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Re: st: MCKelvey and Zavoina


From   Richard Williams <richardwilliams.ndu@gmail.com>
To   statalist@hsphsun2.harvard.edu, <statalist@hsphsun2.harvard.edu>
Subject   Re: st: MCKelvey and Zavoina
Date   Sat, 02 Jun 2012 11:05:46 -0500

At 07:19 AM 6/2/2012, enrico wrote:
Dear Statalist,

my name is Enrico and I am an italian student. I'm working with Stata but I
have a problem. I know that the formula to calculate the Pseudo R-square
MCkelvey and Zavoina is R^2=Var(y*)/(Var(y*)+Var(error)), where Var(error)
in the Logit is equal to 3.14^2/3 while in the Probit is equal to 1.

Why if I use this formula in this case I don't obtein the exact value? In
fact  6.84/(6.84+3.29)=0.675 and not 0.519. Which formula do you use
instead?

Wrong formula. V(y*) already includes V(e). You need to SUBTRACT V(e) from the numerator rather than add it to the denominator. Then it becomes the logical analog of Explained variance/ Total variance. So,

(6.84 - 3.29)/6.84 = .519


logit honcomp female read science
fitstat, sav(r2_1)

Measures of Fit for logit of honcomp

Log-Lik Intercept Only:       -115.644   Log-Lik Full Model:
-80.118
D(196):                        160.236   LR(3):
71.052
                                         Prob > LR:
0.000
McFadden's R2:                   0.307   McFadden's Adj R2:
0.273
ML (Cox-Snell) R2:               0.299   Cragg-Uhler(Nagelkerke) R2:
0.436
McKelvey & Zavoina's R2:         0.519   Efron's R2:
0.330
Variance of y*:                  6.840   Variance of error:
 3.290
Count R2:                        0.810   Adj Count R2:
0.283
AIC:                             0.841   AIC*n:
168.236
BIC:                          -878.234   BIC':
-55.158
BIC used by Stata:             181.430   AIC used by Stata:
168.236

Thank you,
Enrico



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Richard Williams, Notre Dame Dept of Sociology
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