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  • Interpreting interactions and margins in a non-linear poisson model

    I need some help to interpret regression models with interactions and margins. I have 18 outcomes and 18 regression models. I am posting one model with interactions and margins below with interpretation. Could someone please help with the accuracy of the interpretation.
    From my reading I understand if there are margins I must not interpret the interaction, but the margins alone, is that right? Example at the end.
    Also if the margins give the message “Warning: variance matrix is nonsymmetric or highly singular” should I keep the interaction in the final model, or remove it?

    The main aim is to find predictors of a mother getting an episiotmy in a CY program environment (CY program - Chiranjeevi Yojana (CY) – a program that enables poor mothers free delivery in private facilities)

    The total data set is of 1268 mothers who were surveyed soon after they birthed in public and private obstetric facilities in three districts. The question on episiotomy was analysed for 1048 mothers (excluding those who had a caesarean)

    Dependent variable: Episiotomy (f5cq7) (0.No, 1.Yes)
    Independent Variables:
    Parity of the mother (parity_2cat)(0.Primi, 1. Non Primi),
    Formal education (edu2) (0.No formal education 1.Formal education)
    District where she is form (mdist), (1 Sabarkantha, 2 Dahod, 3 Surendranagar)
    Type of Facility she birthed in (TyFac), (0.Public facility, 1. CY - participating private facility, 2. Non CY – non-participating private facility)
    Eligibility: Her socio-economic vulnerability ie eligibility to received free delivery (cy_elyn) (0.eligible/vulnerable mother 1.non vulnerable mother)

    I checked for 3 interactions and 2 margins picture attached. If the interaction was insignificant I removed it from the model and reran.
    i) District of the mother##Type of Facility
    ii) District of the mother##eligibility <- This shows the warning for margins, but is significant in all models
    iii) Type of facility##eligibility <- This was insignificant, so removed from the model and re-ran

    Finally I had first two interactions the last one was insignificant in the model.

    In stata 12 I used the following command and got the output as:

    Code:
    . svy: poisson  f5cq7  i.b1.parity_2cat i.b1.cy_elyn i.edu2 i.TyFac  i.mdist (mdist##TyFac) (mdist##cy_elyn) if mdist<=3 &  deltyp2cat==1, irr
    (running poisson on estimation sample)
     
    Survey: Poisson regression
     
    Number of strata   =         2                  Number of obs      =      1048
    Number of PSUs     =         6                  Population size    =   1051.56
                                                    Design df          =         4
                                                    F(   4,      1)    =         .
                                                    Prob > F           =         .
     
    -------------------------------------------------------------------------------
                  |             Linearized
            f5cq7 |        IRR   Std. Err.      t    P>|t|     [95% Conf. Interval]
    --------------+----------------------------------------------------------------
    0.parity_2cat |       1.95       0.27     4.85   0.008         1.33        2.87
         0.cy_elyn |       0.92       0.02    -3.40   0.027         0.87        0.99
             1.edu2 |       1.40       0.09     5.40   0.006         1.18        1.66
                  |
            TyFac |
               1  |       1.68       0.41     2.12   0.101         0.85        3.30
               2  |       1.73       0.41     2.33   0.080         0.90        3.34
                   |
            mdist |
               2  |       0.27       0.06    -5.86   0.004         0.14        0.50
               3  |       0.99       0.22    -0.05   0.966         0.53        1.85
                  |
      mdist#TyFac |
             2 1  |       3.35       0.69     5.89   0.004         1.89        5.92
             2 2  |       1.52       0.44     1.43   0.226         0.68        3.40
             3 1  |       1.12       0.28     0.46   0.669         0.56        2.26
             3 2  |       0.96       0.22    -0.18   0.864         0.51        1.79
                  |
    mdist#cy_elyn |
             2 0  |       0.57       0.04    -8.53   0.001         0.48        0.69
             3 0  |       0.95       0.01    -3.61   0.023         0.91        0.99
                  |
            _cons |       0.22       0.05    -6.17   0.004         0.11        0.44
    -------------------------------------------------------------------------------
    . margins, over (mdist TyFac) expression (exp(xb())) post
     
    Predictive margins                                Number of obs   =       1048
    Model VCE    : Linearized
     
