A more complex model to estimate the providers’ probability to move over the observed period is the multinomial logit. The advantage of this model is that it simultaneously considers the entire locations choice set available to providers in each year. Specifically, after controlling for the same characteristics from above, this model provides estimates of the probability of each of four mutually exclusive outcomes: (1) the probability of choosing to remain in the same HPSA and same county; (2) the probability of moving to a non-HPSA location within the same county; (3) the probability to move to another HPSA in another county; and (4) the probability of moving to a non-HPSA in another county.
Inclusion of the NHSC participation variable in the multinomial logit model allows for the estimation of the difference in migration probabilities between participants and non-participants to any of the four HPSA/non-HPSA type locations. In Figure V.3 we present the marginal effects associated with these migration probability differences for primary care HPSAs, while in Figure V.4 we present the marginal effects for mental health HPSAs. The actual coefficients from the multinomial logit models are presented in Tables B.9 and B.10 in Appendix B.
Figure V. 3: Differences in the Participants’ Migration Probabilities Relative to Non-Participants—Primary Care
According to our estimates, participants serving in primary care HPSAs are 36.6% less likely than non-participants to remain in the same HPSA in the first separation/start year. At the same time, they are 25.2 % more likely to move to a HPSA in another county in the first separation/start year, meaning that overall, they are 11.4 percentage points (=-36.6+25.2) less likely to remain in any primary care HPSA. The ‘same HPSA’ and ‘any HPSA’ estimates from Figure V.3 are in line with our estimate from Figure V.1, but the advantage of the multinomial logit model is that it also shows that participants are 6.3% more likely than non-participants to move to non-HPSAs in the same county and 5.2% to move to non-HPSAs in another county.
As shown in Figure V.3, as the retention window after program completion increases, the differences in migration probabilities between participants and non-participants become lower and lower.
Figure V. 4: Differences in the Participants’ Migration Probabilities Relative to Non-Participants—Mental Health
In addition, the multinomial logit model provides an explanation for our previous finding that mental health participants show no difference in retention in any HPSAs relative to non-participants. As shown in Figure V.4, in the first separation/start year participants are 30.6% less likely to remain in the same county same HPSA than non-participants, but 31.1% more likely to move to HPSAs in another county. When these differences are added up they yield an estimate of virtually zero difference between participants and non-participants in terms of retention in any mental health HPSA.