getting 95% CIs for multinomial variable, with clustering

[MJ Smith]

Hi all, I'd like to obtain 95% CIs for a variable with 3 categories - male, female, and unknown; over several years. Some of the same individuals are found in multiple years. To do this, I use proportion, vce(cluster person) where person is the ID for the individual person, and citype(wilson) to obtain Wilson confidence intervals.

Is there anything obviously wrong with this approach, or anything you would do differently?

Note: I'm using Stata 15.

. proportion gender_n, vce(cluster person) over(year) citype(wilson) percent

Proportion estimation             Number of obs   =     15,134

            F: gender_n = F
            M: gender_n = M
            U: gender_n = U

         2007: year = 2007
         2008: year = 2008
         2009: year = 2009
         2010: year = 2010
         2011: year = 2011
         2012: year = 2012
         2013: year = 2013

             (Std. Err. adjusted for 8,237 clusters in person)
--------------------------------------------------------------
             |               Robust              Wilson
        Over |    Percent   Std. Err.     [95% Conf. Interval]
-------------+------------------------------------------------
F            |
        2007 |      59.85       1.17         57.55       62.12
        2008 |      65.17       1.00         63.18       67.10
        2009 |      69.34       0.81         67.73       70.90
        2010 |      71.12       0.96         69.20       72.96
        2011 |      67.63       1.04         65.57       69.62
        2012 |      71.09       0.96         69.16       72.94
        2013 |      66.56       1.32         63.93       69.09
-------------+------------------------------------------------
M            |
        2007 |      16.55       0.88         14.89       18.36
        2008 |      19.97       0.84         18.38       21.67
        2009 |      23.90       0.75         22.46       25.40
        2010 |      20.63       0.86         19.00       22.36
        2011 |      24.71       0.95         22.88       26.62
        2012 |      22.14       0.89         20.46       23.93
        2013 |      26.81       1.24         24.46       29.30
-------------+------------------------------------------------
U            |
        2007 |      23.59       1.01         21.67       25.62
        2008 |      14.86       0.74         13.46       16.38
        2009 |       6.76       0.44          5.95        7.68
        2010 |       8.26       0.58          7.19        9.47
        2011 |       7.67       0.59          6.59        8.90
        2012 |       6.77       0.53          5.80        7.89
        2013 |       6.63       0.69          5.39        8.12
--------------------------------------------------------------

[Carlo Lazzaro]

MJ:
95% CI for multinomial variable is covered in Alan Agresti's textbook https://www.wiley.com/en-gb/Categori...-9780471458760, page 21-26;36 (Exercise #1.36).
I'm not aware of a community-contributed module in Stata along Agresti's textbook formula for this goal.

[MJ Smith]

Great - thank you, Carlo!