    Expression   : exp(xb())
    over         : mdist TyFac
     
    ------------------------------------------------------------------------------
                 |            Delta-method
                 |     Margin   Std. Err.      z    P>|z|     [95% Conf. Interval]
    -------------+----------------------------------------------------------------
     mdist#TyFac |
            1 0  |       0.30       0.07     4.52   0.000         0.17        0.43
            1 1  |       0.69       0.01    66.91   0.000         0.67        0.71
            1 2  |       0.71       0.01   135.85   0.000         0.70        0.72
            2 0  |       0.05       0.01     5.91   0.000         0.03        0.06
            2 1  |       0.30       0.01    48.25   0.000         0.28        0.31
            2 2  |       0.16       0.02     6.74   0.000         0.11        0.20
            3 0  |       0.33       0.00   286.93   0.000         0.32        0.33
            3 1  |       0.70       0.01    48.14   0.000         0.67        0.72
            3 2  |       0.65       0.01    60.53   0.000         0.62        0.67
    ------------------------------------------------------------------------------
    . margins, over (mdist cy_elyn) expression (exp(xb())) post
    Warning:  variance matrix is nonsymmetric or highly singular
     
    Predictive margins                                Number of obs   =       1048
    Model VCE    : Linearized
     
    Expression   : exp(xb())
    over         : mdist cy_elyn
     
    -------------------------------------------------------------------------------
                  |            Delta-method
                  |     Margin   Std. Err.      z    P>|z|     [95% Conf. Interval]
    --------------+----------------------------------------------------------------
    mdist#cy_elyn |
             1 0  |       0.58          .        .       .            .           .
             1 1  |       0.73          .        .       .            .           .
             2 0  |       0.11          .        .       .            .           .
             2 1  |       0.25          .        .       .            .           .
             3 0  |       0.49          .        .       .            .           .
             3 1  |       0.61          .        .       .            .           .
    -------------------------------------------------------------------------------
    1. My interpretation of the results: (please advise if this is right, can be more precise?)
    Among mothers who had vaginal births, approximately 41% experienced an episiotomy. The predictive margins for episiotomy suggested that the prevalence of Episiotomy was more than double in private than public facilities in all three districts. Dahod was peculiar in that the practice of Episiotomy was relatively higher in CY than nonCY private facilities (marginal effect 0.14), though much lower than that in the other two districts. In Sabarkantha and Surendranagar the practice of episiotomy was much higher, particularly in both CY and NonCY private facilities (marginal effect 0.4).
    Eligibility and District showed significant interactions but predictive margins could not be computed due to asymmetrical variance.
    Among individual variables, prevalence of primiparity was 2 times higher and formally educated mother 1.4 times higher among mothers who experienced episiotomy.
    On the whole, in the three districts, irrespective of eligibility status, a mother birthing in a CY facility had a higher probability (2 to 6 times) of undergoing episiotomy when compared to birthing in a public facility.

    2. I have been studying Stata tip 87, but am not sure if I am applying it right to my study https://www.stata-journal.com/sjpdf....iclenum=st0194

    For the multiplicative effect, what is the reference term
    a. Would it be right to interpret interaction Dist#Type of Facility as
    The prevalence of Episiotomy among mothers who birthed in Dist 2 and TyOfFacility1 was 3.35 times more than

    in mothers who birthed in Dist1 and TyOfFacility 0 OR in mothers in Dist1 and TyOfFacility 1?
    The stata tip interprets it the second way and it would be more meaningful for me. But this is a 3X3, so I am not sure which is the reference in my model?

    b. Is it correct to interpret this multiplicative effect when I have margins for this interaction?

    Thanks a lot!

  • #2
    The purpose of that Stata tip is to encourage you to not use margins, but to interpret the (in your case) risk ratios directly.
    ---------------------------------
    Maarten L. Buis
    University of Konstanz
    Department of history and sociology
    box 40
    78457 Konstanz
    Germany
    http://www.maartenbuis.nl
    ---------------------------------

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    • #3
      Are you saying that there I shouldn't try to compute margins at all? But if the reference group for program private facilities' births in one district is public facilities births in a completely different district, I am not able to assess the program fairly, .... am I right in that? That's why I thought that the margins were giving me more ability to assess failrly.

      The prevalence of episiotomies was 3.35 times higher in mothers who birthed in CY facilities in Da compared to mothers who birthed in public facilities in Sk. Is this all I can say from this model?

      Thanks.

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      • #4
        Please help.. i have to give up the whole thing if i dont get it right..

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