# Vuong test has different results for R and Stata

I am running a zero inflated negative binomial model with a probit reference to R ( http://www.ats.ucla.edu/stat/r/dae/zinbreg.htm ) and Stata ( http://www.ats.ucla.edu /stat/stata/dae/zinb.htm ).

There is a Vuong test to compare if this specification is better than the usual negative binomial model. Where R tells me I would be better off using the latter, Stata says ZINB is the preferred option. In both cases, I assume that the process leading to excess zeros is the same as for negative binomial distributed nonzero observations. The odds are indeed the same (except that Stata prints another digit).

In `R`

I am running (data code below)

``````require(pscl)

ZINB <- zeroinfl(Two.Year ~ length + numAuth + numAck,
data=Master,
)

NB <- glm.nb(Two.Year ~ length + numAuth + numAck,
data=Master
)
```

```

Comparing both with `vuong(ZINB, NB)`

with the same package gives

``````Vuong Non-Nested Hypothesis Test-Statistic: -10.78337
(test-statistic is asymptotically distributed N(0,1) under the
null that the models are indistinguishible)
in this case:
model2 > model1, with p-value < 2.22e-16
```

```

Hence: NB is better than ZINB.

In Stata, I ran

``````zinb twoyear numauth length numack, inflate(numauth length numack) probit vuong
```

```

and get (suppression of iteration suppressed)

``````Zero-inflated negative binomial regression        Number of obs   =        714
Nonzero obs     =        433
Zero obs        =        281

Inflation model = probit                          LR chi2(3)      =      74.19
Log likelihood  = -1484.763                       Prob > chi2     =     0.0000

------------------------------------------------------------------------------
twoyear |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
twoyear      |
numauth |   .1463257   .0667629     2.19   0.028     .0154729    .2771785
length |    .038699    .006077     6.37   0.000     .0267883    .0506097
numack |   .0333765    .010802     3.09   0.002     .0122049    .0545481
_cons |  -.4588568   .2068824    -2.22   0.027    -.8643389   -.0533747
-------------+----------------------------------------------------------------
inflate      |
numauth |   .2670777   .1141893     2.34   0.019     .0432708    .4908846
length |   .0147993   .0105611     1.40   0.161    -.0059001    .0354987
numack |   .0177504   .0150118     1.18   0.237    -.0116722    .0471729
_cons |  -2.057536   .5499852    -3.74   0.000    -3.135487   -.9795845
-------------+----------------------------------------------------------------
/lnalpha |   .0871077   .1608448     0.54   0.588    -.2281424    .4023577
-------------+----------------------------------------------------------------
alpha |   1.091014    .175484                      .7960109    1.495346
------------------------------------------------------------------------------
Vuong test of zinb vs. standard negative binomial: z =     2.36  Pr>z = 0.0092
```

```

In the very last line, Stata tells me that in this case ZINB is better than NB: both the test statistic and the p-value are different. Why?

