Pseduo R2 after xtmelogit

[Kenny Ostel]

Dear community,
to calculate the pseudo R2 after my xtmelogit-estimation, I found this two possibilities:
di "The McFadden pseudo-R2 is: " ( e(ll_c) - e(ll) )/e(ll_c)
The McFadden pseudo-R2 is: .02392622

. di "The Cox and Snell pseudo-R2 is: " 1 - exp( (-2*(e(ll)-e(ll_c))) /e(N))
The Cox and Snell pseudo-R2 is: .02006514

Both of them seem very low to me, since the Pseudo R2 in the single-level-(logit)-estimation was quite good. Now I found a formula in an article to calculate the pseudo R2 this way:
for the single-level: 1 - (var(single-level full model) + var(context-level full model)) / (var(single-level Random intercept only model) + var(context-level RIOM)).
for the context-level: 1 - (var(single-level full model)/average group size + var(context-level full model)) / (var(single-level Random intercept only model)/average group size + var(context-level RIOM)).

My question is: How can I calculate each of those variances?

Best,
Kenny

[Emad Shehata]

Try to get Tjur R2 may be better:

Tjur, T. (2009) “Coefficients of determination in logistic regression models—A new proposal: The coefficient of discrimination.” The American Statistician 63: 366-372.

sysuse auto , clear
logit foreign weight mpg
* Pseudo R2 = 0.3966

predict yh if e(sample)
reg foreign yh
* R2 = 0.4110

ttest yh , by(foreign)
* Tjur R2 = |-0.4253| = 0.4253

. sysuse auto , clear

Logistic regression                               Number of obs   =         74
                                                  LR chi2(2)      =      35.72
                                                  Prob > chi2     =     0.0000
Log likelihood = -27.175156                       Pseudo R2       =     0.3966

------------------------------------------------------------------------------
     foreign |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      weight |  -.0039067   .0010116    -3.86   0.000    -.0058894    -.001924
         mpg |  -.1685869   .0919175    -1.83   0.067    -.3487418     .011568
       _cons |   13.70837   4.518709     3.03   0.002     4.851859    22.56487
------------------------------------------------------------------------------

. * Pseudo R2 = 0.3966
.  predict yh if e(sample)
(option pr assumed; Pr(foreign))

.  reg foreign yh

      Source |       SS       df       MS              Number of obs =      74
-------------+------------------------------           F(  1,    72) =   50.25
       Model |  6.35452901     1  6.35452901           Prob > F      =  0.0000
    Residual |  9.10493045    72  .126457367           R-squared     =  0.4110
-------------+------------------------------           Adj R-squared =  0.4029
       Total |  15.4594595    73  .211773417           Root MSE      =  .35561

------------------------------------------------------------------------------
     foreign |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
          yh |    .966399   .1363286     7.09   0.000      .694633    1.238165
       _cons |   .0099895   .0578928     0.17   0.863    -.1054177    .1253966
------------------------------------------------------------------------------
. * R2 = 0.4110

.  ttest yh , by(foreign)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
Domestic |      52    .1708459    .0318593    .2297409    .1068857    .2348062
 Foreign |      22    .5961823    .0533607     .250284    .4852126     .707152
---------+--------------------------------------------------------------------
combined |      74    .2972973    .0354902    .3052979    .2265655    .3680291
---------+--------------------------------------------------------------------
    diff |           -.4253364    .0600016               -.5449475   -.3057254
------------------------------------------------------------------------------
    diff = mean(Domestic) - mean(Foreign)                         t =  -7.0887
Ho: diff = 0                                     degrees of freedom =       72

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.0000         Pr(|T| > |t|) = 0.0000          Pr(T > t) = 1.0000

. * Tjur R2 = |-0.4253| = 0.4253

[Kenny Ostel]

Thank you Emad, but I'm looking for a R2 after xtmelogit, not after logit. At xtmelogit you need to R2's: one for the single level and one for the contextual level..