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:
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!
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 . . . . . -------------------------------------------------------------------------------
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!
Comment