Title



     ivmsmm -- Multiplicative structural mean model



Syntax



        ivmsmm depvar [varlist1] (varlist2 = varlist_iv) [if] [in] [weight] [, log noirr
              ivpoisson_options]



    varlist1 is the list of exogenous variables.



    varlist2 is the list of endogenous variables.



    varlist_iv is the list of exogenous variables used with varlist1 as instruments for varlist2.



    options               Description
    ----------------------------------------------------------------------------------------------
      noirr               Do not display exponentiated estimates
      log                 Show the GMM iteration log
      ivpoisson_options   ivpoisson##optionstbl



Description



    ivmsmm implements the multiplicative structural mean model (MSMM) of Robins (1989) as a
    wrapper to ivpoisson with the multiplicative option.  ivpoisson performs generalized method of
    moments (GMM) estimation of the relevant moment condition using gmm.



    The equivalence of the models of Robins (1989) and Mullahy (1997), which was implemented in 
    ivpois, Nichols (2007) and ivpoisson with the mult option, and discussed in detail by
    Windmeijer and Santos Silva (1997) and Windmeijer (2002), was shown by Palmer (2011). These
    models produce moment conditions equivalent to gamma regression Dukes and Vansteelandt (2018).



Options



    Please see ivpoisson##options



Examples



    Read in binary outcome data; y outcome, x exposure, w covariate, z* instrumental variables
    (genotypes).



        . use https://raw.github.com/remlapmot/ivonesamplemr/main/data/ivbinoutdata, clear



    Fit the model with a single instrumental variable.



        . ivmsmm y (x = z1)



    Fit the model with multiple instruments.



        . ivmsmm y (x = z1 z2 z3)
        . estat overid



    Adjusting for w.



        . ivmsmm y w (x = z1 z2 z3)



    Fit the model with multiple exposures, and instruments, and adjusting for w.



        . ivmsmm y w (x1 x2 = z1 z2 z3)
        . estat overid



    Comparison with ivpois (specify onestep option to ivmsmm/ivpoisson for equivalence).



        . ivpois y, endog(x) exog(z1) eform(RR)
        . ivpois y, endog(x) exog(z1 z2 z3) eform(RR)
        . ivpois y w, endog(x) exog(z1 z2 z3) eform(RR)
        . ivpois y w, endog(x1 x2) exog(z1 z2 z3) eform(RR)



Stored results



    Please see ivpoisson##results



References



    Cameron AC, Trivedi PK. Regression analysis of count data. 2nd ed. 2013. New York, Cambridge
        University Press.



    Clarke PS, Palmer TM, Windmeijer F.  Estimating structural mean models with multiple
        instrumental variables using the Generalised Method of Moments.  Statistical Science,
        2015, 30, 1, 96-117.  DOI



    Dukes O, Vansteelandt S.  A note on G-estimation of causal risk ratios.  American Journal of
        Epidemiology, 2018, 187, 5, 1079-1084.  DOI



    Hernán and Robins. Instruments for causal inference: An Epidemiologist's dream?  Epidemiology,
        2006, 17, 360-372.  DOI



    Mullahy J. Instrumental-variable estimation of count data models:  applications to models of
        cigarette smoking and behavior.  The Review of Economics and Statistics. 1997, 79, 4,
        586-593.  DOI



    Nichols A. ivpois: Stata module for IV/GMM Poisson regression. 2007.  URL



    Palmer TM, Sterne JAC, Harbord RM, Lawlor DA, Sheehan NA, Meng S, Granell R, Davey Smith G,
        Didelez V.  Instrumental variable estimation of causal risk ratios and causal odds ratios
        in Mendelian randomization analyses.  American Journal of Epidemiology, 2011, 173, 12,
        1392-1403.  DOI



    Robins JM.  The analysis of randomised and nonrandomised AIDS treatment trials using a new
        approach to causal inference in longitudinal studies.  In Health Service Research
        Methodology: A Focus on AIDS (L. Sechrest, H. Freeman and A. Mulley, eds.).  1989.
        113–159. US Public Health Service, National Center for Health Services Research,
        Washington, DC.



    StataCorp. Stata Base Reference Manual. Release 13.  ivpoisson - Poisson model with continuous
        endogenous covariates. 2013.  URL



    Windmeijer FAG, Santos Silva JMC. Endogeneity in Count Data Models:  An Application to Demand
        for Health Care.  Journal of Applied Econometrics. 1997, 12, 3, 281-294.  DOI



    Windmeijer, F.  ExpEnd, A Gauss programme for non-linear GMM estimation of EXPonential models
        with ENDogenous regressors for cross section and panel data.  CEMMAP working paper
        CWP14/02. 2002.  URL



Author



INCLUDE help ivonesamplemr-author