Data (R code)

``````Master <- <-read.table(text="
Two.Year    numAuth length  numAck
0   1   4   6
3   3   28  3
3   1   18  4
0   1   42  4
0   2   17  0
2   1   10  3
1   2   20  0
0   1   28  3
1   1   23  7
0   2   34  3
2   2   24  2
0   2   18  0
0   1   23  7
0   1   35  11
4   2   33  13
0   2   24  4
0   2   21  9
1   4   21  0
1   1   8   6
2   1   18  1
0   3   28  2
0   2   17  2
1   1   30  6
4   2   28  16
1   4   35  1
2   3   19  2
0   1   24  2
1   3   26  6
1   1   17  7
0   3   42  4
0   3   32  8
3   1   33  23
7   2   24  9
0   2   25  6
1   1   7   1
0   1   15  2
2   2   16  2
0   1   23  6
2   3   18  7
0   1   28  5
0   1   12  2
1   1   25  4
0   4   18  1
1   2   32  6
1   1   15  2
2   2   14  4
0   2   24  9
0   3   30  9
0   2   19  9
0   2   14  2
2   2   23  3
0   2   18  0
1   3   13  4
0   1   10  4
0   1   24  8
0   2   22  9
2   3   29  5
2   1   25  5
0   2   17  4
1   2   24  0
0   2   26  0
2   2   33  12
1   4   17  2
1   1   25  8
3   1   36  11
0   1   10  4
9   2   60  22
0   2   18  3
2   3   19  6
2   2   23  7
2   2   26  0
1   1   20  5
4   2   31  4
0   2   21  2
0   1   24  12
1   1   12  1
1   3   26  5
1   4   32  8
2   3   21  1
3   3   26  3
4   2   36  6
3   3   28  2
1   3   27  1
0   2   12  5
0   3   24  4
0   2   35  1
0   2   17  2
3   2   28  3
0   3   29  8
0   2   20  3
3   2   28  0
11  1   30  2
0   3   22  2
21  3   59  24
0   2   15  5
0   2   22  2
5   4   33  0
0   2   21  2
4   2   21  0
0   3   25  9
2   2   31  5
1   2   23  1
2   3   25  0
0   1   13  3
0   1   22  7
0   1   16  3
6   1   18  4
2   2   19  7
3   2   22  10
0   1   12  6
0   1   23  8
1   1   23  9
1   2   32  15
1   3   26  8
1   3   15  2
0   3   16  2
0   4   29  2
2   3   24  3
2   3   32  1
2   1   29  13
1   3   26  0
5   1   23  4
3   2   21  2
4   2   19  4
4   3   19  2
2   1   29  0
0   1   13  6
0   2   28  2
0   3   33  1
0   1   20  2
0   1   30  8
1   2   19  2
17  2   30  7
5   3   39  17
21  3   30  5
1   3   29  24
1   1   31  4
4   3   26  13
4   2   14  16
2   3   31  14
5   3   37  10
15  2   52  13
1   1   6   5
2   1   24  13
17  3   17  3
3   2   29  5
2   1   26  7
3   3   34  9
5   2   39  2
3   1   26  7
1   2   32  12
2   3   26  4
9   3   28  8
1   3   29  1
4   1   24  7
9   1   40  13
1   2   27  21
2   2   27  13
5   3   31  10
10  2   29  15
10  2   41  15
8   1   24  17
2   4   16  5
17  2   26  20
3   2   31  3
2   2   18  1
6   3   32  9
2   1   32  11
4   3   34  8
4   1   16  1
5   1   33  5
0   2   17  11
17  2   48  8
2   1   11  2
5   3   33  18
4   2   25  9
10  2   17  5
1   1   25  8
3   3   41  16
2   1   40  13
4   3   25  2
16  4   32  13
10  1   33  18
5   2   25  3
3   2   20  3
2   3   14  7
3   2   23  4
2   2   28  4
3   2   25  19
0   2   14  6
3   1   28  18
8   3   27  11
1   3   25  17
21  2   33  15
9   2   24  2
1   1   16  14
1   1   38  10
16  2   37  13
16  2   41  1
7   2   24  18
4   2   17  5
4   1   37  32
3   1   37  8
13  2   35  6
15  1   23  11
7   1   47  11
3   1   16  6
12  2   36  6
7   1   24  17
4   2   24  8
14  2   24  9
15  2   24  11
0   3   19  4
0   4   28  9
1   1   5   3
11  1   28  15
5   1   33  5
10  2   21  9
3   3   28  8
2   3   13  2
11  2   41  8
4   2   24  11
3   1   32  11
4   2   31  11
7   2   34  3
11  6   33  6
7   3   33  7
2   2   37  13
7   3   19  9
1   2   14  3
6   2   15  11
11  3   37  12
0   2   20  5
7   4   13  6
17  1   52  14
9   3   47  30
1   2   32  27
30  3   36  19
2   2   12  5
3   1   30  7
4   2   19  11
