata 10
set seed 89675430
series u=normal()
series y=(u>0)
series x = uniform()
probit y const x
scalar lnL=$lnl
this is the place where you should store $rsq
probit y const
scalar lnL0=$lnl
# McFadden R-squared as in Greene's Econometric Analysis
scalar McR2= 1-lnL/lnL0
scalar McR2_gretl = $rsq # added
this is saving the $rsq of the last model without x, 0 by definition
scalar test = McR2_gretl - McR2 # added
</script>
-sven
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yinung＠Gmail