Re: st: running tab and ttests with multimple imputation

[weddings@stata.com (Wesley D. Eddings, StataCorp)]

Fernando Andrade <fandrade.stat@gmail.com> asked about computing Pearson
chi-square statistics and t-tests from multiply imputed data:

> i looked at the estimation options and seems
> there is not an option to run a chi2 for a contingency table.
> is there another option or do i have to compute it by hand? is there
> also an option top run t-test for multiple imputed data?

Fernando is correct that the -mi estimate- command does not support -tabulate-
or -ttest-:  multiple imputation is better suited to statistical models than to
statistical tests per se.  One alternative, as Fernando suggested, is to report
the model F statistic after fitting a model with the -mi estimate- prefix and
either -logit-, -mlogit-, or -regress-.  Fernando may use the i. factor-variable
prefix to include indicator variables for his categorical predictors.

Suppose we'd performed the following -ttest-:

. sysuse auto, clear
(1978 Automobile Data)

. 
. ttest mpg, by(foreign)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
Domestic |      52    19.82692     .657777    4.743297    18.50638    21.14747
 Foreign |      22    24.77273     1.40951    6.611187    21.84149    27.70396
---------+--------------------------------------------------------------------
combined |      74     21.2973    .6725511    5.785503     19.9569    22.63769
---------+--------------------------------------------------------------------
    diff |           -4.945804    1.362162               -7.661225   -2.230384
------------------------------------------------------------------------------
    diff = mean(Domestic) - mean(Foreign)                         t =  -3.6308
Ho: diff = 0                                     degrees of freedom =       72

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.0003         Pr(|T| > |t|) = 0.0005          Pr(T > t) = 0.9997


Now we'll create some missing values, declare our -mi- settings, impute the
missing values, and analyze the data with -mi estimate: regress-.  (The
imputation model is naive and is used only for illustration.)


. set seed 12345

. 
. replace mpg = . in 1/10
(10 real changes made, 10 to missing)

. 
. mi set wide

. 
. mi register imputed mpg

. 
. mi impute regress mpg foreign weight length price, add(20)

Univariate imputation                   Imputations =       20
Linear regression                             added =       20
Imputed: m=1 through m=20                   updated =        0

               |              Observations per m              
               |----------------------------------------------
      Variable |   complete   incomplete   imputed |     total
---------------+-----------------------------------+----------
           mpg |         64           10        10 |        74
--------------------------------------------------------------
(complete + incomplete = total; imputed is the minimum across m
 of the number of filled in observations.)

. 
. mi estimate, dftable: regress mpg i0.foreign

Multiple-imputation estimates                     Imputations     =         20
Linear regression                                 Number of obs   =         74
                                                  Average RVI     =     0.0497
                                                  Complete DF     =         72
DF adjustment:   Small sample                     DF:     min     =      67.87
                                                          avg     =      68.97
                                                          max     =      70.08
Model F test:       Equal FMI                     F(   1,   67.9) =      11.06
Within VCE type:          OLS                     Prob > F        =     0.0014

------------------------------------------------------------------------------
             |                                                      % Increase
         mpg |      Coef.   Std. Err.      t    P>|t|           DF   Std. Err.
-------------+----------------------------------------------------------------
   0.foreign |  -4.811563   1.447082    -3.33   0.001         67.9        1.47
       _cons |   24.77273   1.195503    20.72   0.000         70.1        0.00
------------------------------------------------------------------------------