32  3   45  14
13  1   17  7
16  2   24  4
5   1   32  13
7   3   29  14
5   2   46  2
1   2   21  6
1   3   13  17
11  1   41  16
6   2   33  1
7   1   31  20
0   1   16  13
6   3   26  8
11  2   46  7
8   2   20  5
8   1   44  7
2   2   33  12
1   3   22  5
0   4   14  2
4   1   25  8
5   3   24  11
1   1   21  18
5   1   28  5
2   1   51  19
2   1   16  4
17  2   35  2
4   1   35  1
9   3   48  8
2   1   33  16
0   3   24  7
18  2   33  12
11  1   41  5
5   2   17  3
8   1   19  7
4   3   38  2
23  2   27  10
22  3   46  13
5   3   21  1
5   2   38  10
1   2   20  5
2   2   24  8
0   3   30  9
7   2   44  16
7   1   21  7
0   1   20  10
10  2   33  11
4   2   18  2
11  1   45  17
7   2   32  7
7   2   28  6
5   2   25  10
3   2   57  6
8   1   16  2
7   2   34  4
5   2   22  8
2   2   21  7
4   2   37  15
2   4   36  7
1   1   17  4
0   2   23  9
12  2   48  4
8   3   29  13
0   1   29  7
0   2   27  12
1   1   53  10
3   3   15  5
8   1   40  29
2   2   22  11
10  2   20  7
4   4   27  3
4   1   24  4
2   2   24  5
1   2   19  6
10  3   41  10
57  3   46  9
5   1   20  11
6   2   30  4
0   2   20  5
16  3   35  8
1   2   44  1
2   4   24  8
1   1   20  9
5   3   19  11
5   3   29  15
3   1   21  8
3   3   19  3
8   3   44  0
11  3   34  15
2   2   31  1
11  1   39  11
0   3   24  3
4   2   35  6
2   1   14  6
10  1   30  10
6   2   21  4
9   2   32  3
0   1   34  10
6   2   32  3
7   2   50  11
11  1   35  15
4   1   27  9
1   2   32  27
8   2   54  2
0   3   15  8
2   1   31  13
0   1   31  11
0   4   14  5
0   2   37  15
0   2   51  12
0   2   34  1
0   3   29  12
0   2   22  11
0   2   19  15
0   2   39  13
0   3   25  12
0   1   46  2
0   4   42  10
0   1   38  5
0   3   31  4
0   3   33  1
0   2   24  11
0   1   28  16
0   2   28  13
0   1   29  17
0   1   23  13
0   3   36  21
0   2   30  15
0   2   25  12
0   2   26  17
0   3   19  2
0   2   37  5
0   2   47  12
0   1   21  20
0   3   27  21
0   2   16  7
0   1   35  5
0   2   32  24
0   3   31  6
0   3   36  13
0   2   26  20
0   1   31  13
0   2   46  6
0   2   34  12
0   1   18  13
0   1   29  3
0   3   40  9
0   1   25  3
0   3   45  9
0   2   31  3
0   2   35  4
0   3   29  10
0   2   33  13
0   3   22  4
0   2   26  9
0   2   29  19
0   2   28  12
0   2   30  5
0   4   30  3
0   3   32  14
0   3   45  20
0   2   42  9
0   2   25  4
0   2   20  22
0   3   31  5
0   1   26  13
0   2   32  11
0   1   31  2
0   2   42  17
0   1   37  8
0   3   37  16
0   3   25  10
0   2   33  11
0   2   29  7
0   2   21  16
0   3   30  33
0   1   35  8
0   3   25  6
0   2   54  3
0   2   41  10
0   3   35  1
0   4   26  4
0   2   31  4
0   3   26  11
0   3   34  11
0   2   27  7
0   1   19  14
0   1   38  9
0   2   24  1
0   3   30  20
0   4   43  13
0   2   20  10
0   2   38  1
0   2   41  6
0   1   20  9
0   2   34  2
0   2   24  5
0   2   24  2
0   1   31  19
0   3   49  7
0   1   26  0
0   2   44  6
0   3   36  13
0   3   31  14
0   2   30  20
0   1   27  13
0   2   28  9
0   2   22  20
0   4   36  34
0   3   25  3
0   2   29  17
0   2   40  8
0   2   39  17
0   4   29  8
0   1   27  22
0   1   21  10
0   3   17  5
0   3   28  10
0   1   27  7
0   3   40  7
0   2   21  4
0   1   33  14
0   1   31  14
0   3   37  13
0   2   23  9
0   2   25  1
0   2   30  1
0   2   30  12
0   1   41  8
0   2   26  1
0   2   25  14
0   2   26  3
0   3   36  1
0   4   23  1
0   2   18  0
0   2   34  2
0   1   39  6
0   1   16  15
0   3   34  4
0   4   35  6
0   1   22  10
0   1   35  8
0   2   36  13
0   2   50  8
0   2   28  6
0   1   30  14
