milrtest 
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Syntax

        milrtest test_varlist

May be used after using mim to estimate models using: regress, logit and ologit.

by may not be used with milrtest.

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Warning
    milrtest is not compatible with the current version of mim due to changes in the information 
returned by . An updated version of milrtest may become available in the future. In the mean time, 
should you wish to use milrtest, an older, compatible version of mim (v1.1.1) is still available 
(see net sj 8-1 st0139).


Description 
    milrtest performs a likelihood ratio test of nested models after analysis of multiply imputed datasets
using  mim. This test is described in Meng and Rubin (1992, see Allison, 2001 for a more accessible source).
The null hypothesis is that the unconstrained model (i.e. the model with more independent variables) fits the
data no better than the constrained model (i.e. the model with fewer independent variables). The user runs the
unconstrained model, then specifies in test_varlist the variables to be constrained in the constrained model.
milrtest should be run immediately after mim.
milrtest does not take if or in, instead restrictions on the sample, etc.  are taken from mim.

Saved results

milrtest saves the following in r()

Below h0 and h1 represent the null and alternative hypotheses respectively. Unconstrained models are those where
betas (for both h0 and h1) are freely estimated each of the m imputed datasets. Constrained models are those
where all betas (and in the case of ologit cutpoints) are constrained to the mean of the estimates from the
unconstrained model (that is, they are constrained to the MI estimate of the coefficients).

scalars:
          r(d_m)          mean of likelihood ratio chi-squares for h1 vs h0 in unconstrained models
          r(d_L)          mean of likelihood ratio chi-squares for h1 vs h0 in constrained models
          r(p)            p value of final statistic
          r(df_d)         denominator degrees of freedom
          r(df_n)         numerator degrees of freedom
          r(test_stat)    F statistic
          r(m)            number of imputed datasets used in estimation

Scalars containing the log likelihoods for each of the m imputed datasets under various models:
          r(h0_c_m)       Constrained model under h0 
          r(h1_c_m)       Constrained model under h1
          r(h0_uc_m)      Unconstrained model under h0
          r(h1_uc_m)      Unconstrained model under h1


macros:
          r(cmd)        Name of the estimation command
          r(h0_model)   Model under the null hypothesis
          r(h1_model)   Model under the alternative hypothesis

matrices:
          r(h0_coefs)   Coefficient estimates for null model 
          r(h1_coefs)   Coefficient estimates for alternative model

Note: The coefficient estimates for the null model r(h0_coefs) and the alternative model r(h1_coefs) are the
estimates of the regression coefficients based on the analysis of m MI datasets.  These are the values to which
the coefficients are constrained for the constrained model.


References

Allison, P. D. (2001) Missing Data. Save University Papers Series on Quantitative Applications in the Social
    Sciences, 07-136. Thousand Oaks, CA: Sage.

Carlin, J. B., Calati, J. C. & Royson, P. (2008) A new framework for managing and analyzing multiply imputed
    data in Stata. The Stata Journal 8(1): 49-67.

Little, R. J. A., & Rubin, D. B. (2002) Statistical analysis with missing data. Hoboken, N.J: Wiley.

Meng, X. & Rubin, D. B. (1992) Performing likelihood ratio tests with multiply-imputed data sets. Biometrika
    79(1):103-111.


    
Author 

     Statistical Consulting Group
     Institute for Digital Research and Education, UCLA
     idrestat@ucla.edu