0   2   33  26
0   3   28  1
0   1   18  10
0   2   27  4
0   2   27  5
0   2   8   2
0   4   32  16
0   3   40  6
0   4   45  15
0   2   38  3
0   2   29  6
0   1   25  9
12  1   27  5
2   1   33  8
4   3   31  3
1   1   33  4
0   3   20  5
0   2   28  6
2   2   32  12
0   3   30  2
0   3   19  3
1   1   14  19
0   2   28  2
0   3   26  3
0   2   32  13
1   3   21  7
1   4   20  0
2   2   40  8
0   2   35  18
1   1   20  6
6   2   21  3
3   2   33  10
1   1   31  15
1   2   22  5
0   2   24  7
2   2   22  3
3   2   17  6
9   2   30  12
2   4   39  9
0   2   46  8
0   2   26  5
1   2   28  5
6   1   18  3
5   2   19  13
1   3   27  3
1   1   20  10
0   1   27  6
0   4   26  1
0   2   19  4
0   1   26  8
1   1   30  8
0   2   22  2
3   3   42  4
3   1   10  5
3   1   30  12
1   1   25  8
1   2   38  8
2   1   28  13
3   1   18  12
2   2   20  11
2   2   29  0
1   2   18  3
1   1   6   2
0   1   6   3
2   2   24  1
0   1   14  1
1   1   17  5
2   2   20  9
1   4   24  0
1   2   8   10
0   2   18  1
1   1   25  5
2   2   12  7
0   3   18  1
0   1   19  1
8   2   21  2
1   2   23  5
7   2   19  6
1   1   21  5
0   1   16  6
1   1   24  1
0   2   19  3
1   2   14  6
3   2   24  2
6   1   32  21
0   1   16  0
1   2   15  0
1   2   8   8
0   1   14  5
0   2   27  5
2   2   17  2
1   1   19  7
1   2   21  2
0   1   29  7
0   2   18  2
0   2   15  6
2   3   27  3
0   2   57  4
2   3   17  2
1   1   18  8
1   1   17  5
0   1   18  1
1   2   18  4
1   1   12  1
0   2   15  6
1   2   24  4
3   2   14  9
0   1   24  6
3   1   30  9
0   1   19  5
3   1   16  7
5   3   21  1
2   2   17  5
4   1   34  9
1   1   17  7
3   2   30  10
12  1   17  6
2   1   26  6
1   1   18  2
2   2   24  0
0   1   12  2
0   2   3   2
1   1   11  4
1   4   18  13
0   1   25  9
8   2   20  7
0   1   11  7
7   3   26  19
6   1   18  6
6   2   32  5
1   1   31  2
1   2   33  9
4   1   17  6
1   2   34  11
5   1   37  3
0   3   27  10
12  2   25  14
3   1   40  6
6   2   27  9
0   2   31  2
1   1   28  7
2   1   37  11
1   1   19  0
5   2   30  17
4   3   40  6
0   1   27  6
5   3   31  7
0   3   26  10
3   2   32  4
1   3   43  6
3   1   19  3
2   2   37  4
0   3   28  4
6   3   30  11
1   1   30  9
4   3   31  26
1   2   14  1
10  1   35  27
1   1   36  7
5   1   32  8
2   1   28  6
3   1   34  16
3   2   32  5
1   3   11  0
2   2   42  5
0   2   30  7
0   1   32  9
3   3   43  2
7   2   43  6
1   2   21  5
2   1   27  20
1   2   37  7
2   1   37  8
0   1   19  3
0   3   28  5
2   2   33  3
3   1   41  6
13  2   41  9
2   1   38  3
4   1   32  5
2   1   34  8
1   1   27  9
8   1   29  7
4   1   17  6
0   1   20  8
1   2   34  4
1   1   16  11
4   2   33  5
0   2   15  6
1   1   27  4
2   3   15  8
1   1   30  8
3   2   41  20
0   1   25  15
1   3   35  24
4   2   30  21
6   2   30  6
16  2   33  21
2   3   37  3
2   2   30  12
4   1   57  11
0   2   18  16
4   4   20  13
3   1   43  10
3   1   25  15
7   2   31  11
2   1   31  3
5   2   40  11
3   2   28  7
4   2   27  10
0   1   26  6
4   2   24  14
4   2   23  8
0   2   25  11
21  2   33  12
1   3   37  0
3   2   28  7
4   2   27  10
1   2   41  15
2   2   30  16
2   2   28  7
6   1   19  8
4   4   22  19
0   2   38  33
1   1   29  11
1   2   27  2
4   2   24  6
2   1   22  5
```

```
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The above issue happened with `pcsl`

version 1.4.6. I spoke with the author as in version 1.4.7 he fixed a bug. The actual release as of February 2015 is 1.4.8.

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